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## Is AV better than FPTP?

On May 5th the UK will vote in a referendum for only the second time ever. (The first time was in 1975, when we voted on whether to remain in the EU, or the Common Market as it was then called.) Now we have a chance to decide whether to retain our current voting system, misleadingly known as First Past The Post, or whether to switch to the Alternative Vote. Let me come clean straight away. Although in this post I shall try to write dispassionately about these two voting systems, my actual attitude is anything but dispassionate: I have yearned for a better voting system ever since I have had any political awareness at all, and am steeling myself for what is probably going to be a huge disappointment when the country votes for the status quo. And I am writing this post in the genuine hope of making a difference. Since it is extremely hard to change anybody’s mind in politics, I think the best I can hope for is to persuade somebody to vote yes (the question will be phrased in such a way that “yes” means you want AV and “no” means you want FPTP) who might otherwise not have bothered to vote at all. This is a mathematics blog, so I will give this post a mildly mathematical slant, but all I really mean by this is that I know when I write that a typical reader of this post will be mathematically literate, which may make the post different in tone from how it would be if I were writing for a more general readership.

A little history.

Let us look at the election results from 1979, when Margaret Thatcher first came to power, to 1997, when Tony Blair first won. These are results of elections held under FPTP, the system where the country is divided into constituencies, each of which gets a seat in parliament, and the seat goes to whichever candidate gets the most votes in the constituency.

In 1979 the results of the three main parties were as follows:

Conservatives, 43.9% of the vote, 339 seats

Labour, 36.9% of the vote, 269 seats

Liberals, 13.8% of the vote, 11 seats.

So the Conservatives got a little over three times as many votes as the Liberals, and just over thirty times as many seats. To put that another way, it took about ten times as many votes (on average) to elect a Liberal MP as it took to elect a Conservative MP.

The next election was an interesting one. A couple of years into Thatcher’s premiership, a new political party, the Social Democratic Party, was formed by moderate Labour Party politicians who did not like the lurch to the left that had taken place under Labour’s then leader Michael Foot. Within a short time, they were coming top in opinion polls, but this did not last until the General Election, largely because the Falklands War gave Mrs Thatcher a huge boost to her popularity. It was clear that the Social Democrats had a lot in common with the Liberals (with whom they were later to merge), so they agreed not to stand against each other at the 1983 General Election, instead forming the Alliance. The results of the election were as follows:

Conservatives, 42.4% of the vote, 397 seats

Labour, 27.6% of the vote, 209 seats

SDP/Liberal Alliance, 25.4% of the vote, 23 seats.

Let us note a couple of anomalies in this result. Most strikingly, the Alliance got almost as many votes as the Labour party but Labour got roughly nine times as many seats. Second most strikingly, the Conservative share of the vote went down slightly, but they now had a truly thumping majority, much higher than after the previous election.

How was this possible? Well, under FPTP, if you want to maximize the number of seats you will get for a given share of the vote, then there are two things you must avoid. Most importantly, you don’t want to spread your vote about too evenly: if you get 28% of the vote in every single seat, you probably won’t win a single seat. So FPTP penalizes parties that have a uniform appeal throughout the country. This suggests that what you want is for your support to be geographically concentrated, and indeed that is the case up to a point, but you must also avoid having too many seats where you have an overwhelming majority: if you get 90% in a seat, then at least 40% of those votes would have been more useful to you if they had been cast in other constituencies. So FPTP favours parties with support that is geographically concentrated but not too concentrated. The Alliance’s support was dispersed, and the consequences for them at the election were disastrous.

The second anomaly — the hugely increased majority for the Conservatives despite a drop in their share of the vote — was a consequence of a phenomenon that frequently arises in this country under FPTP, the splitting of the left. At that time, both Labour and the Alliance were clearly on the left (the Alliance was much less so, but they were certainly not in favour of the Thatcherite programme that the country officially voted for) so there was a clear majority in favour of broadly left-wing politics. However, that majority was roughly evenly split between two parties, so there were many constituencies where the Conservatives won the seat with well under half the vote.

The next election, in 1987, was similar but less extreme.

Conservatives, 42.2% of the vote, 376 seats

Labour, 30.8% of the vote, 229 seats

Alliance, 22.6% of the vote, 22 seats.

In 1990 Margaret Thatcher resigned and John Major took over. The next election was in 1992 and the results were as follows. By this time, the SDP and the Liberals had merged to become the Liberal Democrats.

Conservatives, 41.9% of the vote, 336 seats

Labour, 34.4% of the vote, 271 seats

Liberal Democrats, 17.8% of the vote, 20 seats.

Something odd happened here too: the Conservative vote dropped by 0.3% but their majority went down very substantially (which led to numerous rebellions throughout the parliament, particularly on the thorny subject of Britain’s relationship with Europe). The explanation is that the split on the left, which still existed, was less severe.

Next was 1997, the year that Blair was elected.

Labour, 43.2% of the vote, 418 seats

Conservatives, 30.7% of the vote, 165 seats

Liberal Democrats, 16.8% of the vote, 46 seats.

Again there are some strange aspects of this result. The Liberal Democrats had their best result for many decades despite their lowest vote percentage in all the elections I have discussed. (However, their share of seats was still significantly lower than it would have been under a proportional system.) Labour got about two and a half times as many seats as the Conservatives for under one and a half times as many votes, and got a massive majority with only 43.2% of the vote.

Does FPTP reflect the will of the voters?

It is very easy to slip into thinking that the answer to this question is yes by definition: whatever the result of an election, the interpretation given to it by the media will be that “the voters have said” whatever FPTP deems them to have said. For instance, when I think back to the election that John Major won, my impression of it is that the mood of the country swung against the Tories, but not by enough to unseat them. I had completely forgotten that the Tory vote remained virtually unchanged from the previous election and that it was only the change to how the votes on the left split that caused the Tories to lose seats. So a more correct interpretation of the result is that the Labour party had become more electable again, improving its appeal relative to that of the Liberal Democrats.

I don’t think it is possible to defend the view that the 1983 election reflected the will of the voters: over a quarter of voters ended up being represented by about 3% of MPs, and the representatives of just over 40% of voters were given free rein to continue with a program that was (I am pretty sure) bitterly opposed by the majority.

It is reasonable to say that when Tony Blair was elected, the result reflected the national mood to some extent: the Conservatives had been in power for 17 years and John Major’s government had lost the country’s respect after Black Wednesday, from which it never really recovered. However, it is not reasonable to say that the size of Blair’s majority — he had almost two thirds of all seats — reflected the national mood. The large swing was reflected, but in a distorting mirror that greatly expanded it.

Similarly, since the Liberals, or Liberal Democrats, always come a distant third in elections, one naturally thinks of them as a minor party, but their share of the vote, often over 20%, is anything but minor.

And I haven’t mentioned elections from further back that were won by parties that did not get the most votes. In 1951, the Conservatives under Winston Churchill won an absolute majority of seats (though a small one) with 48.0% of the vote. In the same election, Labour under Clement Attlee got 48.8% of the vote.

Do people’s votes reflect the will of the voters?

This question looks a bit silly. Is the answer not trivially yes?

No it isn’t. Under FPTP, we often receive election literature that looks something like this.

That was a bar chart put out by the Liberal Democrats in Cambridge at the last general election. They reasoned that Conservative voters would prefer the Liberal Democrats to Labour, so tried to persuade potential Conservative voters to vote Liberal Democrat on the grounds that voting Conservative might well let in Labour. It is only fair to say that this argument has been employed much more often in the past against the Liberal Democrats. The slogan, “A vote for the Liberals is a wasted vote,” used to be heard frequently at elections.

But the general point is that under FPTP it is often rational to vote for a party that is not your first choice. This is a very important point, since it hugely weakens one of the main arguments of those who are campaigning against AV. I will come back to this later.

(In parentheses, let me remark that the result in Cambridge at the last election was

Liberal Democrat 19,621 (39.1% of vote)
Conservative 12,829 (25.6% of vote)
Labour 12,174 (24.3% of vote)
Green 3,804
UKIP 1,195
others 507

So it seems that Conservative voters were not persuaded to vote tactically.)

Going back to some of the results under FPTP, one cannot know how many people voted for parties that were not their first choice. However, all the main political parties urge people to vote tactically in individual constituencies (even if the senior politicians do not always admit it), and it is obvious that many people heed the call. I cannot prove it, but I find it pretty obvious that some of the results from the 1980s that were so unfair to the Liberals, the Alliance and the Liberal Democrats were in fact more unfair even than they looked, since many people would have voted for them if they had not been persuaded by the wasted-vote argument.

Is AV any better?

So far all I have done is discuss some of the deficiencies of FPTP. (OK, perhaps “deficiencies” isn’t a neutral enough word. I have been discussing some of the interesting phenomena that can occur, and often have occurred, under FPTP.) But does AV do any better?

The first thing to say is that AV is not proportional representation. Under AV it is still possible for a party to get a share of seats that is very different from its share of the votes. Before I say any more about AV, let me quickly say what it is (though I imagine that most people interested enough to get this far know already). Under AV, you don’t just vote for one candidate. Instead, you number the candidates 1,2,3 until you no longer wish to express a preference. For instance, if you are a UKIP supporter (the United Kingdom Independence Party is a right-wing party that wants Britain to leave the European Union) then you might put UKIP first and the Conservatives second, but not express a preference between Labour, the Liberal Democrats, the Greens, etc.

When the votes are counted, the following algorithm is applied.

1. Count all first-preference votes not yet counted.
2. If some party has over 50% of first-preference votes, then HALT. (That party then wins.)
3. Take the party with the smallest number of first-preference votes and change each vote for that party by removing the first-preference votes and turning $k$th-preference votes into $(k-1)$th-preference votes for each $k.$
4. Remove that party from the list of preferences of all other voters.
5. GOTO 1.

As an example, suppose that the parties in your constituency are Labour, the Conservatives, the Liberal Democrats, UKIP and the Greens. Suppose that your preferences are Green, Lib Dem, Labour, Conservative, UKIP in that order. Then if no party has over 50% and UKIP comes bottom, nothing happens to your voting paper. If after the next count (when the UKIP second preferences have become first preferences) it is still the case that no party has over 50%, and this time the Greens are eliminated, then your preferences are shunted up by 1, so they now read Lib Dem, Labour, Conservative (UKIP and the Greens having been eliminated). Perhaps by this stage Labour have reached the magic 50% (with a boost from those Greens who put Labour as their second choice). Or perhaps no party has and the Liberal Democrats are now third. In that case, your preferences become Labour over the Conservatives, and one or other of those will now have over 50%.

One of the criticisms of proportional representation is that it weakens the constituency link: it is hard to have a fully proportional system where each MP represents his or her constituency. AV does not suffer from this defect, since there is still a constituency system. But the price for that is that there is no obvious reason to expect AV to be proportional. So why is it any better than FPTP (from the point of view of representing the will of the voters)?

The reason is that under AV there is far less reason to vote tactically. Under AV, a vote for a minor party is not a wasted vote: you can express your preference for the minor party while still having an opportunity to decide which of the major parties you would prefer. For instance, you could vote Green and not worry that you were letting in the Conservatives, or you could vote UKIP without thinking that you might let in Labour. And if you are an anyone-but-the-Tories person, you can express that sentiment without being forced to guess which party has the best chance of defeating them.

Is tactical voting eliminated under AV?

The scope for tactical voting is greatly reduced under AV, because the wasted-vote argument no longer applies. But it is possible to come up with circumstances under which it would make sense even with AV to vote tactically. I’m not sure these circumstances would be relevant: typically they would require voters to know more about the preferences of other voters than they are ever likely to in practice. But let me give what I think is the simplest situation where tactical voting would in theory be rational under AV. To make it easier to understand, I’ll use actual parties, and will try to make people’s second preferences as plausible as possible given their first preferences.

Suppose you are voting in a constituency where the Conservatives typically get around 40% of first-preference votes, Labour get around 30%, the Liberal Democrats get around 30%, and the other parties get almost nothing. (This is not entirely realistic, but it could well be the situation after all but three parties have been eliminated.) Suppose you are an ardent supporter of the Conservatives. What should you do? Well, you might judge that Liberal Democrat voters are more likely to put the Conservatives as their second choice than Labour voters are. If that is what you think, then paradoxically it might make sense to vote Labour (the party you like least out of the three) so that when the second-choice votes are counted the Conservatives will get enough to push them over 50%. To see how this could work, imagine that the second-preference votes for Labour split 5:1 in favour of the Liberal Democrats (that is, 25% of voters have Labour first and Lib Dems second, and 5% of voters have Labour first and the Conservatives second), while the second-preference votes for the Lib Dems split 3:2 in favour of Labour (so 18% of voters have Lib Dems first and Labour second, while 12% of voters have Lib Dems first and the Conservatives second).

Labour and the Lib Dems are neck and neck. If the Lib Dems come second, then Labour will be eliminated and the total percentages of votes will be 45% for the Conservatives and 55% for the Liberal Democrats. If Labour come second, then the Lib Dems will be eliminated and the percentages will be 52% for the Conservatives and 48% for Labour.

So in a situation like this, we have the strange phenomenon that it may be in the interests of some Conservative voters to put Labour as their first preference in order to gain a substantial block of Liberal Democrat second-choice votes.

However, there are some pretty serious problems with actually voting tactically in this situation. Obviously if all Conservative voters were to do so it would be a disaster for the Conservatives. And you can’t coordinate your votes. So how do you decide what you, an individual Conservative voter, should do? If you are a mathematician, then you will probably toss a coin a few times and make a probabilistic decision, but something tells me that that practice is unlikely to catch on. And of course, it is ridiculous to suppose that you will know what proportion of Lib Dem voters are likely to put the Conservatives as their second choice.

To get an idea of just how much less tactical voting there would be under AV, try to imagine a slogan as punchy as “A vote for the Liberals is a wasted vote.” You won’t get very far with “A vote for the Conservatives might let in the Lib Dems with the help of Labour second preferences, whereas a vote for Labour will help the Conservatives win with the help of Lib Dem second preferences, but could only a few people pay attention to this please?” In practice, hardly anyone will have a good reason to do anything other than put in order of preference the parties that they have a view about.

Is the First Past The Post system the First Past The Post system?

This is another question that seems to have a trivial answer but actually doesn’t. Presumably First Past The Post is a metaphor. Indeed, it is a metaphor — from horse racing. So let us try to work out how the metaphor works. Presumably there should be a post somewhere. So what is the post? Hmm … it’s hard to say.

A natural answer might be that you pass the post when your party reaches 50%. That is, you would have a sort of race, and the first party to get over 50% would be declared the winner. Are there any systems like that? Oh yes, AV. (And not just AV, but that is the one we have the chance to choose.)

For the most part I want to stick to rational argument, but sometimes it’s quicker and more effective to use slogans. Here’s one I like:

FIRST PAST THE POST IS NOT FIRST PAST THE POST!

And to those who think it is, how about

WHAT IS THE POST?

(Under some circumstances, the first word might perhaps be replaced by “wtf”, but not on this nice family blog.)

If I want to vote selfishly, then how should I vote?

Suppose that you firmly support one political party and your only interest is to do what will best serve that party, ignoring all questions of fairness, democratic principle, etc. How should you vote in the referendum?

If you support the Conservatives, then probably you should vote no. It was the FPTP system that allowed Mrs Thatcher to rule for eleven years with large majorities and well under half the votes. It is possible that the Liberal Democrats are so damaged by the current coalition that we will see a return to straight two-party politics for a while (in which case whether we have FPTP or AV will not make much difference to the outcomes of elections). But unless the political landscape really has permanently changed, FPTP gives the Conservatives the best chance of exploiting the split on the left, whereas AV allows those of a broadly left-wing persuasion to vote in an anything-but-Tory way.

If you support the Liberal Democrats then it’s a no-brainer.

If you support Labour, then it is less clear what you should do. Perhaps you will look back at the three elections won by Tony Blair, and at the current unpopularity of the coalition, and think that you don’t need the help of AV. But if that is your view, then I suggest you look back further to the dark days of the 1980s. Under AV there is a real chance that Labour would have won the 1983 election, or at least been able to form a grand coalition with the Alliance, and the same goes for the subsequent elections: it is unlikely that John Major would have had his shock victory in 1992, for instance. And AV would not have stopped Blair from winning his resounding victories. Probably in 2005 it would have left Blair a little more punished for the Iraq war, but probably you wouldn’t regard that as a defect of AV. And as for the future, when the Conservatives reduce the number of seats you will have a lot of electoral ground to make up. If the Lib Dem vote collapses then AV won’t harm you, and if it doesn’t collapse then AV will make it much more likely that you will be in a position to defeat the Tories.

To put it in slogan form again,

A LABOUR SUPPORTER VOTING FOR FPTP IS A TURKEY VOTING FOR CHRISTMAS.

Or to be more visual about it,

As I’ve said above, it’s a little more complicated than that, but the whole point of slogans is to ignore all those little qualifications.

Some claims by the NO2AV campaign.

I would like to assess some of the claims about AV that have been made by those campaigning against it.

1. Under AV the person who comes second or third can win.

I find this argument laughable. The truth that the above sentence expresses is that under AV the person who would have come first under FPTP will not always win. Well I’ll be: it turns out that AV and FPTP do not lead to identical results. So that is why we are having a referendum. Duh.

This objection to AV is so blatantly question-begging that it is quite extraordinary that anyone can seriously advance it as an argument. The NO2AV campaign has a TV advertisement involving a horse race. At the end of the race, to everyone’s bemusement, the horse that comes in third is deemed to have won. This is supposed to be an argument against AV.

If I had the resources, I would make a counter-advertisement. It would go something like this. There is a mile-long horse race. As the horses approach 4/5 of a mile, Tory Boy is in the lead, but Labour Lad is storming up from behind and clearly about to overtake. Meanwhile Demon Libby is flagging badly and may not finish.

Suddenly the race stewards run on to the track and stop the race. To general bemusement, Tory Boy is declared the winner, despite the fact that the race was not yet over and Labour Lad clearly had more in the tank for the vital closing stages.

Final slogan: UNDER FIRST PAST THE POST, YOU DON’T HAVE TO BE FIRST PAST THE POST!

2. AV is unfair/undemocratic.

I don’t actually know what the NO2AV campaigners mean here. But I think they again mean that AV yields results that are different from the results of FPTP. The extreme unfairness of relatively large third parties getting a negligible share of the seats under FPTP does not figure in their calculations.

The idea that AV is less democratic than FPTP makes even less sense to me. AV allows people to express their actual political preferences rather than being forced (if they don’t want to waste their vote) to vote tactically.

I suspect that the NO2AV campaigners would rather not specify what they mean by calling AV unfair and undemocratic, since that way their arguments cannot be properly scrutinized. However, it may be that in the back of their minds is another objection that has been made several times, which is the following.

3. Under AV, some people get more votes than others.

The beauty of this objection (from the point of view of its political effectiveness, by which I mean its ability to persuade people who don’t feel like thinking critically) is that it cleverly confuses a true statement with a false statement. It would be ludicrously unfair if some people were given more ballot papers to fill in than others. But that, it hardly needs pointing out, is not what happens. What does happen is that some people’s second (or lower) preferences are taken into account and other people’s are not.

This is presented as an unfair advantage to those whose lower preferences are taken into account. A hypothetical example sometimes given by the NO2AV campaign is of a BNP supporter getting five bites of the cherry whereas decent Conservative and Labour supporters get only one. (The British National Party is our lunatic far-right party. A typical quote from its manifesto: “At current immigration and birth rates, indigenous British people are set to become a minority well within 50 years. This will result in the extinction of the British people, culture, heritage and identity.”)

Is there any significant sense in which AV gives more votes to the BNP? There are various ways of thinking about this question, and none of them is of much comfort to BNP supporters.

Consider first what it means if you get five bites of the cherry. It means that your first-choice party is eliminated, and your second-choice party, and your third-choice party, and your fourth-choice party. Compare that with the poor old voter who gets just one bite of the cherry. Their party is either the party that wins or the party that comes second. In the first case, they obviously do better by far. In the second case, it is not clear: if you vote Labour and Labour come second to the Conservatives, then you might well have preferred the Liberal Democrats or the Greens. But (i) they were behind Labour and (ii) right until the final round your vote was counting for your favourite party rather than for lower and lower choices.

A quick slogan:

GETTING MORE BITES OF THE CHERRY IS A DISADVANTAGE STUPID!

The idea that it is unfair for some people to have their vote counted more often than others is — in so far as it means anything at all — just plain wrong. The NO2AV campaigners are saying that supporters of unpopular parties get more votes. What they actually get is more opportunities to change their vote. Since each change is from a higher preference to a lower preference, changing one’s vote is not something one wants to do. Simple isn’t it?

Here is another way of thinking about this bizarre objection to AV. Let us contrast it with a different system that is manifestly fair. I’ll call it MR for Multiple Rounds. Under this system, everybody votes for just one candidate. If no candidate gets over 50%, then the least popular candidate is eliminated and there is a new round. Again, if no candidate gets over 50%, then the least popular candidate is eliminated and there is a new round. This process continues until a candidate does get over 50%.

This time, everybody gets one vote per round. How does that differ from AV? The answer is that under MR you have more flexibility in how you vote, for two reasons. The first reason is that if you put a party as your first choice in one round, you can put a different party as your first choice in a later round, even if the first party is still in the running. Secondly, you can allow your votes in later rounds to depend on the results of earlier rounds, which increases the opportunities to vote tactically.

Why might you want to change your first preference if the party you voted for is still in the running? I can think of a few reasons. One is that you might want to vote tactically because of something like the scenario I outlined earlier that can occur under AV: you want to eliminate a party so that the party you actually like can pick up votes from the supporters of that party. Another is that you like backing a winner, and you sense that a candidate has “momentum”. The first reason is a legitimate one but an undesirable feature of MR (so it is good that AV lacks it). The second is not, I think, rational in a vote for an MP, though it might be rational if you are voting for a party leader and want a display of unity.

So AV is effectively MR under two restrictions: you are not allowed to change your vote from round to round unless the party you are currently supporting is eliminated; and you are not allowed to know anything about the votes cast in previous rounds except which parties have been eliminated. Given those restrictions, you might as well just list your preferences in advance, and if you do then you’ve got AV.

A quick slogan:

AV IS MULTIPLE-ROUND VOTING MINUS TACTICAL GAME PLAYING.

If you think about AV that way, then you can see easily that no voter has an unfair advantage over any other voter — and supporters of unpopular parties are the worst off.

4. AV is unfair because the least popular party gets its second-choice votes counted first.

Oh dear. There was even an article published in the Guardian that made this completely wrong point. If you buy the equivalence of AV and MR with restrictions, then you have an instant proof that the objection is wrong: under MR with restrictions, the least popular party does not get its second-choice votes counted first and yet the result is precisely the same.

Here is a different argument. Suppose there is a constituency with four candidates, representing Labour, the Conservatives, the Liberal Democrats, and the British National Party. The first preferences are

Labour, A
Conservative, B
Lib Dems, C
BNP, D

where $A+B+C+D=100$ and (let us suppose) $A>B>C>D.$

Those lucky BNP supporters now get their second-choice votes counted. Let’s suppose that $D=E+F+G$ and that $E,$ $F$ and $G$ are the percentages of votes transferred to Labour, the Conservatives and the Lib Dems, respectively. So after the first elimination the position is

Labour, A+E
Conservatives, B+F
Lib Dems, C+G

Suppose now that the Lib Dems are third. Now we have $C=H+J$ and $G=K+L$ and the standings are

Labour A+E+H+K
Conservatives B+F+J+L

Let us think carefully what $H, J, K$ and $L$ stand for. $H$ is the number (expressed as a percentage of the total number of voters) of Lib Dem voters who transfer to Labour, which means Lib Dems who either put Labour as their second choice or put the BNP as their second choice and Labour as their third choice. $J$ is the same thing but with “the Conservatives” replacing “Labour”. $K$ is the number of BNP supporters who put the Lib Dems second and Labour third, and $L$ is the number of BNP supporters who put the Lib Dems second and the Conservatives third.

To see that this is exactly symmetrical between the BNP and the Lib Dems, let us see how the Conservative vote now breaks down. The votes they have are from

(i) people who put the Conservatives as their first choice,
(ii) people who put the BNP as their first choice and the Conservatives as their second choice,
(iii) people who put the BNP as their first choice, the Lib Dems as their second choice and the Conservatives as their third choice,
(iv) people who put the Lib Dems as their first choice and the Conservatives as their second choice,
(v) people who put the Lib Dems as their first choice, the BNP as their second choice and the Conservatives as their third choice.

Notice that the situation is entirely symmetrical between the BNP and the Lib Dems. The fact that the BNP second preferences are counted first is just a procedural convenience that does not affect the outcome. It does not give the BNP more power than the Lib Dems.

Here is a third, more concise, way of making the point. In the rounds where the BNP supposedly has an advantage over the Liberal Democrats, the BNP has been eliminated. So the BNP has lost and they have to make do with their second choices, while the Lib Dems are still in with a chance and can still have their first choices counted. In which position would you rather be?

5. AV helps the BNP.

If that is the case, then it is odd that the BNP is against AV. But it is also odd that about half the Labour party is against AV, so perhaps the BNP is just being stupid (a possibility that, in the light of other evidence, cannot be discounted).

I have just explained why being eliminated first does not give you any advantage under AV, even over the party that is eliminated second. But perhaps it is nevertheless the case that your average BNP supporter is better off under AV, merely by virtue of being able to express a second preference at all. Under the current system, a BNP supporter has two options that are not completely daft. The first is the obvious one of voting BNP. (When I say that that is not completely daft, I mean that it is not daft if one’s object is to help the BNP. That object itself is of course completely daft.) The second is to buy the wasted-votes argument and choose the most racist party one can find that has a decent chance of being elected. The Conservatives tend to be tougher on immigration than Labour or the Lib Dems, so they will probably be the one to choose.

Under AV, this BNP supporter will no longer have a dilemma: it will be possible to vote BNP first, then UKIP (probably number two in the racism stakes), then Conservative, then Labour, and finally the Lib Dems.

This sounds like a big disadvantage of AV: it gives people a chance to vote BNP without wasting their vote.

Here are two counterarguments. The first is that it is not just BNP supporters who benefit in this way: all voters are freed from the shackles of the wasted-votes argument. If you are a Conservative supporter in a constituency where the Conservatives came third last time, you don’t have to agonize about whether to vote Conservative and risk letting in Labour: you can vote Conservative first and Lib Dem second, for instance. And the vast majority of the country who detest the BNP can express their dislike more forcefully by showing not just that the BNP is not their favourite party but that it is their least favourite party. To argue for FPTP on the grounds that AV helps the BNP by letting them express their preference for the Conservatives over Labour is to suggest that all voters should be punished for the sins of a tiny minority.

Slogan time.

WE SHOULD NOT LET THE BNP DICTATE HOW WE RUN OUR POLITICS.

A related point is this. Under AV the larger parties will know that once the BNP is eliminated, the second choices of BNP voters will count every bit as much as the first preferences of other voters. Since the BNP will, with probability 1, be eliminated, it would appear that there is now more reason to court the BNP vote than there was under FPTP. So AV could lead to parties adopting more unpleasant racist policies than FPTP does.

This argument sounds plausible but doesn’t stand up to scrutiny. First of all, it is simply untrue to say that FPTP gives a party no reason to court the racist vote. After all, under FPTP those racist voters are still out there, and they still might decide not to vote BNP (either because it is a wasted vote, or because they are embarrassed to vote for a party that is explicitly racist rather than dressing up their racism as concern for ordinary hard-working British families). And we do see, at every election under FPTP, parties talking tough on immigration in an unpleasant way — or being punished for not doing so.

One further point is that in most constituencies the BNP are a smaller party than the Lib Dems or the Greens or UKIP. So they will be contributing far fewer of those precious second-choice votes. Therefore, courting the BNP (which in any case is politically hard to do explicitly) is not a sensible strategy, since for each BNP supporter that you attract, there will probably be ten Lib Dems that you alienate.

6. AV is expensive.

Here is how the NO2AV campaign breaks down the cost of AV.

The referendum itself: £91 million.
Electronic vote counting machines: £130 million.
Explaining AV to voters: £26 million.

This adds up to £250 million (or rather, they say it does — actually it adds up to £247 million). We can take that straight down to £156 million with the help of the following simple observation:

THE REFERENDUM IS HAPPENING ANYWAY! DUH.

Just to make that point clear, imagine that a group of friends want to go to the cinema. Some people want to see Avatar, which is the film showing in a single-screen cinema just round the corner. But others are not so sure, so they suggest catching a bus to a large multiplex cinema where there are three films that look promising, one of which is Avatar. This plan is agreed upon, and when they are at the multiplex a discussion ensues about which film to watch. The Avatar supporters argue that the cost of the bus fare is an argument against choosing another film, since it would have been possible to watch Avatar without a bus journey. The rest of the group laugh in their faces.

£156 million is still a lot of money. Luckily we can take it down further: it is a straightforward lie that AV requires electronic vote-counting machines. That gets us down to £26 million.

Does it take that much money to explain AV to voters? If so, could I please please be the one who is paid £26 million to say “Put the candidates in order of preference until you don’t care any more”? Obviously, to explain how these preferences will affect the outcome is more difficult, but it is also not necessary, since following the simple instruction to put the candidates in order of preference is the right and rational thing to do (given that there will tend not to be enough information to make tactical voting a practical possibility).

But for those who think it’s necessary, here’s another slogan.

AV IS EXPLAINED ON THE INTERNET.

7. AV is complicated/obscure/perverse.

I’ve just dealt with this objection. My basic answer to it is, “No it isn’t.”

Let me repeat how to vote under AV:

PUT THE CANDIDATES IN ORDER OF PREFERENCE UNTIL YOU DON’T CARE ANY MORE.

That is not complicated, obscure or perverse.

In case you want to know how your vote will count:

THERE ARE MULTIPLE ROUNDS. AS SOON AS A CANDIDATE HAS AN ABSOLUTE MAJORITY THAT CANDIDATE WINS. AFTER EACH ROUND THE LEAST POPULAR CANDIDATE IS ELIMINATED. IN EACH ROUND YOUR VOTE GOES TO YOUR TOP PREFERENCE AMONGST THE CANDIDATES STILL IN PLAY.

That takes a bit longer to explain, but it is still pretty simple. Simple enough, for example, for leadership elections in the main political parties. And if, despite that, you don’t understand it, it doesn’t matter, since it is still in your interests to put the candidates in order of preference. (An analogy: your computer is very useful to you even if you don’t understand in detail how it works. And if you did understand how it worked, it wouldn’t affect how you surf the internet, send emails, etc.)

8. AV leads to the election of mediocre candidates.

The argument here is that under AV you often end up electing the candidate who is least disliked rather than the candidate who is most liked. This is supposedly a recipe for mediocrity.

Let us set aside the obvious point that mediocre people do not seem to be blocked from the House of Commons by FPTP. It might still be the case that more mediocre people would get in under AV. But would they?

Let us consider a typical case where AV and FPTP lead to different results. Suppose that there is a constituency with a solid 40% support for the Conservatives and a split of the left vote between Labour and the Liberal Democrats (with Labour getting 35% and the Lib Dems 25%, say). If the Lib Dems tend to prefer Labour to the Conservatives, then Labour will probably win this seat under AV, while the Conservatives would win it under FPTP.

The question we are now considering is this: would the Labour candidate be likely to be more mediocre than the Conservative candidate? If you are sufficiently right wing, then perhaps you will think that the answer is yes merely because the Labour candidate is a Labour candidate. But in that case you are not thinking about the merits of AV in the abstract but merely about whether it helps your party. And I’ve already made the point that AV probably wouldn’t help the Conservatives, which is why they are campaigning vigorously against it.

Does it favour mediocre candidates (or parties) if second preferences have a significant effect on the vote? Let us try to imagine how AV would affect an election campaign in the hypothetical constituency just discussed. Under FPTP the Conservatives could afford to reach out to their core support and be pretty confident of winning the seat. But under AV they would know that that was not enough: they would need to attract at least two fifths of the Lib Dem voters. Similarly, Labour would know that they needed to attract at least three fifths of Lib Dem voters.

Since the Lib Dems are somewhere in the centre, it would probably be a bad idea to push for extreme right or extreme left policies. So in this constituency, the need for the two largest parties to attract the second preferences of Lib Dems would act as a curb on extremism. I’m not talking here about BNP-style extremism but just the sort of extremism-lite that you get on the right of the Conservative party and the left of the Labour party. Does that mean that candidates would become bland and mediocre? Well, it’s true that some of our more colourful politicians, people like Enoch Powell, Tony Benn, Dennis Skinner, Norman Tebbit, have been on the extreme wings of their parties. But some pretty notable politicians have come from the centre too, such as Kenneth Clarke, Tony Blair, David Owen, and many more. And AV isn’t going to get rid of those with extreme views since there will still be safe seats where they do not need to attract Lib Dems — it’s just that there won’t be as many of them.

To sum this up in a slogan:

FPTP HELPS EXTREMISTS.

In general, suppose we have a constituency where one candidate is liked by 40% of voters and loathed by 60%, while another candidate is liked by 35% of voters and quite liked by a further 20% of voters. Which candidate best represents the views of the constituents? There is a strong case for saying that it is the second. Certainly, if you were to ask the constituents which they preferred just out of the leading two candidates they would say the second.

In fact, I can feel a slogan coming on.

UNDER FPTP A CANDIDATE IS OFTEN ELECTED EVEN THOUGH MOST PEOPLE PREFER A DIFFERENT CANDIDATE.

9. AV leads to more coalitions and hung parliaments.

In the UK there have been a number of coalitions and hung parliaments under FPTP, as well as periods where one party has been dominant. Would there have been more under AV? The evidence from other countries is inconclusive. I suspect that there might well have been a hung parliament in 1983 under AV, since the split on the left would no longer have given Margaret Thatcher her huge majority. But in general it is far from clear that AV has this effect: indeed, some have argued that AV leads to swings that are even larger than those under FPTP. As an example, consider the 1997 election. There the Conservatives were extremely unpopular but held on to 165 seats with the help of FPTP. I don’t know the figures, but probably they had outright majorities in many of those seats. However, there will also have been several seats where they won with less than 50% of the vote, and it seems likely that in many of those they would have lost out under AV, since Labour and Liberal Democrat voters would have been unlikely to put the Conservatives as their second choice.

There is also the question of whether, if AV leads to more coalitions (which is debatable), one should regard this as an advantage or a disadvantage. Such is the unpopularity of the present coalition that many people have now decided that they don’t like coalitions at all. But the alternative to coalitions is that representatives of a minority of the country have unfettered power to do what they like. It is not obviously better.

10. AV benefits the Lib Dems and nobody else.

This is false. It benefits any party that is small but large enough to have a serious chance of getting seats. (I am not including the Scottish and Welsh Nationalists or the parties in Northern Ireland, because I count those as large parties in the areas that they represent.) The Greens are an example, and perhaps UKIP will be another. The Lib Dems are so unpopular now that at least for the time being it is unlikely that any voting system will help them. And if it ever does, we will be talking about an overhauled and rehabilitated Lib Dem party. And AV would in the past have helped Labour on a number of occasions, because they could have picked up Lib Dem (or Lib, or Alliance) second-choice votes.

11. Voting AV will give a big boost to Nick Clegg.

Yes, if AV wins then it will put a big creepy smile on Nick Clegg’s face. So a slogan is needed again.

THIS REFERENDUM HAS NOTHING TO DO WITH NICK CLEGG!

If you are planning to vote no to spite Nick Clegg, you should bear in mind the following points.

(i) The chance to change the voting system comes around very rarely because under FPTP the parties in power tend to have no interest in changing it, and hung parliaments, which give the Lib Dems a chance to negotiate, come around about once a generation.

(ii) You may hate the Liberal Democrats now, but think back to when you hated other parties. If you vote no to AV, then today’s Liberal Democrats will be very disappointed. But so will the Liberal Democrats of fifteen years time, who will be a completely different bunch of people, chastened by the experience of this coalition and certain to make keeping their pre-election promises their absolute top priority. Or perhaps they will have been annihilated completely and a different party, such as the Greens, will occupy the ground that they have traditionally occupied.

DON’T TAKE A LONG-TERM DECISION FOR SHORT-TERM REASONS!

(iii) Why do you hate Nick Clegg so much? Presumably because you hate the Conservatives, and Nick Clegg has allowed the Conservatives to govern with a minority. So it’s really the Conservatives you don’t want. And who has most to gain from retaining FPTP? The Conservatives.

Let me summarize:

NICK CLEGG IS TOAST ALREADY. VOTE YES TO SPITE DAVID CAMERON AND GEORGE OSBORNE!

Let me summarize again:

12. FPTP makes it easier to get rid of unpopular governments.

This is a clever argument that was put forward a couple of days ago by David Cameron. Once again, I mean clever from the political point of view: it sounds persuasive despite being wrong. In fact, it is better still, since it suggests a general technique that all politicians can use. If your party stands for X and Y is an adverse consequence of X, defend X on the grounds that not-Y is a consequence of X. For example, if, as all economists will tell you, spending cuts lead to increased unemployment, go out and say that you are making spending cuts in order to create jobs in the future.

The idea that FPTP has made it easy to get rid of unpopular governments is one that you can hold only if you wilfully ignore history. Mrs Thatcher’s government was deeply unpopular but proved to be extremely hard to dislodge. Blair was loathed after the Iraq war but went on to win another election, and his successor, Gordon Brown, though defeated in 2010, came close to having enough seats to form a viable coalition with the Liberal Democrats. Under AV it would have been much easier to get rid of Mrs Thatcher, for reasons I have already discussed: she would not have been able to exploit the split on the left. However, it is also worth saying that part of the reason that it was so hard to get rid of Thatcher and later Blair was that Labour in the 1980s and the Conservatives in the 2000s were going through periods of internal conflict and were not obviously electable. If you want to get rid of an unpopular government, it helps to have a viable opposition.

Perhaps it’s worth having a look at the results of another election, the one that took place in 2005, not long after Blair’s decision to invade Iraq. A large number of people were furious with him for misleading them about weapons of mass destruction, with the result that his share of the vote dropped substantially. The results were

Labour, 35.2% of the vote, 355 seats

Conservatives, 32.4% of the vote, 198 seats

Liberal Democrats, 22.0% of the vote, 62 seats.

With barely over a third of the votes, Blair still had a comfortable majority in the House of Commons. It is difficult to reconcile this with the idea that FPTP makes it easy to get rid of unpopular governments. Under AV, the most likely result would (I am guessing) have been a hung parliament with Labour the largest single party. There is no chance that Charles Kennedy would have formed a coalition with the Conservatives, so we would probably not have got rid of Blair. But he would have been properly punished for Iraq by being forced to cooperate with the Lib Dems, who were the one strongly anti-Iraq-war party.

Here’s what I think David Cameron might have meant by his statement. He thinks that AV leads to more coalitions, so he has a picture of an unpopular government managing to survive by forming a coalition with a smaller party. But how much of a danger is that? Nick Clegg was desperate, after the last election, not to be seen to be playing that role for Gordon Brown.

Another slogan:

AV MAKES IT EASIER TO GET RID OF UNPOPULAR GOVERNMENTS!

To explain why in the abstract: if a government is unpopular, under AV you can vote for anything-but-the-status-quo. The party in power cannot rely on its core support. FPTP allows unpopular governments to cling on with the support of a minority of voters.

13. FPTP gives equal votes to everybody.

I have already explained why it is nonsense to suppose that AV gives “more” votes to supporters of unsuccessful parties. In another post I explained in detail why FPTP does not give equal votes to everybody. To put that slightly better, although everyone gets one vote, some votes count far more than others: if you are in a marginal constituency, you have a far bigger chance of influencing the result of the election, and if you are in a safe seat then the politicians can afford to ignore you (whichever side they are on). Under AV this would still be a problem, but there would be fewer safe seats so the problem would be reduced.

If you want this point in slogan form, here it is:

VOTE YES TO AV UNLESS YOU LIVE IN BASILDON!

14. FPTP has served us well for over a century.

There are variants of this, such as that FPTP is a traditionally British institution, part of how we do things here, etc. FPTP has given us long periods of stable Conservative or Labour rule, supported by a minority of voters. It has also given us periods of instability, such as in the 1970s, the mid-1990s, and perhaps — we shall see — the 2010s. It has been manifestly unfair on a number of occasions. It has provided us with a strange cycle where, to oversimplify grotesquely, Labour spends too much of our money, which is lovely for a while but eventually gets the economy into a mess, then the Conservatives promise to sort out the mess but do so in a brutal way without much regard for the social consequences. (Because economic decisions tend to have effects only after quite a long time lag, we also have the phenomenon that a party’s reputation for economic competence depends a lot on the economic consequences of decisions made by its predecessors.)

Is FPTP serving us well? I don’t think so. If there were more of a need to court the centre (as there would be under AV, since Lib Dem second-choice votes would be more important), then perhaps, just perhaps, the boom/bust cycle could be stabilized. I don’t want to say that that would be an inevitable result of AV, since short-termism is always going to be very tempting for politicians, but with FPTP we can be pretty sure of getting more of the same (unless the current economic crisis is so severe that recovering from it takes decades rather than years).

If you are voting no because you regard FPTP as a Great British Tradition, then you might be interested in this article in the Independent.

Conclusion.

I realize that I have largely failed in my aim to adopt a neutral tone. However, that is because most of the arguments put forward by opponents to AV have been clearly wrong, in several cases so wrong that one can actually prove mathematically that they are wrong. I find it very dispiriting to live in a country where it can benefit a politician to use a provably incorrect argument. I have complained about this in other posts on this blog: a short, succinct, punchy statement that is wrong trumps a longer and ever so slightly complicated explanation of why it is wrong. That is why I have interspersed my longer explanations, which, if I were to make them in parliament would probably be met with derisory who-is-this-guy laughter, with shorter slogans. Perhaps you can think of some better ones. In my wildest dreams, I wonder whether some people might consider tweeting them. Could “WTF IS THE POST?” go viral? Well, probably not, but if it did then it would change more minds than dull and not obviously correct pro-AV slogans such as “Make your MP work harder.”

I don’t for a moment suppose that the power of incorrect arguments is a uniquely British phenomenon. I thank my lucky stars that we don’t (yet) have Fox News to contend with and that we don’t have to waste time explaining that Barack Hussein Obama is not a Muslim or that free universal healthcare in Britain doesn’t make us communists. (Unfortunately in Britain we do have to waste time, and probably trillions of pounds of our grandchildren’s money, explaining that there is an overwhelming consensus amongst people who know what they are talking about that man-made global warming is a serious problem. But the opposition to this view is more virulent in the USA.)

OK, rant over. I’ve wasted hours of precious work time on this, but I think it is a lost cause and need to get back to some mathematics.

### 625 Responses to “Is AV better than FPTP?”

1. Chris Campbell Says:

Hi Tim,

I am writing an article for a student science newspaper on voting systems and such and would be very grateful if I could use ideas from this and your other article (Is the British voting system fair?). Would that be ok? I don’t mean copy-paste of course.

Thanks,
Chris

• gowers Says:

I’d be only too pleased: help yourself. Since students are typically left-leaning, but angry with Nick Clegg and too young to remember what it was like under Thatcher, it seems particularly important that they understand what they would be letting themselves in for by voting for FPTP.

• Stephen Johnson Says:

Chris,
I am not sure what sort of article you plan, but if you have an open mind about Electoral systems, have a look at DPR Voting. On the can it claims to offer uncomplicated PR where every vote makes a difference to the election result, but I will leave you to judge.

2. Simon Byrne Says:

As an Australian living in the UK (and who is, for some strange reason, actually allowed to vote in this referendum), I have found the whole debate a bit strange, as we have had the system for almost a century (and yes, democracy did more or less survive). I agree that “First Past The Post” is a silly name, but then so is “Alternative Vote”. Why not go with the self-descriptive “Instant Runoff Voting”?

As you point out, the individual voter doesn’t really have the incentive for tactical voting under AV, but the parties themselves do: hence I predict the subsequent arrival of the “how-to-vote card”. Parties, even small ones which don’t expect to win any seats, can try to direct where their supporters preferences will go. There are some interesting game-theoretic puzzles here, particularly for a party such as the Lib Dems which may have enough voters to determine which of the other two parties may win.

In fact, this may keep extremist parties out of power, if all the other parties direct their supporters to put the BNP last in the list of preferences. This was the tactic used by the major parties in Australia in the 90s against One Nation.

• Mike Says:

Yes, but there is are two fundamental differences between here and Australia. Firstly, voting there is compulsory, which means that you get a lot of people who have to vote despite not caring about the outcome (and, thus, are likely to just follow the party line) and secondly in Australia you are required to give an exhaustative list of preferences, whereas over here you won’t be (and, given that some of the multi-voter constituencies have 20 or more candidates, you can understand why people follow those preferences…).

3. Tom Says:

There’s a system that is much, much simpler than AV that I would expect to lead to much the same results: range voting. Simply give each candidate a score out of 10, say, and add all the scores together. The highest score wins.

• gowers Says:

I quite like that too, but I think counting votes would become pretty expensive. Another system I like, but that I think has no chance of ever being used, is where you are simply allowed to vote for as many candidates as you like (not in order of preference) and the candidate with the most votes wins. Then if, for example, you happen to be an anyone-but-the-Tories person you can vote Labour and Lib Dem, whereas if you are a diehard Labour supporter you can just vote Labour. I think this system is even simpler and would again give similar results to AV.

Of course, this system is just range voting with the smallest possible non-trivial range.

• Tom Says:

Yes, when the range is [0,1] it’s often called approval voting and I like that too. It’s very simple.

• Tom Says:

I should say “the range is {0,1}”

• Peter Millican Says:

The big problem with range voting is that it positively invites tactical voting. Suppose you’re in a LibDem/Labour marginal, and your preference is 1. LibDem, 2. Labour, 3. Tory. You will probably vote 10/10 for LibDem, and 0/10 for the other two, even if you actually think Labour is nearly as good as LibDem. Since the real contest is between LibDem and Labour, you’ll want to do as much as possible to favour LibDem and to damage Labour. So you have no motive to express your true opinions.

• gowers Says:

That’s one of the reasons I prefer a small range. However, even in your example you might decide to vote 10/10 for Labour if you didn’t think the Lib Dems had a chance. (Of course, that’s tactical too.)

• Isaac Says:

Isn’t the problem with the system you just mentioned, Gower, that it would just revert to a FPTP system under a different name? i.e. Conservatives would vote Tory, Labour for Labour, Lib Dem for Lib Dem, etc. because by voting for Lib Dem, and Labour and Green, in a traditionally Labour constituency your Labour vote would negate any chance of your Lib Dem vote having an effect?
Forgive me, that doesn’t emphasis the problem I feel is with the system you just mentioned (in fact, it feels like I just wrote some incorrect propaganda for the NO2AV campaign… but… well, it sounds like there is a massive potential for flaw in the above system.)
Forgive me for not arguing my point well, I am relatively politically nieve.
The range voting system Tom mentioned seems like it would work well though.
(I am all for AV, however I am not yet elligible to vote. I only wish you could make this blog post into an hour long BBC documentary, which might then wipe the mud that has been thrown by NO2AV campaigners from the eyes of the every-day referendum voter.)

• polleetickle Says:

Is this simply an anti-tory GOWERS blog declaring an ulterior motive for tactical voting to achieve personal left-wing ambitions rather than an attempt to enshrine democracy and integrity? Just asking.

• gowers Says:

For what it’s worth, my political views aren’t a very good fit with any political party: I’m fairly right wing about some things and fairly left wing about others. On social issues I’m very much a liberal. I don’t like party politics, or the yah-boo politics that David Cameron promised to put an end to, and then said after about five minutes as leader of the opposition that he couldn’t resist. I’d like to see rational debate on an issue-by-issue basis. For that reason the idea of coalition government, or better still minority government, appeals to me.

I realize that none of what I want to see has any chance of happening, but I think of AV as a very tiny step towards it.

4. Doormat Says:

Brilliant! But, one thing to add: The Conservative Party, which appears to be against AV, actually use MR to elect their leader. And you pretty convincingly argue that AV is just MR without a couple of flaws. I find it utterly bizarre that a voting system a political party USES TO ELECT ITS OWN LEADER is apparently wrong to use for the general public to elect MPs!

[The rules for electing the leader of the Conservative party: http://en.wikipedia.org/wiki/Conservative_Party_%28UK%29_leadership_election,_2005#The_current_rules ]

• Tim Roll-Pickering Says:

The Conservatives have initial ballots of MPs only to ensure the candidates put to the membership have sufficient support in the parliamentary party. Party members get just one vote in one single round.

If we were to directly adapt party leadership rules to elect Westminster then the logical conclusion of your point is that all seats should have only two candidates, chosen by sitting MPs only.

• Tom Rees Says:

Tim, it’s the other way round: if we were to adapt AV to the Conservative Leadership election, then every conservative party member would be able to vote at every stage. Clearly a fairer, more representative system!

AV is a run-off system, just like the system used to elect Cameron. The only difference is that the entire electorate can participate in every round, and that you state your preferences up front (to avoid everyone having to keep going back to the ballot box).

• Tim Roll-Pickering Says:

The MPs’ only rounds are to demonstrate that the candidates have a strong base of support within the parliamentary party – they’re closer to an extended nominations process than anything else. Personally I would scrap them and have a single FPTP ballot of all party members with all the candidates (which I believe Cameron would have won in 2005).

If people wanted to establish the system as AV, why was that term not heard in 2005 when there was a lengthy review of the system and much discussion about it?

5. Blaise Pascal Says:

Here in the US there are some terminology differences. The subsequent rounds in MR are called “runoffs” (and are usually restricted to just the top candidate), and AV is therefore called “Instant Runoff Voting” (IRV). At least one minor party (the Green party) has conversion to IRV on it’s platform. IRV is also used in some local elections in some jurisdictions.

Given a choice between FPTP/Plurality (my favored term for “the party with the most votes wins”) and AV/IRV, I would definitely choose AV, so in that regard, I’m on your side. But it isn’t my preference.

1 — Any Condorcet method
2 — IRV/AV
3 — Approval
* — FPTP/Plurality

My two biggest complaints against IRV are (a) it doesn’t choose the Condorcet Winner if one exists, and (b) it doesn’t allow computing the winner in multi-precinct election by aggregation of precinct-level results.

The “Condorcet Winner” in an election is the single candidate who, if in a 2-way race against any other opponent on the ballot, would win a majority of votes. As an example of this, imagine a 4-way race with candidates A, B, C, and D. Imagine 32% voted BACD, 33% voted CADB, and 35% voted DABC. FPTP would elect D, AV would elect C, but the Condorcet winner is A — 68% prefer A to B, 67% prefer A to C, and 65% prefer A to D. Clearly more people would be satisfied with A than with C or D, but neither AV or FPTP give them A.

The main problem is that there isn’t always a Condorcet Winner. Sometimes you will have a majority preferring A to B, a different majority preferring B to C, and a different majority preferring C to A. The Condorcet methods differ in how they resolve this issue.

The other big, practical problem I see with IRV is aggregation of multi-precinct results. I believe a simple, realistic example might highlight the issue. Imagine it’s Florida in 2000. There are 10 candidates on the ballot for President of the US, and the rest of the US has come out so close between George Bush and Al Gore that the outcome in Florida will determine the national election. Also, the 1st-preference votes are extremely close: less than 2,000 votes out of almost 6 million cast, with both Bush and Gore getting approximately 48.85% of the vote, about 69,000 votes shy of a majority. The 7 candidates with the smallest 1st preferences have between them only 40000 or so votes, so AV would not be able to determine a winner even after 7 elimination rounds. Each round would involve counting, modifying, and redistributing all 6 million ballots. There were voting and balloting difficulties requiring careful examination and interpretation of ballots which could not be machine-read. This would have to be done 8 times. If a mistake was discovered at a single polling place (such as a batch of misplaced ballots, which did happen) the count would have to start over again from the beginning.

It is probable that such large-scale elections with those issues won’t happen in the UK, as I don’t think any single election covers nearly as large of a population or geographic area. But there are problematic elections in recent US history which AV would have made more of a nightmare.

Compare Condorcet voting in this mess: While there are more than N! possible ballots in IRV and Condorcet, a set of Condorcet ballots in a voting precinct can be summarized into N*(N-1) pair-wise results, which can be summed across precincts. A change caused by a recount or error correction at a local level causes an easily-reported change in the aggregate amounts without causing all ballots globally to be re-examined.

In short, I agree that AV is better than FPTP, and would vote for it in the referendum if I were a British subject, but I don’t think it’s the best.

• Tea Says:

I disagree slightly with your example in Florida. Under IRV/AV, one would only need to redistribute a small portion of those six million ballots, not all of them. After all, 97.7% of the ballots are allocated to one of the two main parties, and thus needn’t be touched (you could have pathological elections where the results in each precinct are drastically different from the overall percentages, but that seems unlikely to actually be the case.). Given that, you only redistribute approximately 3% of the ballots, and that’s with a hefty chunk of ballots that are redistributed multiple times. This is notably rather less than ‘all’.

• Anonymous Says:

Florida’s voting system could also be saved if the votes of black people were actually counted….

• OWJ Burnham Says:

The really big advantage to using AV/IRV in the US is that for Presidential Elections you are not, technically, electing the President, rather each state is electing voters to the Electoral College. Accordingly, each state can be views as a multi-member district (with, in the case of Florida, 25 winners) and so AV becomes, in effect, STV, it’s multi-winner, proportional cousin.

Each state’s EC votes would, therefore, be distributed proportionally, stopping the massive swings garnered by getting a few thousand extra votes in Florida and forcing/allowing candidates to campaign across more states. After all, how much action does that bluest of blue states, Massachusetts see? With STV, if the distribution of EC votes followed the proportion of ballots cast in the state as it was in 2008, Obama would have picked up 7 or 8 of the 12 votes, with McCain getting 4 or 5. Suddenly, the parties have to work in every state (except, possibly, Vermont). In addition, the winner would more closely correspond to the national popular vote, but the system would still retain the slight bias towards smaller states that is currently mandated by the Constitution.

• Cleigh Says:

‘British subject’ indeed?? We in the UK prefer to think of ourselves as citizens, even if the existence of a constitutional monarch may mean the archaic term ‘subject’ still applies in theory. No self-respecting Briton would ever refer to themselves as a subject, and I even find the term vaguely insulting.

Excellent article though!

• David N Says:

The example voting given is clearly artificial and unrealistic. A situation where you have roughly equal numbers of voters voting for candidates B, C and D in the orders BCD, CDB and DBC, but no-one voting in the other three permutations, is totally implausible. If someone can come up with a realistic (or better still, real) scenario where there is a Condorcet winner and AV does not produce the same winner, then I would be quite surprised. I also suspect that conducting a manual count under a Condorcet system would be impractical, and therefore the cost argument would be genuine, so if it would produce the same results as AV in practice, I see no advantage in favouring it over AV, given where we are starting from.

• David N Says:

Clearly I hadn’t thought very hard before making the above comment. If we take the actual votes for the three main parties in Northampton North last year, ignore the rest, and assume that these would have been the first preferences under AV, we have: Con 37.34%, Lab 32.08%, LD 30.58%. If at least 52.01% of Con voters voted LD second, and at least 60.54% of Lab voters voted LD second (both highly plausible), then the LD would be the Condorcet winner, but would, of course, be eliminated under AV.

• MorningTory Says:

As someone who will be voting No, it doesn’t of course bother me that AV fails the Condorcet winner criteria since neither does FPTP. But as you asked for an example, David, I would offer Hampstead & Kilburn in 2010.

The FPTP results were as follows:

Labour – 17,332
Conservative – 17,290
Liberal Democrat – 16,491

Ahead of the day, polling was all over the place with the Lib Dems claiming “Labour can’t win here”, and Labour claiming the exact opposite. The point being that there was no incentive for an “anti-tory voter” to vote tactically. We can, therefore, assume that AV first preference votes would most likely have mirrored the FPTP vote.

If we assume a political spectrum with Lab somewhere on the left, Conservative on the right and the Lib Dems somewhere in the middle (and I think that’s reasonable) then the Lib Dems would clearly have been the Condorcet winner.

National polling has suggested that Lib Dem 2nd preference would be split between the Tores and Labour, with 60% in Labour’s favour. But even if it was an exact even split, Labour would still have been victorious under AV (ith a massive majority which is absurd!).

If there’s a moral to this story, then if we actually do want to change from FPTP then let’s at least do it for a system that is better not worse!

• David N Says:

Thanks for providing another example. However, as AV would probably have produced the same winner as “FPTP”, as you say, it’s difficult to see how you conclude from “this story” that AV is worse. While AV doesn’t necessarily elect Condorcet winners, “FPTP” frequently produces winners who would not have won a head-to-head against ANY other candidate (or at least any major-party candidate). AV cannot do that by definition.

And if there is a better system than either “FPTP” or AV, as you seem to imply (and I agree), then why are we not being given that option?

• Chris Purcell Says:

“If there’s a moral to this story, then if we actually do want to change from FPTP then let’s at least do it for a system that is better not worse!”

As has been mentioned elsewhere, Condorcet winner systems have their own major flaw. If our hypothesis is true, Lib Dem is the preferred second choice of many, so will often win. Knowing that, it is in the interest of both Labour and Conservative voters to lie about their preferences, or not put them at all, to avoid second-best becoming defacto winner. Under AV, you take a much bigger risk trying to game the system (since it involves lying about your first choice, not your second).

• MorningTory Says:

“And if there is a better system than either “FPTP” or AV, as you seem to imply (and I agree), then why are we not being given that option?”

Because coalitions are about shady back-room deals. Whiich is one of the reasons why AV is worse!

• David N Says:

Pathetic. Which was the party that wanted to offer us a better system than either AV or “FPTP”? Clearly not the one that wanted to keep the status quo and not give us any choice at all.

• gowers Says:

Political parties are themselves coalitions of people with differing views — often quite widely differing. The principle of cabinet responsibility (that is, publicly advocating the line agreed in cabinet even if you privately disagree with it) could just as easily be described as a shady back-room deal. In fact, the reason people find the coalition deal harder to stomach is that it is less shady and less “back-room”: it is not possible for the Lib Dems to pretend that they like the reforms to the NHS or that they believe in the heart of hearts that the pace of cuts is right, because their real views are too much out in the open.

6. juliawolf Says:

Sort of surprisingly I had been undecided on the question FPTP vs. AV until last night, mainly for lack of investing any serious thought (and a certain lack of exposure to the debate across the Channel). If Tom Sanders hadn’t already done a pretty good job on the phone last night you would have scored at least one additional AV vote with this excellent post.

I first came across AV in my first year at Clare where we used it for student rep elections, and the sentiment I recall most clearly from this early experience is that going through all possible tactical voting manoeuvres in my mind did my head in, so it left a somewhat unpleasant aftertaste. However, I completely accept the argument that it is actually one the big advantages of AV that tactical voting is made so difficult, if not impossible.

The other source of my hesitation to embrace AV without reserve was that I always thought of myself as a strong supporter of PR. So what if the referendum goes in favour of AV but AV turns out not to be such a good idea in practice? There would be no chance of even considering a change to a fairer system in the next 50 years. But perhaps there is no need to worry about the effectiveness of AV since wikipedia tells me:
“Instant runoff voting is used to elect members of the Australian House of Representatives, the President of Ireland, the national parliament of Papua New Guinea, and the House of Representatives of Fiji.”

Having grown up with an election system in which half the seats in parliament are allocated by FPTP and half by PR, I can confirm that plenty of tactical voting goes on in this system on a regular basis. More importantly, the electoral process regularly produces technical “exceptions” (so-called “Uberhangmandate”) which I suspect make it rather intransparent to the population at large (but very interesting for TV networks on election night). I also remember receiving my postal vote forms from Germany while I was in college and having a whole room full of people laugh at me as I pulled the 25 sheets of paper and six different coloured envelopes out of the package. No, FPTP plus PR is certainly neither a simple nor an elegant alternative.

7. juliawolf Says:

I should perhaps clarify the first line of what I just wrote: I had been undecided between pro-AV and not voting at all, which probably became clear from the remainder of my post.

8. esme Says:

“Before I say any more about AV, let me quickly say what it is (though I imagine that most people interested enough to get this far know already)”

Well, no, there are readers from other countries here. Thank you for your interesting post even if I am not at all the intended audience.

I come from a country which votes for parliament in a practical proportional way (very small parties are eliminated) with all the problems coming from no constituencies. The candidate lists are drawn up by the parties and they are always very unhappy when the recently installed additional preference votes for candidates mess up the order of the lists and thus their inner-party balance.

You explain the differences between FPTP and AV very well, and you rightly crush the pitiful counter-arguments listed, but I am sure that there are problematic situations with a system as complicated as AV. (Complicated from a game-theory and thus tactical viewpoint, not from a how-to-use-the-ballot standpoint.)

I think that AV is great to elect a single person, say the president of the republic, but not so great for a parliament vote, because I do not see why my effective vote should depend on my county when I want to decide on whether my country should go to war. Constituency is a good thing, but it is not the single most important thing and I have lived most of my live in a county where my vote would have been dead without representative voting.

My personal favourite is a mixture of constituency and proportional vote: The number of vote regions should only account for a part of the MPs (say 50%), the rest of the seats should be filled proportionally to the popular vote by the parties candidate list and the most successful runner-ups.

(To give you an example:
In my country, the Communist Party has a negligible popular vote that would certainly be enough to have a couple of proportional MPs. They did have one candidate who regularly got mor than 15% in his own otherwise anti-communist region. It would clearly be the “will of the people” to have him in parliament because he was that popular that people would even vote the communists because of him. His share of voters was much more than necessary for a proportional seat, but not in a single county and he would never have won a county in any voting system.)

9. esme Says:

Note to juliawolf:

The German system of Überhangsmandate are not at all a necessary consequence of mixing FPTP and reprentative votes. This is just a result of the crazy decision to resolve the conflict between geographic and party representation by haphazardly adding some seats here and there and thus losing both types of representation.

10. Nicholas Wilson Says:

I generally agree with the article, which is exceedingly thorough, with one flaw. Tim concedes that it might be fair enough for Conservatives to vote No if they think they will be sufficiently advantaged. While I voted Conservative in the last election, and reckon that AV will hurt their seats the most, I will be voting Yes. The argument that Tim left which could fill this hole is a moral appeal. Arguments against AV on the grounds of method do not work, while arguments against it on the grounds of what outcome you want might have some purchase. A moral argument is precisely what is needed here. Suppose that, in addition to wanting your party to win, you also want them to do so fairly. Are we really keen enough on our candidate to support, for example, rigging the voting system against the others? This is the line we need to pursue to make the Conservatives pause for thought when they rightly observe that coalitions might be more common under AV, which is another way of saying that LibDems might gain seats at their expense. We should consider the voting system on its own merits, and be cautious about how much we tweak that system to support one or another balance of power. At the end of the day, whether or not we have a coalition should most democratically be left to the voters: if they get fed up with coalitions, they will stop voting for minor parties; if 25% of the population continue to support a third or lower party, then it is legitimate to see three-party coalition-forming politics.

So, while I agree with Tim’s arguments, there is one missing. At the end of the day, voting No to keep your party in is highly questionable. This is about what way we want to see democracy enacted (both FPTP and AV are democratic, but in different ways); be cautious about whether it is right to allow consideration of the outcome to influence us. Vote Yes for a better voting system.

• Lucy Says:

I agree completely with Nicholas, the moral argument for AV is pretty compelling. I have even felt this with all the (inaccurate!) hysteria surrounding the BNP and AV. I personally find the BNP completely loathesome, but *if the will of the people* were that they had a strong parliamentary presence, or even became the ruling party, then I would respect that. I’d probably emmigrate, but I’d respect it none the less. That’s what democracy is (or should be) – if enough people support a party that party has a say i government! I find it counter intuitive, as a liberal, to say: lots of people vote for the BNP, but these people are stupid and wrong, so let’s make it as hard as possible for their votes to mean anything. That is NOT democracy, it is edging towards a benign dictatorship by educated humanists. I have some secret sympathy for this position, obviously, but overall, the idea of a true democracy is more appealing than the idea of lots of BNP votes is unappealing.

I still have enough faith in the voting public to be 99% certain this wouldn’t happen anyway.

• gowers Says:

I should point out here that when I said that Conservatives should vote no, I carefully preceded that by saying that I was talking about what people should do if they are voting out of narrow self-interest. I entirely agree that a principled Conservative should vote yes, but am realistic enough to think that it is unlikely that many will do so. That is why my main target in this post is Labour voters who are planning not to vote or to vote no, and it is why I am mainly appealing to their self-interest. The fact that FPTP is ludicrously unfair to the Lib Dems is a blight on our democracy, but unfortunately it is not one that many people are too bothered about at the moment.

• Charles Roddie Says:

Prof. Gowers:
1. This assumes that support for particular parties is a matter of self-interest, whereas support for voting systems is a matter of principle.
However the effect of both election of parties and choosing a voting system is the same – determination of governments and policies. So surely neither or both are matters of principle, or of self interest.
2. If you want to make a distinction between principle and self-interest, the rational approach is to form preferences about governments and policies out of principle/out of self-interest, and these will then determine both support for parties AND a voting system. (Once the consequences of both are established.)
3. Once this is done, the rhetorical purpose of your principle/self interest distinction is then lost.
4. The reason that arguments that have been aired publically pro/anti-AV are bad is that they have argued about voting without respect to who will win and lose, i.e. ignored the direct effects of the change. Arguments
that go “vote for AV because my party has great policies and will gain” not only involve two parts, so are complex, but will both increase support among the own party, and decrease it for other parties. So they are not effective rhetorically.
5. You are right to criticize those bad arguments. But in trying to be persuasive you have adopted similarly “principled” arguments that suffer from the same methodological flaw of arguing for the superiority of a voting system without looking at policy consequences.
6. They also don’t take a consistent position, and your “principled” arguments don’t seem to come from any unified or unifiable position. How do values in favor of “fair” voting systems / non-tactical voting / coalitions rather than majorities get combined? What is the underlying preference?
7. The use of “self-interested” arguments is out of place in an argument that claims to answer a question about “principle” under the assumption that this is distinguished from “self-interest”.

In fact to answer the question whether AV is better, we need to know: 1. what the effects of AV are on who gets elected and how parties position themselves, and 2. what consequences (policies, governments) are better. I set out such an approach here if you are interested:

11. Andrew Hickey Says:

The Liberal Democrats didn’t form til *after* the 1987 election, which they fought as the Alliance, as in the previous election…

[Many thanks -- I've corrected it now.]

• David N Says:

If we’re being strictly accurate, the two Alliance parties merged to form the Social and Liberal Democrats, before changing the party name the following year.

12. Andrew Marshall Says:

At the risk of sounding slightly pretentious, your goal of persuading someone to vote ‘Yes’ to AV who previously was undecided has been reached. I only wish the ‘Yes’ campaign would use easily-understandable mathematical arguments rather than ‘Stephen Fry says it’s OK so it must be cool.’

13. Anonymous Jester Says:

Scandal! Fields medalist is paid 26£ million for explaining the AV voting system to the public! MP Cameron would have been able to do it for half of that, saving 13£ of taxpayer money!

Next up: Research mathematicians waste millions of pounds to prove that 1+1=2!

14. Mark C Wilson Says:

Tim – you are obviously frustrated and I sympathize. I haven’t been following the AV debate in UK from NZ, but of course we have had plenty of experience with electoral reform. When we switched from FPTP to the German-style MMP system in the 1990s, there were plenty of arguments made for the status quo, very few of which made sense. We have another referendum coming up this year, as far as I can see just because the current “Conservative-type” government here think they would do better out of FPTP right now.

A bigger issue than the current AV referendum is the meta-issue of why the level of public debate on such issues is so low. Your post, suitably sloganized, would surely have been much more effective a few months ago – it is getting a bit late now. The traditional news media are almost beyond hope these days, but I would expect that the Electoral Commission (or whatever you call it in UK) would provide high-quality information. The missing ingredient (probably even more so here, one of the few countries more in need of real public intellectuals than UK) is contributions by people like you, and those with more expertise (social choice theorists). I can’t understand why advice from such people is not solicited, let alone listened to when given for free. A related problem is the lack of an international perspective on such issues.

The news is not all bad, but almost all is. For example, the voting rules in the European Council of Ministers have been revised several times. The last time, a petition by voting power theorists was disregarded. However, there is a move to devise a system for expansions of the European Parliament as countries join in the future, and input from some experts (including your colleague Geoffrey Grimmett) – http://www.europarl.europa.eu/en/headlines/content/20110218STO13924/html/si-min-b-pidM-MEPs-try-Maths-Cambridge-Compromise.

To conclude a very long comment, I urge you to think about how we as academics can best contribute to public debate on important issues. The marginal value of one more theorem by a Fields’ Medallist may be much less than the value of some work as a public intellectual. And of course, forming a group for the latter purpose (of which you have some experience with Polymath) will likely have much greater value.

15. Jason Crease Says:

Fantastic. This has made me wonder though: Can AV be used tactically to express the preference “Anyone BUT X”?

Let’s say there are 26 parties standing, and I rank them: C, F, B … everyone else … X . Should I vote: 1C 2F 3B and leave it at that, or should I vote 1C 2F 3B 4A 5D 6E … 25Z 26X?

• David N Says:

Jason, if the parties other than C, F, B and X have no realistic chance of winning, it probably won’t make any difference. However, for personal satisfaction, I would suggest ranking everyone except X – leave them blank. If we get AV, I intend to do that (not that I want to vote for “anyone but X”), even though my vote probably won’t get transferred beyond my first or second preference (depending on which parties stand).

• Chris Purcell Says:

I’ve been thinking about this. Under AV as proposed, you cannot say “anyone but X” without accidentally expressing false preference between two candidates you really couldn’t care less about; I would recommend just voting the three you do care about.

However, a simple modification to the rules would make it possible: allow voters to rank two or more candidates equally, by giving them the same number. In your case: 1C 2F 3B 4A 4D 4E 4G…4W 5X. In each round, set any ballots whose top two remaining candidates are tied aside for a round.

This lets me, for instance, cast 1 LD 1 Lab 2 Con: I’m a lefty but I don’t care which, and I prefer Conservatives to the inexperienced parties. In the first few rounds, until either Lib Dems or Labour are knocked out, my ballot is ignored. Once one goes, my vote goes to the other. If both go, I support Tories. If all three go (blimey!), my ballot is discarded.

Interestingly, under this system, ranking all your least favourite candidates the same, or leaving them blank, gives identical consequences (as you’d hope).

• David N Says:

Chris, the problem with your suggestion is that, if your ballot ignored, the preferences that you HAVE expressed are ignored. Say all but the three main parties have been eliminated, and 5000 voters have done the same as you. The Tory could scrape 50% of the vote at this stage because 5000 votes against them have been ignored. If you really have no preference between two parties, but want to rank them both ahead of a third, you may as well toss a coin. If the 5000 do that, then the Tory won’t have 50%, and may well be beaten in the head-to-head.

• Chris Purcell Says:

“The Tory could scrape 50% of the vote at this stage because 5000 votes against them have been ignored.”

I was unclear, apologies. I said ‘set aside’, not ‘ignored’; my intent was that those ballots would still count for the purposes of the 50% optimisation.

• David N Says:

OK, Chris, but if those ballots are not counted for any party, it may result in the Tory getting through to the head-to-head when they should not. Also, if the Tory is eliminated, then those ballots would need to be excluded from the total in the final round, otherwise you could end up with no-one getting 50%.

Apart from anomalies that may affect the result, you may well have to set aside ballots where numerous different numbers and combinations of candidates are ranked equal first by different voters. Unless you are going to sort these out, either wholly or partly, into different piles for different combinations, you will have to review them all at every round of the count to pick out the ones that now need to be counted. Whether you sort them or not, this could slow down the counting process considerably if there are a large number of ballots set aside.

Logically, I think it would make more sense for those ballots to be counted as half a vote for each of the two parties. However, in a constituency with a lot of candidates, you could have various voters ranking various different numbers of candidates equally, so trying to use fractions could be rather complicated.

16. Purple Says:

Great discussion.

Small typo:
“Those lucky BNP supporters now get their second-choice votes counted. Let’s suppose that D=E+F+G and that D, E and F are the percentages of votes transferred to Labour, the Conservatives and the Lib Dems, respectively.”

I think that should be “E,F and G are the percentages of votes transferred…”

[Thanks -- now changed.]

17. Gesar Says:

I happen to come from Basingstoke, and feel I’m missing something when it says ‘VOTE YES TO AV UNLESS YOU LIVE IN BASINGSTOKE!’. Someone care to tell me where this particular Basingstoke joke originates?

• gowers Says:

Unless I am muddling it up with another constituency, Basingstoke is one of those key Labour/Conservative marginals that decides the outcomes of elections, in the sense that whoever wins Basingstoke will probably win the election. Under FPTP, if you live there then your vote counts for much more than it does if you live in, say, Ebbw Vale in Wales. Under AV, your political influence would be reduced. The joke originated in my head …

18. Gesar Says:

Basingstoke has a long history of voting Tory. In fact, the last time in recent times it didn’t have a Tory MP was 2002, when the then MP became independent before switching to DUP (strangely). He was promptly kicked out in 2005 for another Tory.

The last time it had a non-Tory elected was 1923.

19. Gesar Says:

So I think you got it confused with another constituency Though the joke does now make sense to me.

• gowers Says:

Ah — I’ve worked it out now. I was indeed confusing it with another constituency, and that constituency was Basildon. I have now changed it.

20. Tom Says:

Thanks for this post. I’ve been equally frustrated with the flood of crap spewing from the “no” campaign and its apparent effectiveness, and it’s good/depressing to see solid evidence of just how dishonest they are.

But I would still be interested to hear those arguments against AV that you think are valid…

• gowers Says:

I don’t think it is obviously wrong that AV leads to more coalitions or that coalitions are a bad thing. So I think there is room for legitimate debate there. However, my personal view is that AV would probably not lead to a big increase in the number of coalitions, and I also like the principle of parties having to negotiate and reach compromises.

• Peter Millican Says:

So would I – actually, I don’t believe that there are any decent arguments whatever that favour FPTP over AV. The strong arguments against AV would tell in favour of other systems, e.g. on grounds of wanting proportionality (which AV doesn’t deliver) or wanting a “Condorcet winner” when there is one. Suppose, for example, that in a straight vote between A and B, A would win, and in a straight vote between A and C, A would win. A is thus the “Condorcet winner”, and it’s plausible to argue that he should win. Nevertheless, it might be that in terms of first preferences, B and C both score more than A (so A is a sort of compromise candidate). Under AV, A would be eliminated before the last round, and so wouldn’t get the chance for either straight vote that he would have won.

21. Anonymous Says:

“To see how this could work, imagine that the second-preference votes for Labour split 4:1 in favour of the Liberal Democrats (that is, 25% of voters have Labour first and Lib Dems second, and 5% of voters have Labour first and the Conservatives second),”

You could fix the numbers and then delete this comment.

[Thanks -- I've fixed the numbers now. I'll retain the comment for the sake of transparency (but will remove your next comment since it is more or less a duplicate).]

22. F Pait Says:

I mean no offense to Englishmen, but in this respect I believe the French are ahead of you. Their system of two-round elections retains all advantages of constituency voting, most good aspects of AV, and it’s simpler to understand. The latter is a big advantage because you don’t want any complications distracting during an election.

As for the winning party having disproportional powers, the answer was given by in plain English the founding fathers here across the Atlantic: checks and balances, 3 separate branches of government, and a split legislature. The problem is the parliamentary system, not the method of voting.

Now the most important point is to retain constituency, or district, voting. In Brazil representatives are elected at large. That makes campaigns very expensive and removes the link between the voter and the representative. It’s a a complete disaster.

So now the Brazilian Congress wants to change the system to a party-list vote. Fortunately indirect voting is extremely unpopular, and banned by the Brazilian Constitution, but the politicians are trying to make the change anyway. After taking into account your criticism of the English system, I still say it is the 3rd best in the world.

• Emmanuel Kowalski Says:

The French system has its own disadvantages. For those who do not know it, here is a rough outline: (1) there are two rounds; (2) the candidates that go to the second round can be (i) either the first two of Round 1 (e.g., Presidential election); or (ii) any candidate who got a minimal percentage of the votes in Round 1 (e.g., parliamentary). “Left” or “Right” splits can lead to pretty bad results in case (i) [e.g., the 2002 presidential election], and in case (ii), since the winner of the second round is whoever gets most vote, it often happens that one party gets an overwhelming majority in parliament even with a countrywide 55/45 split.

One thing the French parties have done with little hesitation is change the voting system a year or so before an election to (try to) help their side: in 1985 or so, the socialists who were almost certain to lose badly the parliamentary electrion in 1986 shifted to a one-round proportional system; they still lost, but the parliamentary margin wasn’t as bad as it would have been otherwise… Of course, the winners did immediately change the rules again. Is there any reason, besides the fact that this doesn’t feel like cricket, that the Labour party didn’t try to do something like this before the last elections?

• F Pait Says:

Thanks. You certainly know more about the French system than I do. In Brazil we have been using two-round voting for executive positions since redemocratization, and the results are excellent, specially if you compare to the previous one-round votes. I agree that constantly changing the rules is a disaster, and that proportional elections in the large are very problematic. But I still believe that 2-round voting in each constituency would be a simple and effective way to do achieve similar results to AV.

• Emmanuel Kowalski Says:

I think it depends a lot on the country; France is relatively small and homogeneous, in some sense, so that a 55/45 split at the national level will at least remain 50+/50- in a large majority of consistuencies, leading to lopsided majorities in parliament. This is not good for democracy, because when, after a year or two, public opinion turns against the majority, it has not good way to express itself in parliament…

• David N Says:

Emmanuel, in answer to your question about Labour, they would probably have done better under AV. However, if they had introduced it without a referendum, I suspect that the punishment they would have received at the polls as a consequence would have outweighed the advantage gained, and they would have set a precedent allowing future governments to do likewise, as in the French example.

23. gowers Says:

If you want to see David Cameron spouting dishonest nonsense, then here he is doing so:

24. MikeAlx Says:

Excellent post – though I’m afraid it’s done no more than re-affirmed my existing decision to vote Yes. I fear the vote is doomed by the No campaign’s ridiculous scaremongering, and people’s general inclination to make emotional rather than rational decisions.

25. gowers Says:

No comment.

• Julie Says:

Enough! You’ve convinced me. Thought I was ‘NO’ but I Am now going to vote…’YES’.

• Charles Roddie Says:

The argument against strong governments is that some bad things are harder for governments to do. But good things are also harder to do. The negative value that markets always place on results that yield no majority or a slim majority seems to indicate that, as far as economic competence goes, the second effect outweighs the first.

26. gowers Says:

For a nostalgia trip, this one’s worth a watch too (with thanks to From Calculus to Columbia for drawing my attention to it in a comment on my earlier post about the British voting system).

27. Lorna Says:

“If you are a mathematician, then you will probably toss a coin a few times and make a probabilistic decision, but something tells me that that practice is unlikely to catch on.”

I’ve done this in a european election (it might have been council but I think it was european). I was annoyed with Labour but not really positive about the Libdems. The only thing I did feel positive about was voting against the Tories. Most people I told about it were horrified.

28. Top Posts — WordPress.com Says:

[...] Is AV better than FPTP? On May 5th the UK will vote in a referendum for only the second time ever. (The first time was in 1975, when we voted [...] [...]

29. Alistair Says:

Thank you, it’s good to see other people are as frustrated with the coverage. I’m currently trying to convince my parents that collecting voter’s preferences might be a good thing.

My attempt at an illustrative example is in the rare event of a tie (as in the Great Yarmouth council elections last year): currently it has to be decided by drawing lots. Wouldn’t it be better to find out what the other voters thought, and use that information? What about in the case where one party has a tiny majority (say, by 1 vote): is it fair to ignore preferences that could swing the result massively in the opposite direction? A system that takes account of this extra information from the start can be a lot more effective.

I also like to lead up to the idea of vote splitting power of the spoiler effect with this example from Russia: http://www.economist.com/node/18400554
The Kremlin exploits the spoiler effect by setting up dummy parties with views similar to their opposition parties, to make sure they keep a majority. Once you see that this deliberate practice is unfair, it also starts to seem unfair when it happens inadvertently.

A slightly tongue-in-cheek argument I read elsewhere, that appealed to me, is that the UK already has something approximating a two-round voting system: but the first round takes place in the media and election material when they decide who the top two contenders are, and is therefore completely unaccountable.

30. WTF is “the post”? « Since it is not … Says:

[...] Timothy Gowers on why people in Britain should vote to change their current voting system. [...]

31. Colin Says:

There’s a Dirty Little Secret they don’t want you to know about AV – you can find out all about it with this short video:

• gowers Says:

For those who want a quick summary of what’s in the video, it gives an example similar to the one that I gave in the post to illustrate the fact that tactical voting can exist under AV. However, the video makes a further point that I did not think of while writing: that in this kind of situation, a party might harm itself by campaigning more effectively. This is clearly an undesirable consequence of AV (and, according to the video, has happened in one or two places in the US, leading to the abandonment of AV).

Against that, we are talking about an election with hundreds of constituencies and a phenomenon that will be very rare. So although there can be the occasional unfairness in three-way marginals under AV, those will be places where the views of the constituents are pretty ambiguous anyway, and they will not have a susbstantial effect on which party wins power nationally. Under FPTP, thanks to the split on the left, you can make it less likely that policies you like will be pursued if you vote for the party that best represents those policies. And that routinely happens in dozens of constituencies at every election and makes a huge difference nationally.

• Tom King Says:

So wait: in the first example, Labour got a majority of the vote, and got elected. In the second, the Conservatives got a majority of the vote, and got elected.

That seems pretty reasonable compared to the current system.

• gowers Says:

I’ve just discovered that the video above hides a dirty little secret of its own. The system that the good folk of Aspen Colorado disliked wasn’t AV (or IRV as they call it there) but a variant of it, and the good old traditional system they returned to definitely wasn’t FPTP but just a different system with multiple rounds and runoffs. For details, see this Wikipedia article.

• Colin Says:

While gowers looked at a Wiki Article, it does not tell the whole story. His cherry picking tries to support his argument. Fact is Aspen used the same AV being proposed here in selecting it’s Mayor. It used a variation for electing a two person seat. They have now repealed AV and returned to at least 40% for Council, and 50% for Mayor.

Which leads to a good question – which type of AV will be used and who decides? If you skip a rank, what happens? Maybe you selected #1 and #3 and #4. In San Francisco, they will use your 3rd choice if #1 drops. But it Hawaii’s method, your ballot is scrapped if you skip a rank. If you select two in a rank (overvote) what happens? In Oakland, your ballot is discarded, but in Hawaii’s proposed method, it counts if one of the choices are still in the race.

In Fort Collins, they recently rejected AV by 61% to 39% and kept FPTP.
http://www.docstoc.com/docs/77605380/Fort-Collins-Rejects-Ranked-Choice-Voting-(RCV)-Keeps-first-past-the-post-system

Honolulu just rejected AV as well:
http://www.docstoc.com/docs/77605260/Honolulu-Rejects-Instant-Runoff-Voting-(Ranked-Choice-Voting)

Though you may lament about “anomalies” in FPTP, you will NEVER hurt your favorite candidate for voting for them.

You mention that anomalies are rare with AV, but they are not. Burlington VT (which repealed AV) also selected a mayor who was not the favorite of the voters:

To spend 250,000 pounds to implement this much maligned system is looney.

• gowers Says:

I didn’t pick the cherry — I took the one that the video handed me on a plate.

Another point I’d like to make here is that I don’t definitely disagree with you about the anomalies of AV being a serious problem when it comes to an election for just one person, the person who is actually going to wield power and make decisions that will affect your life. But it’s very different when we have 650 (soon to be 600) constituencies and are aggregating the results from all of them. The occasional anomaly there will be regrettable, but it is very unlikely to change who ends up in charge in the country as a whole. And since the campaigns are largely national rather than local, it will never be in a party’s interests not to campaign as vigorously as it can and get as many votes as it can.

• gowers Says:

I’ve just watched some of the video and it spends a lot of time discussing head-to-head comparisons. So it’s worth pointing out that it is extremely easy under FPTP for the result not to respect head-to-head comparisons. Here’s an example.

Suppose we are in a seat where Conservative and Labour supporters hate each other, and the votes under FPTP are Conservative 40%, Labour 35%, Lib Dem 25%. Since Conservative voters hate Labour, a majority prefer the Lib Dem candidate to the Labour candidate. Since Labour voters hate the Conservatives, a majority prefer the Lib Dem candidate to the Conservatives. And finally, just for good measure, it happens that in this constituency the Lib Dems are somewhat left-leaning, so a majority prefer the Labour candidate to the Conservative candidate.

In such a constituency, the head-to-head competitions would suggest that the Lib Dem candidate is the most popular, followed by the Labour candidate, followed by the Conservative candidate — exactly the opposite of the result provided by FPTP!

As you may know, Arrow’s theorem tells us that such anomalies happen in every voting system.

• David N Says:

Colin, who is planning to spend 250,000 GBP on implementing AV? The majority of that figure is for voting machines, which Australia don’t use for their AV counting, and the Electoral Commission and the LibDem website say are not required, so it would be up to the government whether they use them, i.e. if anyone is planning to spend money on voting machines if there is a Yes vote, it must be the Tories. Effectively, they are threatening (probably an empty threat) to spend a load of money unnecessarily if they don’t get their way, as a tactic to try to win the referendum.

• MorningTory Says:

“if anyone is planning to spend money on voting machines if there is a Yes vote, it must be the Tories. Effectively, they are threatening (probably an empty threat) to spend a load of money unnecessarily if they don’t get their way, as a tactic to try to win the referendum.”

David, this is plain wrong. The decision would be up to individual local authorities (any of which are not controlled by the tories), and subject to the strutiny of the INDEPENDENT electoral commission. Challenge the £250m estimate if you want, but don’t make up lies it! You assertion has even less substance that the £250m estimate does!

• David N Says:

OK MorningTory, thanks for the correction of my misunderstanding (which doesn’t make me a liar, btw), but where is the evidence that ANY local authorities would spend ANY money on vote counting machines, given that they would not be required? I note that you seem to imply that you accept that the £250m claim has little substance (and on the Tory leaflet distributed here it is an outright claim that “AV will cost the country £250m including vote counting machines” – no mention of estimates or any doubt).

• MorningTory Says:

“where is the evidence that ANY local authorities would spend ANY money on vote counting machines, given that they would not be required?”

Well, since we don’t yet have AV,it’s extremely unlikely that any plans to spend money on vote counting machines. However, the UK does have preferential elections (e.g. London Mayor) and vote-counting machines are used in those elections so it’s not wholly unreasonable to assume they would be in General Election conducted under AV.

I don’t actually care either way about the £250m claim, but in my judgement, <£60k per local authority doesn't sound like a wild estimate (either with or without vote-counting machines).

• David N Says:

I suggest that the use of vote-counting machines in the London Mayoral Election is due to the sheer scale of that election – the number of votes cast in 2008 was nearly 53 times that of the average constituency in the 2010 General Election. According to Wikipedia, the 2008 count took “over 15 hours”, compared to “up to 3 days” that London Elects said it would take to count manually, so I can see why they would use machines in that election – and possibly in any other elections in London if they already have the machines (and therefore presumably won’t need to buy any new ones specially for future General Elections even if they do choose to use them). Do you have any evidence that machines are used in any such elections outside London where the number of votes is of a similar scale to a GE constituency?

I am not surprised that you don’t care about the £250m claim, since it is not being used against your point of view. I am equally unsurprised that the No campaign does not seem to care whether or not the claims it makes are actually true.

• MorningTory Says:

“Do you have any evidence that machines are used in any such elections outside London where the number of votes is of a similar scale to a GE constituency?”

No, I don’t have any such evidence. Though, I do believe they are used in Scotland (I may be wrong). The point I was making was with or without vote-counting machines, a figure of £60k per local authority doesn’t sound particularly outlandish.

32. Tama Says:

This is a rather excellent post. I was going to vote yes to stick two fingers up to the Tories, but you’ve convincingly laid out the strengths of the system in a much more followable way than any other explanation I’ve read. Good job!

33. AV vs FPTP | Logic Matters Says:

[...] moment. So I’m voting “yes” in the referendum. For a lot of reasons, see this quite terrific piece by the estimable Tim Gowers. This entry was posted in This and that. Bookmark the permalink. ← TTP, 9. §2.IV A map [...]

34. Tony Hammond Says:

• gowers Says:

If you don’t have quarter of an hour to spare, the video above makes the same point as the video posted by Colin a couple of comments back. Under certain unusual circumstances it is possible for AV to lead to anomalous results: as I pointed out in my post, it is not always in a party’s interests to maximize its tally of first-choice votes, because sometimes what happens to the second choices makes more of a difference to the outcome.

Here’s a slogan that sums up my view of the situation.

UNDER AV THERE CAN VERY OCCASIONALLY BE ANOMALOUS RESULTS. UNDER FPTP ANOMALOUS RESULTS ARE THE NORM.

See the beginning of the post for a justification of the second claim.

35. Ursula Martin Says:

Thank you for an excellent post which I found by chance just as I was thinking I really should try and be a bit less apathetic about this. It has been propagating enthusiastically through my friends on facebook, especially “WTF is the post”.

In Scotland there were referenda on devolution in 1979 and 1997. The second led to a majority in favour of both propositions, viz “there should be a Scottish Parliament” and “a Scottish Parliament should have tax-varying powers.”
In response to the majority voting for ‘Yes’ to both proposals, leading to the creation of the Scottish Parliament and Scottish Executive.

36. Kai Says:

I’ve very much enjoyed reading this, and I’m glad you did /not/ refrain from explaining AV again, as I as a German guy didn’t know it yet.
To convince a lot of those who are not yet decided yet, however, I’m afraid your article is too long. It took me quite some time to read it all, and it would be more efficient just to make some of the most important points well known to people.
Anyway, I keep my fingers crossed that you /do/ get AV and that it’s not a lost cause.

• Tom Says:

That’s exactly why things look bleak for the referendum, Kai. You can make ten false claims in the time it takes to debunk one of them, and when your battlefield is a five minute news report which voters are half-listening to that’s enough to swing opinion.

37. Chris Says:

Exactly the comprehensive article on the topic that we all need. I would venture two more ‘political’ arguments:

Although it might make sense for a Tory voter to vote “no”, it might make more sense for them to vote “yes”, on the basis that it props up Nick Clegg. The coalition seems to be having interesting effects in terms of where second preferences are now going, with the rump LD vote now favouring the Tories, and both parties will benefit from AV if this trend holds.

Presumably it’s rational for a diehard Labour or Tory voter in a safe seat that their party controls to favour maintaining the current system, because then they never have to vote again.

Splendid summary, it’s got ‘facts’ and ‘logic’ in it.

39. Kirsty Says:

I loved this. Thank you. I wish everyone would read it.
That is all.
Kirsty x

40. Ben Millwood Says:

1. The Lib Dems were not formed until 1988, not 87 (minor, I know)
2. SDP-Lib second preferences, it has been shown, were in favour of the TORIES. Under AV, the 1983 Tory majority would have been EVEN LARGER, not smaller. Most SDP MEMBERS saw themselves as about -3 on the left-right axis (and saw Labour as -7) whereas most SDP VOTERS put themselves around 0 or +1.
3. In 1997 under AV the Labour majority, again, would have been EVEN LARGER. This was proved by the Jenkins Commission.
4. In 1992 the Tories actually got the highest popular vote in terms of raw numbers that they had ever had. The national mood was not against them in any real sense.

That said, he seemed to like it and it’s now been reposted by about five other people. There’s still time to make a little difference!

• David N Says:

Under AV, what’s to say that the Alliance would even have happened? There would have been less need for it. In 1983, I suspect that there would have been a much larger proportion of SDP/Lib voters expressing no second preference than there would of LibDem voters now, simply because the parties were much further apart politically.

I don’t think we needed the Jenkins Commission to prove point 3. It’s surely a statement of the blindingly obvious to anyone who was even remotely politically aware at the time.

• David N Says:

As for 1992, ISTM that that could be described as a “lesser of two evils” election (the same could probably be said about 1983, 1987, 2005 and 2010, and probably some earlier elections that I’m too young to remember). The Tories were pretty unpopular, though they had probably gained a bit of a respite by dumping Margaret Thatcher, but Labour still weren’t seen as sufficiently trustworthy. The increase in the raw Tory vote was, I think, largely due to the expected closeness of the election drawing more of their supporters out to vote – the total turnout increased by about a million, while the Tory increase was about a third of that.

41. Kirsty Says:

The NO campaign has listed the “AV MYTHS” – does anyone else see QUESTIONS?! (Am I being pedantic?)

http://www.no2av.org/why-vote-no/av-myth-busting/

42. Ben Millwood Says:

(I know you’ve fixed the first one at least, sorry for forgetting to mention that; it was a while between that comment being posted and me relaying it here)

• gowers Says:

The points you (or your friend) make are very interesting, especially point number 2. I was forgetting just how unelectable Labour was in the days of Michael Foot, Tony Benn, the Trade Union block vote, etc. Probably AV would have given the Alliance more seats at the expense of Labour, which would at least have partially corrected one of the great injustices of that election.

43. Costermonger Says:

I have just discovered your site and I wish to congratulate you on this article about AV. I have been trying for the past three weeks, on various sites, to counter the lies perpetrated by the No campaign with no success. There are some who form a view and will not be moved from it no matter how often you can demonstrate the fallacy of their case. Nevertheless, as someone who studied mathematics more than 50 years ago it is great to find a mathematics flavoured take on current issues.

44. Susan A. Wilson Says:

Thanks very much for this article….made me feel so much happier having sent my YES postal vote in yesterday!….now I KNOW I have done the right thing

45. Russ Says:

Here’s how to vote:
1. Yes to AV.
2. No to AV.

46. Jonathan Phillips Says:

Great stuff!

(1) Votes “of unequal value”: I might vote tactically for the Labour candidate to keep the Tory out (my vote counts as one) or truthfully for the Green candidate (my vote counts as zero). Under AV I vote Green1, Labour2. Why would my transferred vote under AV be thought somehow to count more than my tactical vote under FPTP?

(2) Effect of AV on BNP: wouldn’t any mainstream party fight tooth and nail *not* to see a heap of BNP votes transferred to their candidate?

(3) AV unfair? So why is it used for election of Commons committee chairs and Lords Speaker? (http://bit.ly/fAmLaU)

(4) “Voters number candidates in order of preference” is unhelpful. This is slightly adapted from the wording used on Scottish LA ballot papers:

“Instead of using a cross, number the candidates in the order of your choice.

“Put the number 1 next to the name of the candidate who is your first choice.

“You can then put 2 next to the name of the candidate who would be your second choice if your first could not win, 3 next to your third choice, and so on.

“You can mark as many or as few choices as you like.”

It’s essential that voters see the point of marking alternative preferences. Note use of “choice” (on Sc ballot papers) and my addition of “would be” and “if your first could not win” – second and later choices are *conditional*.

I make some of Tim’s points far less academically in Ourtown Votes! (http://bit.ly/fldUMZ) and The Voter’s Dilemma (http://bit.ly/fgHxR0).

And finally, some Some suggested mottoes for the No campaign:
(a) The mass of people will more readily fall victim to a great lie than to a small one, (b) Make the lie big, make it simple, keep saying it, and eventually they will believe it, and (c) What good fortune for governments that the people do not think.

A nasty piece of work, that Adolf Hitler, but nobody’s fool.

47. Is AV better than FPTP? « Gowers’s Weblog « Netcrema – creme de la social news via digg + delicious + stumpleupon + reddit Says:

[...] Is AV better than FPTP? « Gowers’s Webloggowers.wordpress.com [...]

48. Scott Speight Says:

I suppose my only criticism of AV, is that in a Tory/Labour marginal, the Lib Dem voters get to decide which one wins, even if both Tory voters and Labour voters ALL put the Lib Dems as second preferences (I think this goes back to the concorde system someone mentioned earlier).

I would prefer a weighted voting system rather than AV, but that would definately require counting machines.

• nevsvent Says:

But those LibDem voters won’t know in advance that they have that influence, so the result will be a balance of opinion of the electorate, in other words, democratic. Why shouldn’t someone who votes for someone other than Labour or Conservative have an influence?

• Ronald Says:

“I suppose my only criticism of AV, is that in a Tory/Labour marginal, the Lib Dem voters get to decide which one wins, even if both Tory voters and Labour voters ALL put the Lib Dems as second preferences”

This criticism is interesting. It’s quite probable that Lib Dems *already* decide the result in a Tory/Labour marginal under FPTP. It’s only that they have to tactically vote away from Lib Dem.

FPTP disguises true voter preference – under the current system, we can never know how many voters really support another party but are voting for the “lesser of two evils”.

• David N Says:

The LibDem voters may affect whether the Tory or the Labour candidate wins, but they don’t get any more say in the matter than the Tory or Labour voters, or those of any other party.

‘under the current system, we can never know how many voters really support another party but are voting for the “lesser of two evils”’

… or the lesser of two goods! When someone votes for one of the leading two parties under “FPTP”, all we can really be fairly confident of is that they preferred that party to the other one. Under AV, we would get a much clearer picture of each party’s real support, and some parties’ supporters in some constituencies may even find that they have previously been voting tactically unnecessarily, due to the cycle where a party deemed to have little chance loses voters to tactical voting, leading to low expectations at the next election, etc, which could eventually lead to the party doing poorly in a seat where they actually have enough underlying support to be competitive or even win.

• MorningTory Says:

The AV data on people’s preferences is somewhat flawed. If I have two parties that I prefer (say the Tories and UKIP) then I would be better off voting UKIP 1st and Tory 2nd (even though my genuine preference is the Tories) as UKIP are far more likely to get eliminated before the tories (i.e if I want my “support” for UKIP to be noted, then I must artificially place it above my genuine preference in order for it to be noted).

Or, in onther words, under AV it’s not the AMOUNT of support that counts, but the order in which it is counted.

• David N Says:

You have a point there, MorningTory. So under AV, support for minor parties may be a little overstated, whereas under FPTP it may well be substantially understated.

49. Jonathan Phillips Says:

Scott Speight: in any system of weighted votes, wouldn’t your lower preferences count against your first preference? If you can allocate whole vote, half vote, third vote, quarter vote… and they all get weighed, isn’t your vote cancelled out altogether?

50. kathz Says:

This is much clearer and less condescending than any account I’ve read. However, apart from its lack of proportionality, I have two worries about AV, which don’t apply to STV.

The Electoral Reform Society’s study of the results of the 2005 election, which included an intensive survey of second preferences, etc., shows that results under AV can be even more skewed than under FPTP. I find it worrying that under AV a party with fewer than 30% of first preferences could gain an overall majority – that wouldn’t reflect the will of the people in any sense that I understand.

The need to canvass votes from small parties could easily lead major parties to advance policies to attract those voters at the expense of their own supporters. In other words, in a marginal constituency with a biggish (say 8%) BNP vote, the three biggest parties might indulge in racist rhetoric and would, moreover, be less likely to select a non-white candidate. Given the conduct of mainstream parties in the last few years, this doesn’t seem unlikely.

My objections are based on the nearest thing to solid evidence I can find.

I should add that I’ve been campaigning for STV for nearly forty years and would like to think a vote for AV might really improve democracy and accountability. I don’t have much time for FPTP, perhaps in part because I haven’t yet voted for the winning candidate in a general or council election.

• Daniel Beecher Says:

While it is most certainly true that AV is not a proportional system, neither FPTP or AV can be proportional while you maintain a single winner per constituency. I find it a little premature to talk too much about whether one system is more or less proportional that the other: we rely on geographical clusters of support to magically reflect the overall preference. If every single area voted the same way then you would have all the seats going a single party! Obviously it is unsatisfactory to hope that random fluctuations in support share out the constituency results in a representative fashion.

That said, multi-member constituencies and proportional systems are not up for vote at this point in time. The Alternative Vote is merely STV but with a single winner per constituency (similarly, FPTP is AV but with everyone only expressing one preference).

The biggest weakness of AV is that it is single-winner; hence, not proportional. As single-winner systems go it is far better than the current one. A system that selects the Condorcet Winner would be preferable but that is a minor issue (some will raise specific examples where AV breaks down, a Condorcet system would deal with those but they are somewhat contrived examples).

It would be a great shame if this opportunity to empower voters to select their preferences in good faith was lost, especially if the major sticking point is proportionality.

It is not the best single winner system — Condorcet methods seems stronger — and it is not proportional — our “betters” not letting us vote on that issue so a non-starter — but it is easily a better system for electing representatives than the current one.

The biggest problem the country faces with the voting system is that our single vote is conflicted. We are supposed to be voting for a local representative but we cast our vote trying to give that representative’s political party control of the government. A single-winner system is better for selecting a representative of local people, a proportional system is preferable for selecting a government. Decoupling the conflicted voting intent would help immensely here.

• David N Says:

“I find it worrying that under AV a party with fewer than 30% of first preferences could gain an overall majority”

That could happen, and possibly has happened, under “FPTP”. I say that it possibly has happened because many voters do not vote for their real first preference, so we don’t actually know what those preferences were.

In last year’s General Election, one MP was elected with fewer than 30% of the votes. Such occurrences would be likely to become more frequent under “FPTP”, simply because there is a trend towards larger numbers of candidates and smaller proportions of the vote going to the main parties. Therefore is may be just a question of time before a party would gain an overall majority with fewer than 30% of votes, never mind first preferences, under “FPTP”.

As for mainstream parties pandering to extremist views in order to attract transfers from extremist parties, I can’t see that working because any major party doing so would be likely to lose far more transfers from other more moderate parties, and may well lose many first preferences as well. The best way to attract transfers will be same as the best way to attract tactical votes under “FPTP”, i.e. by tending towards the centre ground, which will only continue the trend of the major parties over the last few decades.

51. Is AV ‘unfair’? « Antony Eagle Says:

[...] (21 April): I notice that Tim Gowers has a post on a similar theme, though at much greater length, where he makes some similar points as well as [...]

52. Gregor Manby Says:

Hmmm…. Seems you just convinced me to vote yes to AV. Kudos….

53. Jonathan Phillips Says:

Discussions tend to focus on individual elections. We also need to reflect a little on what happens when people change their vote from one election to the next. Where I live our ward councillors are all LD, but until the early ’90s it was a pretty safe Tory ward. I’ve always voted LD hitherto, but this year I intend swapping to the Greens (who do well in Norwich, but not in this ward) even though this will clearly not make the election of a Green councillor more likely but will rather tend to let the Tories back in. Perverse or what?

• David N Says:

Yes, Jonathan. Although there may be a few cases where it happens under AV, voting for your first choice under “FPTP” is counter-productive far more often.

It is sad that local elections seem to have become more about punishing governments than about electing councillors, but in this election, punishing the LibDems for “letting the Tories in” by voting in a way that could let the Tories in seems particularly illogical. I’m not aiming that comment at you specifically, as I don’t know your motivation for switching.

54. Alex Says:

I was going to vote ‘no’ about twelve minutes ago. Now I am voting ‘yes’, because I’ve realised that I don’t know wtf the post is either.

55. Agein' Sam Says:

Professor Gowers has convinced me that AV is a superior system to FPTP for some purpose; but I am not sure that I know what that purpose is and it seems to me, in all humility, that one should define the objective first. Talking about “the will of the people” sounds good, but what does it mean? Are we voting for party manifestos in their entirety, for party leaders or for individual candidates who may hold views radically different to their party’s line on specifics? Is the system intended to discover what people think about any issue or issues or merely to provide some sporadic entertainment and a way of determining which group of (largely) Oxbridge-educated white males (of whom I am one) should exercise power? Are we not being fobbed off with a meaningless choice between almost equally flawed systems as a way of avoiding the real issues? And so long as we have a secondary chamber populated by patronage, who are we trying to kid?

• David N Says:

‘Are we voting for party manifestos in their entirety, for party leaders or for individual candidates who may hold views radically different to their party’s line on specifics?’

Nominally we are voting for candidates, but in reality we are probably voting for all three in combinations that will differ from one voter to another. Both systems are (obviously) designed to determine which candidate is elected in each constituency. While I and many other people find elections entertaining, I would assume that that is just a by-product, not an intention. As far as I know, neither side has advocated their system on the grounds that it is more entertaining!

56. Cesar Ruiz Says:

Very well explain, but the AV alternative is for choosing parties not representatives.
Each district should be represented by a person elected by the people of that district, accordingly with their preferences and not by the general interest of the party that they may belong.

57. links for 2011-04-21 « Kaigani’s Arbor Vitae Says:

[...] Is AV better than FPTP? « Gowers's Weblog The only thing worth reading on the AV referendum #YestoAv: [...]

58. Andy Ray Says:

Thanks to Prof Gowers for putting this polemics on a more scientific footing. [Althoug, unlike his marvellous exposition of the shortcomings of FPTP, his defence of AV fell somewhat short in logical rigour.] Here I won’t go into whether, in strict theoretical/calculus terms, “the Will of the People” (or Rousseau’s General Will?) can ever be consistently reflected in the light of Arrow’s Impossibility Theorem. But, in more practical terms, I’d earnestly wonder : (a) Whether, when masses of people are losing their JOBS and HOMES, the timing of this AV referendum is a cruel (academicesque) distraction by design or default (besides a waste of money in an era of penny-pinching)? (b) What safeguard is there that, even after, say, the Anyone-But-Tory (ABT) voters get to elect Labour and LibDems as the majority (presuming, that is, the latter still to be a leftish party — though the Professor’s own Cambridge example above indicates that they are often elected as Tory proxies against Labour!), like now the LibDems won’t again countermand the Will of 64% of voters and switch to join hands with the Tories to inflict the fastest/deepest job cuts? All this rarified polemics on AV will again look like mere rigmarole then. [Incidentally, it’s Good Friday morning, and someone’s kiss of betrayal readily comes to mind!]

• DunKhan Says:

A few issues:

“(besides a waste of money in an era of penny-pinching)” – the UK budget is in the hundreds of billions a year. As of 2009 EU membership costs £4b a year (good investment imo), the interest on the national debt costs £30b a year, healthcare costs £119b a year and social protection (presumably benefits) costs £190b a year. These figures are all available online. Complaining about the cost of a referendum or running a voting system is completely failing to put the figures in perspective – even NO2AV’s (wrong) £250m figure is pretty damn small in comparison.

“What safeguard is there that, even after, say, the Anyone-But-Tory (ABT) voters get to elect Labour and LibDems as the majority (presuming, that is, the latter still to be a leftish party — though the Professor’s own Cambridge example above indicates that they are often elected as Tory proxies against Labour!), like now the LibDems won’t again countermand the Will of 64% of voters and switch to join hands with the Tories to inflict the fastest/deepest job cuts?”

Labour + LD weren’t a majority in this GE – to form a coalition they would have needed PC, SNP, Greens and NI parties on side, and given that most NI MPs are also MLAs in Stormont relying on NI MPs to come over from Belfast for every vote is a VERY shakey government. Particularly DUP support actually, as they are also way to the right of any of the other parties in this hypothetical rainbow coalition and would probably put a lot of strain on the arrangement.

Ironically, it’s been projected that a straight up Lab-Lib coalition would have been possible under AV. Though that said going by Alistair Darling’s plans for the economic recovery I think we’d've had the same problems we’re having now. Plus the Labour negotiating team on the whole didn’t want a coalition anyway – Mandelson and Adonis were keen but Milliband and Harman were fairly neutral. Balls was downright hostile to the idea.

“[Incidentally, it’s Good Friday morning, and someone’s kiss of betrayal readily comes to mind!]”

That’s a bit over-emotive isn’t it? You do know that Alistair Darling’s deficit reduction plan was pretty similar to the one being enacted now, right? Now, I’m sure that they’d've targetted it in a less stupid way than how the Tories are targetting it but the main thrust of the plan would have been pretty similar no matter who won the election.

• David N Says:

“What safeguard is there that, even after, say, the Anyone-But-Tory (ABT) voters get to elect Labour and LibDems as the majority, like now the LibDems won’t again countermand the Will of 64% of voters and switch to join hands with the Tories”

Although about 64% of UK (63% of GB) voters did not vote Tory, only just over 52% (53% of GB) actually voted for Labour or the LibDems. Even if only 14% of LibDem voters preferred the Tories to Labour (and bear in mind that some of them will have been Tory supporters voting tactically in Lab/Lib seats), then the two parties’ voters did not include a majority of British voters favouring Labour over the Tories.

If the positions of the Tories and Labour in terms of seats had been reversed (i.e. so that the LibDems and the Tories could not form a Commons majority between them), I doubt that the LibDems would have talked to the Tories at all (and the Tories would probably not have been interested had they tried to).

59. Noodle Says:

excellent article. entertaining and through – useful for myself, and recommended to a number of friends who are (were) still a bit unclear, thanks very much

60. Robert H Mercer Says:

Voting is, like anything else connected with politics and the “establishment” a huge joke. Voting is like asking if you want to be mugged by a guy who goes to church or an atheist. It is really merely another form of confidence trick played on the general public by those who may differ in party name but no in essence. Personally having been sick and tired of this continuing pantomime of voting, I ceased to do so in 1973, considering that it is better not to encourage the bastards. For your information I live in Australia and will not vote/enrol no matter how many laws these morons in parliament make. At one time it was only compulsory to vote IF ENROLLED. Now the parasitical pricks have made enrolment compulsory which means one has [supposedly] to enrol and in doing so have to waste time going to a polling booth to mess up a ballot paper. How inane! But then, that’s what politics means doesn’t it?

61. MorningTory Says:

Well, that was long-winded! I can’t be bothered to take it apart piece by pices, but:

“10. AV benefits the Lib Dems and nobody else.

“This is false. It benefits any party that is small but large enough to have a serious chance of getting seats.

Er… that would be the Lib Dems then. The Greens only picked up a seat in Brighton Pavilion because of a peculiar set of demographics. They almost certainly wouldn’t have done so under AV, and there’s no other constituency in the country where they are likely to gain a seat under EITHER system any time soon. UKIP have NEVER looked like they might pick up a Westminster seat.

• gowers Says:

Although I didn’t make it clear in that sentence, I argued elsewhere in the post that AV benefits Labour. And in some constituencies it might even benefit the Conservatives. I concede that it is the Lib Dems who have most to gain, but that is because it is they who have suffered the most monstrous unfairnesses of FPTP.

You’re right that taking apart a series of arguments piece by piece can be a long and time-consuming process, especially if you want to do it properly.

• nevsvent Says:

Morning Tory seems to dislike AV purely to punish the LibDems as though they are irrelevant, but what he’s actually punishing is 7 million LibDem voters. Are they not invited to the Democratic ball?

• MorningTory Says:

I don’t want to punishe the Lib Dems. In 2010 you may well have got less than you’re fair share of seats, but you got a great deal more than your fair share of power. Looking at the number of seats compare the the % of the national vote is not looking at the big picture.

• David N Says:

“I don’t want to punishe the Lib Dems. In 2010 you may well have got less than you’re fair share of seats, but you got a great deal more than your fair share of power.”

Not to the same degree as previous governing parties, I think – 100% of the power for 35-45% of the vote. That would require the LibDems to have 1/2 to 2/3 of the power, which they certainly don’t have.

Also, over the longer term, the LibDems are still a long way in deficit in terms of power to votes ratio.

62. Daniel Thomas' Blog @ Cambridge » Blog Archive » Voting no to AV is just stupid Says:

[...] you have about methodology addressed. Is AV actually always better than FPTP? Well yes and Tim Gowers (Cambridge maths professor) has written a rather good blog post about AV vs FPTP which has been getting a lot of mileage among the Cambridge students. Having read that and perhaps [...]

63. MorningTory Says:

Well, that’s just silly! It cannot simultanously benefit the Lid Dems AND Labour. I’ll concede that there are seats that Labour will benefit in, and indeed the tories. The net effect, however, is going to be more seats for the Lib Dems.

A fact that you conveniently skimmed over is that if the 2010 election had been run under AV, Nick Clegg would have been able to prop up a deeply unpoular Labour government.

Now, you’ve come out in favour of coalitions and that’s fair enough. But to me, a situation where 30 million people vote, and one man decides who forms a government is profoundly undemocratic.

• gowers Says:

You seem to have contradicted yourself. You say it can’t simultaneously benefit the Lib Dems and Labour and then go on to say that under 2010 AV would have led to a result that would have been better for the Lib Dems and for Labour.

I think dislike of the idea of coalitions is a legitimate reason for voting no. In some countries, such as Israel, they can give undue influence to very small parties. But in several countries in Western Europe they are the norm and they don’t look profoundly undemocratic to me.

• David N Says:

“But to me, a situation where 30 million people vote, and one man decides who forms a government is profoundly undemocratic.”

The last time I checked, the LibDems were not a dictatorship, and Clegg made it quite clear that he thought the party with the most votes/seats should have the first opportunity to try to form a government in the event of a hung parliament (and it was obvious which party that was going to be), which seems like a reasonably democratic principle to me, and also that he did not want to “prop up” Brown.

Also, as I recall it, it was Cameron who approached the LibDems. There was nothing to stop the Tories trying to form a coalition with Labour if they had wanted to, or some of the smaller parties for that matter. Unless they have an overall majority, no single party can decide who forms a government if the other parties don’t want them to.

64. MorningTory Says:

I meant it cannot simultanously benefit the Lib Dems and Labour in terms of the number of seats each party secures, as I’m sure you understood perfectly well. The point is, it’s a zero sum game. Significant gains for the Lib Dems mean it’s harder for either Labour or the Tories achieve an overall majority in the Commons.

You don’t seem to think that’s a desirable objective for an electoral system. Personally, I cannot understand why anyone would think it is better who governs is decided politicians in smoke-filled rooms thrashing out murky deals.

• gowers Says:

I didn’t understand that point, because it didn’t occur to me that you meant something quite so blatantly false. It’s perfectly possible for both the Lib Dems and Labour to get more seats if the Tories get fewer seats.

The defence of coalitions would be that a compromise between two parties, each of which represents a sizable minority of the electorate, is more representative than a single party that represents a sizable minority. The current coalition is not the best advertisement for the principle, but that is, in my view, because under FPTP coalitions take us by surprise. If parties routinely had to form coalitions in order to govern, then they would not be able to avoid telling voters IN ADVANCE what they would do in a coalition. Perhaps not down to the last detail, but the Lib Dems wouldn’t be able to behave as the Lib Dems behaved at the last election, refusing to give any detail at all.

I myself can’t think why anyone would think it better to have 35% of voters given a comfortable majority in the House of Commons — except, of course, those voters …

65. MorningTory Says:

“I didn’t understand that point, because it didn’t occur to me that you meant something quite so blatantly false. It’s perfectly possible for both the Lib Dems and Labour to get more seats if the Tories get fewer seats.”

Oh, for crying out loud! Now I understand why your blog post was so long: you assume your readers have absolutely no prior knowledge of a subject! Yes, of course it is POSSIBLE for the Lib Dems AND Labour to benefit at the expense of the tories. But you were talking about Labour, so I was addressing the point about Labour.

You pedantry is not particularly endearing.

“I myself can’t think why anyone would think it better to have 35% of voters given a comfortable majority in the House of Commons — except, of course, those voters …

My views about AV and my party affiliations are unrelated. Can you say the same?

• Yemon Choi Says:

Oh, for crying out loud! Now I understand why your blog post was so long: you assume your readers have absolutely no prior knowledge of a subject!

Isn’t that called “explanation”? Why not grit your teeth and “take it to pieces”, so you can show us why you know better…

The comment with which you enter the fray seems to have misread part of the original post: isn’t one point that while AV might arguably *at present* benefit the Lib Dems and no one else, in the future other parties may find it useful when in positions of weakness? (Cf. all those times the Tories couldn’t make headway against Blair even when his Toniness was not exactly popular.)

You pedantry is not particularly endearing.

Your condescension is particularly un-endearing, old boy.

• gowers Says:

It may well be that you are making a valid point. I’m sorry to say that after rereading your last three comments I am left completely unable to discern what it is.

But I think we agree on the following simple observations.

1. It is impossible for AV to benefit all parties in the sense of giving them all more seats.

2. AV benefits the Lib Dems more than anyone else.

3. AV probably harms the Tories more than anyone else. (Maybe you’ll disagree with this one — I don’t know.)

4. It is possible that AV helps both Labour and the Lib Dems at the expense of the Tories.

5. AV is unlikely to help parties like UKIP enough to win them seats.

I haven’t looked into this, but it seems at least possible to me that AV could help the Scottish or Welsh Nationalists.

I don’t know whether my views about AV are independent of my party affiliations. I’d like to think they are, but the 1983 election wouldn’t have left such deep scars if I had been supporting the Tories, say, rather than the Alliance, and those scars leave me with strong emotions. However, I have an even stronger commitment to correctness and rationality. Some of the comments above have revealed to me that I was wrong in some of the details of what I wrote in the post, and I welcome such comments.

• MorningTory Says:

The point I was making is that – setting aside the Scottish, Welsh and indeed NI parties (I can’t get my head around what AV is likely to do there either!) – it is ONLY the Lib Dems that stand to gain from AV. There may be some future reality in which another party is their position. But that’s in the realm of crystal ball gazing.

And yes, that’s because the current single member plurality system works against the geographical distribution of their support.

Is it desirable that this deficit is corrected? You say “Yes.” I say, “Not at the expense of more coalitions.”

The real issue we have is that we have a plural political landscape. Given that, shouldn’t we EXPECT to be electing MPs who don’t command the support of more than half of their electorate?

AV is sometimes sold as a magic bullet guarantees that an MP is endorsed by a majority of their electorate. But, of course, it does no such thing. You can’t tell the difference between positive 2nd preference (“I like this candidate a lot. In fact, I almost put him down as my first choice.”) and a negative one (“I agree with this candidate on almost nothing, but at least he’s better than that other guy.”). The only thing we can really conclude about a transfered vote is that the voter did not want the recipient to win.

So, AV doesn’t so much solve the problem of a diverse political landscape, as disguise it. I really don’t see the point in doing that. Not with all the other deficiencies of AV.

• DunKhan Says:

“The point I was making is that – setting aside the Scottish, Welsh and indeed NI parties (I can’t get my head around what AV is likely to do there either!) – it is ONLY the Lib Dems that stand to gain from AV. There may be some future reality in which another party is their position. But that’s in the realm of crystal ball gazing.”

No. Under the last election Labour would have gained. The Green party now has a strong enough localised showing that it would be competitive enough in at least a few seats to have a better shot of winning them under AV. It also provides independent candidates with a better chance.

With regards to NI – there are two major nationalist parties (SF, SDLP), two major unionist parties (DUP, UUP) and two moderately significant neutral parties (Alliance, Greens) as well as a few other minor parties (PUP etc). AV would ensure that the vote between the nationalist or unionist communities in a seat isn’t split so that, say, a seat with a slight majority of unionist ends up with a SF MP (could happen, there’s a SF MP with a 7 vote plurality atm). Preferential voting is important in NI.

“Is it desirable that this deficit is corrected? You say “Yes.” I say, “Not at the expense of more coalitions.””

In most countries where coalitions are the norm they explicitly set out which policies they will prioritise in the event of a coalition deal in their manifestos. Under those circumstances I don’t see how a coalition is less democratic than completely ignoring the views of the majority of the 35% of the population who didn’t vote Tory or Labour. This current one is atypical because Westminister isn’t used to coalitions.

It’s also not at all clear that AV would lead to more coalitions. It is considered a majoritarian system.

“The real issue we have is that we have a plural political landscape. Given that, shouldn’t we EXPECT to be electing MPs who don’t command the support of more than half of their electorate?”

Yes and no. The political plural landscape means that, particularly on the left wing, people support multiple parties. In the current landscape it is more important, not less, that people can therefore have additional preferences.

If we want single-member seats then AV is therefore desirable – if there’s a majority who are vaguely left wing in a seat it’s not appropriate for them to get a right wing MP just because different left-wing voters happen to plump for different parties when only given one choice (even if they support multiple parties). The principle would be the same if UKIP was more significant and FPTP let in, say, a Labour MP in a seat where the right-wing vote was split between Con and UKIP.

Under multi-member seats obviously the 50% isn’t really necessary or possible!

“You can’t tell the difference between positive 2nd preference (“I like this candidate a lot. In fact, I almost put him down as my first choice.”) and a negative one (“I agree with this candidate on almost nothing, but at least he’s better than that other guy.”).”

So? If a particular group of voters end up making the latter type of 2nd preference candidate win in the seat they’re still happier than they would have been if “that other guy” got in. The whole point is that you rank down until you don’t care – as in, you see them all as equally bad. Getting a less bad MP is still an improvement, even if the MP isn’t actively what you would want.

“The only thing we can really conclude about a transfered vote is that the voter did not want the recipient to win.”

No. What we can tell is that either the voter didn’t want the recipient to win but wanted another candidate to lose; or the voter wanted the recipient to win but less than someone else or the voter wanted the recipient to win exactly as much as another candidate.

“So, AV doesn’t so much solve the problem of a diverse political landscape, as disguise it”

It improves some of the problems and doesn’t address others. It is certainly more suited for a diverse political landscape than FPTP. It’s less suited for a diverse political landscape than quite a lot of other systems though.

• MorningTory Says:

“No. Under the last election Labour would have gained. ”

That not true. In all likelihood they would have lost ~20 seats (http://www.oxfordjournals.org/our_journals/parlij/gsq042.pdf).

“If we want single-member seats then AV is therefore desirable – if there’s a majority who are vaguely left wing in a seat it’s not appropriate for them to get a right wing MP just because different left-wing voters happen to plump for different parties when only given one choice (even if they support multiple parties). ”

This is an odd way of thinking. People vote for parties, not “left” or “right”. If the “left” was a coherent whole, then there would only be one “left party”. Ditton the “right”.

“So? If a particular group of voters end up making the latter type of 2nd preference candidate win in the seat they’re still happier than they would have been if “that other guy” got in.”

But that gives the 2nd preference of one voter the same weight as the first choice of another. You seem to think that’s a fair situation because the 2nd preference voter is happier, but what about the decisive voter who only puts down one choice? Why is it fair that he/she has less of say? It’s not.

“It improves some of the problems and doesn’t address others. It is certainly more suited for a diverse political landscape than FPTP. ”

I honesty don’t see how AV is better suited.

• DunKhan Says:

“That not true. In all likelihood they would have lost ~20 seats (http://www.oxfordjournals.org/our_journals/parlij/gsq042.pdf).”

That projection predicts that Labour would have lost 10 seats, not 20 – using the gross figure is very misleading. Different projections also give different results, the ones I’ve previously seen indicate that Labour would have gained (net) 4 seats more under AV. I might fish out some other projections later if I have time (rushed now). One reliable projection indicating that Labour would gain more seats surely shows the principle that not just the Liberal Democrats could gain from the system. Particularly given how a lot of Labour supporters no longer like the LDs.

“This is an odd way of thinking. People vote for parties, not “left” or “right”. If the “left” was a coherent whole, then there would only be one “left party”. Ditton the “right”.”

People vote for single parties because they can only put down one preference. Most people don’t like only one party – you get tribalists, certainly, but I’d imagine that most people would put down multiple preferences under AV or multiple votes under approval or range voting.

Broadly lumping together left and right wing is the easiest way to illustrate this as usually tactical voting under FPTP is to either keep a Tory or Labour candidate out (depending on the seat). Obviously you get people who like parties across the left-right axis too – I know someone who is keen on the Tories and Greens for instance.

In any case, the broad principle is that if 40% of the electorate really like a candidate and 60% really dislike the candidate for whatever reason but are split between parties by arbitrarily only being allowed one preference, then it is not right in my view for that candidate to represent the constituency. The MP is supposed to represent the entire constituency, not just his core voter base, and I don’t think an MP who is unable to garner the votes of half his constituents (even if these are not all first preference) is suited to represent a single-MP constituency. If he can’t under a preferential system then it means that more people wouldn’t vote for him, even as a lesser of two evils option, than would.

“But that gives the 2nd preference of one voter the same weight as the first choice of another. You seem to think that’s a fair situation because the 2nd preference voter is happier, but what about the decisive voter who only puts down one choice? Why is it fair that he/she has less of say? It’s not.”

Why shouldn’t it be the same weight? The whole point of AV is to simulate run-off elections. You don’t weigh down the votes of people who voted in the first round for a candidate that is then eliminated. That’s just madness, and as far as I’m aware, out of the (very very many) countries which do run-offs no country down-weighs votes like this.

The vote of someone who picks a non-eliminated candidate is the equivalent of voting in a run-off for the same candidate as in the first round. If someone’s vote gets transferred it’s the equivalent of voting for a different candidate in the run-off than in the first round. Either way it’s one vote.

If you don’t put a second preference and your candidate gets eliminated then it’s the equivalent of not turning up to the run-off because you think all the candidates are as bad as each other. This is entirely your own perogative and the “decisive voter” is exactly where they would be under FPTP. Would you rather be forced to rank every candidate?

“I honesty don’t see how AV is better suited.”

Most people don’t solely like ONE political party or just ONE candidate in their seat and even fewer people would consider every candidate that’s not their first preference as good or as bad as any other. Many people may like multiple parties nearly equally in fact.

Being able to rank preferences means that you are not restricted to supporting one candidate – your vote only counts once but you can say that even if you prefer x candidate that you also like (or wouldn’t mind) y candidate. A list of preferences more accurately reflects most people’s views in today’s more pluralistic political environment than a single cross in a box. Particularly given that cross in a box is likely to just be the candidate that can beat the candidate they dislike most rather than their actual favourite candidate.

Sorry if this got a bit incoherent, I had to rush it as I need to get going right now!

• MorningTory Says:

The only 2010 projections I’ve seen (and I honestly do think I have seen them all) assume no change in first-choice votes. Obviously, that’s complete nonsense. Feel free to post some that don’t.

“People vote for single parties because they can only put down one preference.”

The point here is that we’re all grown-ups. Electing a government is a serious matter. I don’t think it is too much ask that voters make a choice between credible candidates.

“…the broad principle is that if 40% of the electorate really like a candidate and 60% really dislike the candidate for whatever reason but are split between parties by arbitrarily only being allowed one preference, then it is not right in my view for that candidate to represent the constituency.”

You are basically saying that that you think voting AGAINST someone is more important that voting FOR them. It wont surprise you to learn that I think that is profoundly wrong.

“The whole point of AV is to simulate run-off elections”

Yes, but it doesn’t do that adequately, does it? The presence or absence of a candidate in an election might easily affect my preference order, so how can I possibly know how I would vote in each round if I don’t know who is in it?!?!?

“If you don’t put a second preference and your candidate gets eliminated then it’s the equivalent of not turning up to the run-off because you think all the candidates are as bad as each other. This is entirely your own perogative and the “decisive voter” is exactly where they would be under FPTP. Would you rather be forced to rank every candidate?”

The point is, as a rational voter, I MUST (in some circumstances) put multiple preferences so as not to disenfrachise myself. AV and the beneficiary of a second, third… eigth preference might interpret that as “support” or “endorsement” but can you really, hand on heart, say that it is?

“Being able to rank preferences means that you are not restricted to supporting one candidate – your vote only counts once but you can say that even if you prefer x candidate that you also like (or wouldn’t mind) y candidate.”

You’re basically contradicting yourself here. Earlier you said that AV simulates run-offs. In a run-off election I get as many votes as there are rounds; i.e. more than one vote. The same is true for SOME people under AV, but not others. Some AV ballot papers are marked more than once, are physically counted more than once, and affect the outcome of the election more than once. I wont go so far as to say that it is more than one vote (I know that upsets some pro-AV people), but you cannot deny that AV is a system that takes account of some people’s opinions more than once, whilst others only once. It’s not equible and it’s just not fair.

• Anonymous Says:

“You are basically saying that that you think voting AGAINST someone is more important that voting FOR them. It wont surprise you to learn that I think that is profoundly wrong.”

Ummm if you want to reduce democracy down to it’s most fundamental principle, isn’t democracy about reflecting the will of the people? So if the people want to vote AGAINST someone, who are you to tell them that is wrong?

• MorningTory Says:

“isn’t democracy about reflecting the will of the people? So if the people want to vote AGAINST someone, who are you to tell them that is wrong?”

I’m not saying people shouldn’t be entitled to vote against candidates. I’m saying I don’t think it’s healthy to have an electoral system that encourages it. Furthermore, I don’t like the fact that a vote against someone will be deliberately misinterpreted as support for someone else.

• Anonymous Says:

That’s just semantics – as Gowers says below, you can just aswell view putting Labour and Lib Dems first and second as a vote for broadly progressive politics as you can a vote for “anyone but the Tories”. Imagine a future where we have 3 party politics between UKIP, the Tories and Labour (the Lib Dems having been decimated for abandoning every principle they ever stood for in pursuit of power, sorry I digress…). Then someone of a broadly Euroskeptic, anti-immigration small minded Little Englander (sorry I digress again!) persuasion could vote UKIP and the Tories 1 and 2; or you could interpret that as an “anyone but those idiots who gave us this colossal debt” vote. Would you be saying the same thing then? Of course you would…
In short you are imagining your own prejudices in the minds of every other voter, with no warrant.

• MorningTory Says:

“Would you be saying the same thing then? Of course you would…”

My issue is with the system, not with the likely results it would produce (which, incidentally, I don’t think will be especially damaging to the Tories).

• David North Says:

“You can’t tell the difference between positive 2nd preference and a negative one ”

You can’t tell the difference between a positive vote and a negative one under FPTP of course.

“The only thing we can really conclude about a transfered vote is that the voter did not want the recipient to win.”

You proved yourself that we cannot conclude that, when you gave an example of a situation where a voters might vote UKIP 1, Con 2, even though their real preference was the reverse. So, certainly where the vote is transferred from a small party, the voter may well have wanted the recipient to win, and who is to say that, for instance, a voter slightly preferring the LibDem over the Tory, in a seat where the Tory is expected to come a distant third, would not vote Con 1, LD 2 for a similar reason to the one you described (or because they didn’t want the LibDem to get too complacent), while still wanting the LibDem to win?

“Given that, shouldn’t we EXPECT to be electing MPs who don’t command the support of more than half of their electorate?”

We should expect MPs who are not the first choice of more than half of the voters (how many under FPTP have more than half of the electorate, given current turnout levels?), but we shouldn’t have to expect MPs who are the LAST choice, or even the third or fourth choice, of more than
half of voters.

“Under multi-member seats obviously the 50% isn’t really necessary or possible!”

It is if you have multiple votes …

• David N Says:

“But that gives the 2nd preference of one voter the same weight as the first choice of another. You seem to think that’s a fair situation because the 2nd preference voter is happier, but what about the decisive voter who only puts down one choice? Why is it fair that he/she has less of say? It’s not.”

Why is someone who only puts down one choice decisive? They have only made one decision – that they prefer that one choice to any other candidate – whereas someone who ranks all of the candidates has made several decisions. The voter who only puts down one choice has a much of say as anyone else, and their choice will be counted equally up to the point where he/she is eliminated. Any preference they had after that is not accounted for, but that is their own fault for not expressing it.

There is nothing wrong with one voter’s second preference being weighted the same as another’s first. Consider two UKIP supporters in different constituencies whose second choice would be Tory, but UKIP only stands in one of the constituencies. The only other candidates are the three main parties, and the UKIP candidate gets fewest first preferences, but no-one gets 50%. Now we are down to three in both seats, but in one the UKIP vote goes to the Tory as a second preference, whereas in the other it is a first preference, even though there is no difference in the preferences of the two voters, so why should they be given different weights?

“I don’t think it is too much ask that voters make a choice between credible candidates.”

But do you think it’s too much to ask that they make a choice between the other credible candidates? Is more than one decision too much for their tiny minds to cope with? Voters in multi-seat wards seem to cope with voting for more than one candidate.

• David North Says:

“You are basically saying that that you think voting AGAINST someone is more important that voting FOR them. It wont surprise you to learn that I think that is profoundly wrong.”

What – like “NOtoAV”, you mean?

Anyway, many people vote against particular candidates under FPTP.

“Yes, but it doesn’t do that adequately, does it? The presence or absence of a candidate in an election might easily affect my preference order, so how can I possibly know how I would vote in each round if I don’t know who is in it?!?!?”

Under what circumstances would the presence or absence of C change the order in which you placed A and B?

‘The point is, as a rational voter, I MUST (in some circumstances) put multiple preferences so as not to disenfrachise myself. AV and the beneficiary of a second, third… eigth preference might interpret that as “support” or “endorsement” but can you really, hand on heart, say that it is?’

Yes – at least to the same extent as FPTP interprets a tactical vote (used so as not to disenfranchise the voter) in that way.

“In a run-off election I get as many votes as there are rounds; i.e. more than one vote. The same is true for SOME people under AV, but not others. Some AV ballot papers are marked more than once, are physically counted more than once, and affect the outcome of the election more than once. I wont go so far as to say that it is more than one vote (I know that upsets some pro-AV people), but you cannot deny that AV is a system that takes account of some people’s opinions more than once, whilst others only once. It’s not equible and it’s just not fair.”

Utter lies. Everyone’s vote is taken account of once in every round, provided that they have expressed some preference between the candidates remaining in the contest.

“I’m saying I don’t think it’s healthy to have an electoral system that encourages it.”

AV does not do that, it merely encourages voters to express their preferences as far down as they wish to. FPTP, on the other hand, encourages large numbers of voters to vote for candidates who are not their first choice ahead of those who are.

66. Costermonger Says:

One of the problems of this debate is that the opposing sides have different objectives. There is one side that wishes to maximise the chances of single party government (the Executive) at the expense of fair representation in parliament (the Legislature). The other side wishes to maximise ‘fairness’ of representation (in terms of proportionality of seats held to votes cast) at the expense of strong government (or elected dictatorship as Lord Hailsham called it). The campaigns have mixed up these objectives, either ignorantly or deliberately – but the curious thing is that AV would do little to alter the odds of getting single party government, nor would it be likely to produce more overall fairness. What it would do is strengthen the position of individual MP’s against central apparatchiks and thus their ability to to hold the executive to account. It would weaken the elected dictatorship a little bit.

• nevsvent Says:

It would also mean that the 10 million people who voted against Labour and the Tories (more than voted for Labour) last year would be heard, even if only for their second preferences.

Further, remembering the last minute swing away from the Lib Dems last May, how many more people do you think decided to vote Conservative or Labour in order to make a statement AGAINST Brown or Cameron. Under AV they could still do that by voting FOR what they wanted in order of preference.

67. Another Tory Says:

Very intresting article, and I agree with most of it, except for one thing.
I think it would be in the best intrest of Tories to vote in favour of AV as well in the long run. I am a Tory supporter myself and plan on voting yes.
Although we have a situation today where the left is more divided than the right, we cannot be sure this will always be the case. My girlfriend is from Sweden where the exact opposite used to be true, and the right-wing vote was divided on three equally strong parties. Now Sweden has a PR system so it was never a problem, but under FPTP there’d be no Swedish right.
I believe it’s very short-sighted to think there couldn’t be an equivalent of the SDP break-away happening to the Conservatives in the future. So I believe it’s in everybody’s best intrest to adopt a fair(er) voting system, because you never who will be on the wrong side of an unfair system in the future.

68. I_want_FPTP Says:

I really good article that does give a lot of food for thought when debating this whole subject, but by it’s content, and subsequent debate, I believe it illustrates a real issue with the introduction of the AV.

By virtue of the length of the original blog, the content, the mathematical examples. it highlights just how confusing the AV system is. In a true democracy, surely we can only be confident in the decision we allow people to take if they are fully informed decisions – decisions where the decider understands fully the implications of the decision they are making. Is it right to introduce a new system that (a substantial number) of voters do not fully understand the implications of their vote preferences. This would lead to people being elected by exploiting these ‘loopholes’, exploiting the ill-informed – which is just wrong!

Our legal system currently makes allowances where people have broken the law where it can be proven they were unable to make an informed decision – how can we have a voting system that goes against that.

In summary, AV is just too complex for people to understand (the full implications of their decisions) – as demonstrated by the original article.

FPTP is not without issues, but is the current fairest way and every vote counts. The ideal system is similar to AV, but with a fresh round of voting after every count, until there are only two candidates left, but obviously could never be implemented. I don’t like the thought that someone who voted from the Monster Raving loony party, the BNP, other extreme groups and protest candidates, then votes for one of the main parties as possibly the sixth or seventh preference on a slip. yet their vote suddenly carries as much weight as mine. They lost five or six times, but still their views are equal to mine. Can we really say that the duly elected candidate really has +50% of the support of the public if 20%-30% of the electorate had them down as fourth choice or more?

One person, one vote. Not ideal but the best we have.

• gowers Says:

Can you give me a good example where a voter would vote differently if they understood better how their votes were going to be counted afterwards?

• I_want_FPTP Says:

Example 1 – Labour voter does not fully understand AV – knows they can put their other preferences on the form. Voter is very Anti-BNP (one of 4 candidates) so ranks Labour 1, Conservative 2. Lib Dem 3 and BNP 4.

Final vote is between Lib Dem and Conservatives and this vote goes towards a conservative victory. Voter is staunch labour supporter but due to not fully understanding AV, ends up voting Tory as “they wanted to make sure BNP were bottom”.

Example 2 – Tory voter votes Tory 1 and BNP 2 – the BNP is a protest vote against immigration. Tory goes out round 1, so this voter is now voting BNP without really wanting to and understanding that it will actually count (they wouldn’t have wasted a vote as a protest vote in FPTP)

I have used the BNP in both examples, not to scaremonger, just that the BNP are a party that creates radical decisions amongst voters.

I do believe that both of the scenario’s above are real, genuine and likely to happen in the UK if AV was introduced.

• gowers Says:

I don’t think you give enough credit to voters. In your first example, you don’t explain why the voter, who prefers the Lib Dems to the Conservatives, puts the Conservatives ahead of the Lib Dems. (If they prefer the Conservatives to the Lib Dems then their second choice vote is giving them exactly what they want, given that Labour has been eliminated.) In your second example, you are suggesting that a voter might vote for the BNP without understanding that it is possible that that vote might affect things. Such a voter would have to be very dense indeed (I feel free to insult him/her since he/she is so utterly hypothetical). How can you “vote BNP without really wanting to”? I suppose it would be some comfort to that voter that the BNP would not actually get elected. (Also, your example supposes that the BNP does better in the first round than the Tories, which isn’t going to happen any time soon.)

The basic principle of voting under AV is very simple: put the candidates in order of preference until you no longer have a preference.

• I_want_FPTP Says:

You asked for an example – I gave you two and you dismissed them out of hand.

I never said in the first example that the Labour voter preferred the Lib Dems ahead of the Tories – I think you assumed that (Perhaps a reason that so many Lib Dem supporters want AV??) I stated they were staunched Labour and hated BNP – so their only thoughts (by not fully understanding the system) was to put Labour and 1 and put BNP bottom of 4 – not realising they didn’t even need to vote.

By voting Tory in 2nd place, it helps secure a Tory victory – which they didn’t want either but their primary aim was to put BNP bottom.

They should have just marked Labour – but didn’t realise.

A valid example – one I am sure will occur under AV and one that cannot be dismissed.

As for my second example – you have a higher opinion of the Great British Public than I have. I am sorry but up and down the dole queues, sat in front of Jeremy Kyle and in the unskilled manual labour sector there are plenty of people that just won’t get this – despite how simple the instructions.

Be interesting to see what the spoilt ballot paper rate is with AV – if higher than FPTP, then arguable, fewer people will actually have their voices heard at the ballot box.

• MorningTory Says:

I’m pulling figures out of my arse here, because I cannot remember my sources. But, if memory serves me correctly, about 1% of ballots are spoilt here in the UK, whilst 10% are spoilt in Australia. Compulsory voting no doubt plays a part in that, but I wouldn’t be at all surprised to see the number of spoilt ballots rise considerably under AV.

• Jonathan Phillips Says:

Spoilt ballots in Oz.

Voting is compulsory, which some people resent, so they spoil their ballot paper deliberately – it’s a form of abstention.

To be valid (“formal” in the Aussie jargon) a vote in a federal lower-house election must show a full set of preferences, and any ambiguity or gap causes the paper to be rejected even if the initial preferences are clear. Since AV as proposed here (and as used in some non-federal elections in Oz) does not require the expression of a full set of preferences such problems are much less likely to arise.

Have you thought of adding together the number of abstentions and the number of spoilt ballots to determine the democratic validity of a system?

Finally, from an LSE report on the introduction of STV (presumably even more confusing to the poor voter than AV!): “Since the 2007 local elections were concurrent with the Scottish parliament elections held under the AMS/MMP electoral system, voters were faced with a complex set of ballot papers and voting decisions. The evidence is that they dealt with STV well, at least in a comparable way to both parts of Ireland. The proportion of rejected ballot papers was just under 2 per cent (0.77 per cent in 2003), but this was considerably fewer than for the concurrent Scottish parliament election (at 4 per cent) and appeared reasonable given levels of rejected ballots under STV elsewhere.” See http://blogs.lse.ac.uk/politicsandpolicy/2011/03/28/stv-scotland/

• Chris Purcell Says:

I like your first example: someone trying to express a negative preference accidentally expressing one they don’t have. An even better one, perhaps: a voter puts Labour at 1, BNP at 2, and believes that puts BNP last. Labour gets knocked out, voter accidentally supports BNP. Ouch.

Is that worse than a horde of Labour voters who do so because they’re working class and their parents voted Labour — with no real idea what they stand for any more? I don’t know — they’re certainly not mutually exclusive. Perhaps we could at least get meaningful data out of AV voting stats (since this level of noise is hopefully easily detected), even if a few seats go astray due to it.

• WJ Says:

“I never said in the first example that the Labour voter preferred the Lib Dems ahead of the Tories”

If they don’t prefer the Lib Dems to the Tories then why should it matter to them that their vote helped the Tories to win?

• Chris Purcell Says:

“If they don’t prefer the Lib Dems to the Tories then why should it matter to them that their vote helped the Tories to win?”

I imagine it matters to the Lib Dems.

• David North Says:

“I don’t like the thought that someone who voted from the Monster Raving loony party, the BNP, other extreme groups and protest candidates, then votes for one of the main parties as possibly the sixth or seventh preference on a slip. yet their vote suddenly carries as much weight as mine.”

Do you really think anyone voting for the loonies or any other protest vote is likely to use any of their preferences for the main parties? As for the BNP voters and other extremists, if they are going to express a second preference for a major party, they would more than likely vote tactically under FPTP, in which case their votes would still count the same as yours. I would expect only a very tiny proportion of votes to get transferred beyond the third preference. To get to the sixth or seventh, you would probably have to be doing it deliberately, not following your actual preferences.

69. SFoUK Says:

Still not completely decided; but until I read this blog I was 80% certain I would vote no. (At least 20% of this due to my complete antipathy for Clegg and the Lib Dems!). Now I have switched: 80% certain I will vote yes to AV, but still reading all the arguments.

70. Is AV better than FPTP? (via Gowers’s Weblog) « poplarmark Says:

[...] On May 5th the UK will vote in a referendum for only the second time ever. (The first time was in 1975, when we voted on whether to remain in the EU, or the Common Market as it was then called.) Now we have a chance to decide whether to retain our current voting system, misleadingly known as First Past The Post, or whether to switch to the Alternative Vote. Let me come clean straight away. Although in this post I shall try to write dispassionatel … Read More [...]

71. gowers Says:

Here are two pro-AV links, one serious and one less so (though it still makes a serious point).

http://www.independent.co.uk/opinion/commentators/johann-hari/johann-hari-if-you-get-the-x-factor-youll-get-av-2271058.html

http://www.minghella.com/wp-content/gallery/sitephotos/parmav.jpg

72. Fairer Fridays: Asking the right question | Contrasting Sounds Says:

[...] AV is better than FPTP, even though flaws can be identified. Mathematician Tim Gower has written an excellent in-depth piece on the detail, sprinkled with slogan-style simplifications of the various [...]

73. Holden Caulfield Says:

!!! It’s just as well you managed to disguise your prejudice, otherwise it would have been a totally one sided argument.
It’s a shame really, there’s so much bias about that a well written, unbiased piece might have swept the web. As somebody trying to come to terms with the possible consequences of a change I’m really disapponted. It’s well written but the pros are going to lap it up and the antis aren’t going to bother reading it, such a waste, you should be a politician!
Also, it’s

far

far

far

far

far

far

too long.

• Yemon Choi Says:

Shouldn’t you be busy complaining people are phonies?

I am curious as to how many people who are criticizing this post for being too long have actually been reading other posts on this blog. Since Gowers didn’t write this for broad-platform sound-bitey blogs or media columns, I don’t see why people are presuming the post had to be written to conform to the punchy “Easy To Understand For The Grannies in Rochdale” template.

Which isn’t to say that everything claimed in the original post is correct – I haven’t had enough time to fully digest what I’ve read and do any cross-checking. But tl;dr remarks here just make me cross

74. Ronald Says:

It’s hard to understand why the Conservatives support FPTP almost unanimously when they haven’t won a majority of seats in the last four elections.

I suppose it’s that FPTP works particularly well for the Conservatives (even though they still aren’t reaching a majority).

FPTP inherently supports a two-party system, with the large parties themselves forming a ‘coalition’ of various viewpoints working to get a majority.

As you point out, the right-wing have been most successful at maintaining this big party coherence. In some sense, the Conservatives are particularly successful and over-perform at FPTP. They would most likely over-perform under AV as well, but perhaps less so.

The fact that the Liberal Democrats and Labour are two distinct parties under FPTP shows that there is a significant and fundamental difference between them, making it hard for them to work under one banner.
From that point of view, it’s not such a surprise that LD have sided with the Conservatives to form the present government.

But it’s quite possible that not much will change for the Tories under AV. They will still have the opportunity to form coalition with Liberal Democrats, if not an occasional majority.
It’s difficult to predict how LD second choice votes will split – I suspect they will be closer to 50/50 than otherwise suggested.
People under FPTP should only strongly be motivated to vote for the third party locally if they dislike both of the first two options.
It would be unsurprising to me, for example, if current BNP voters didn’t show a strong preference between Tories and Labour in their second choices (that is, if they bother to cast second choice votes).

It’s also possible that factions of the Conservative party (or others) would ultimately split off when faced with the opportunity to form coalitions or gain votes on particular single issues. We start to see this already with UKIP (particularly within European elections).

What’s interesting to me is that AV may change the political system just enough that the political giants might just be motivated to begin to support PR.

75. Hivemind Says:

You don’t need any more analogies but here’s one anyway.

If you’re at the pub and you are getting the drinks in, when someone says they want tequila but if the bar doesn’t have it they’ll have a vodka you don’t start complaining that they are getting two drinks do you? You don’t demand they pick one thing and if that’s not at the bar they get nothing do you?

76. WTF is the point? « A Gentleman's Revolution Says:

[...] Tim Gowers, legendary Cambridge mathematician, has made a post on his blog about how AV is better than first past the post, circulating under the moniker ‘WTF is the post’. [...]

77. Yankee Says:

Whoever named AV “AV” should either be promoted or fired, depending on his/her party affiliation.
Calling AV “LEV” (Lesser Evil Voting) will greatly improve its odds of winning. Not only does the name capture the essence of why AV is superior, it also rhymes nicely with the party it will most likely benefit.

78. UK electoral system referendum - Page 2 Says:

[...] we have in British politics. (Another interesting link for you more intellectual types is this fairly long essay – non-mathematicians can skip the complicated bits and still find lots of food for thought.) [...]

79. Joseph Malkevitch Says:

Mathematics offers a tremendous number of insights into voting and elections. This web page offers the tip of a large iceberg (relatively few people know about mathematical insights into this topic)

http://en.wikipedia.org/wiki/Voting_system

However, a full discussion should include the observation that mathematical modeling issues are at work here.

Thus, the following situations are not identical:

a. A new democratic country (historical and other data is available) is planning to develop a democratic system of electing members to its unicameral legislature. Make a recommendation for what system it should use.

b. An existing democracy with current major political parties X, Y, Z and current method of conducting elections is planning to vote (plebiscite) whether to change its current system from method U of electing parliament members to method Z. What pattern of votes might one expect from members of the major existing parties and what outcome to the plebiscite might be anticipated?

Many other variants could be considered.

• MorningTory Says:

Maths offers SOME insight, yes. But this isn’t really maths problem, with a single right answer. Should a system be designed to help poeple keep their least favoured candidate out, or to help their most favoured candidate get in? Should we concern oursleves only with the best way to elect our local “representative” or should we be thinking about the bigger picture (the election of a government)? How much weight should we give to each?

Ultimately this is moral issue (which can, admittedly, be informed by maths).

80. Joseph Malkevitch Says:

Perhaps the most important mathematical contribution in this area is a result of Kenneth Arrow (for which in part he won the Nobel Memorial Prize in Economics) concerning group decision making. Since many seemingly reasonable methods have put forward to decide elections, Arrow turned the problem on its head and wrote down some “reasonable” conditions that a fair/democratic procedure might obey and then showed that in his setting (at least three alternatives, ranked ballots with indifference, etc.) there was no method that obeyed all his reasonable conditions. The reason why there is so much “heat/acrimony” over these matters is different groups of people think there are different “fairness” conditions that are most important and hence support a particular method but Arrow shows there is no method which will keep everyone happy. In the current context, some will oppose AV since because they feel there are better methods, some will oppose it because they truly think it is worse than “plurality.” If one allowed people to vote for their favorite system (assuming a well informed electorate) one probably get only a plurality for any particular method, many of which you or I might think is better than plurality. That is why the question of deciding on a “good” system for a new democracy is a lot harder than it looks.

Thanks for bothering to make this post. I’m a strong supporter of PR who happens to live in a very safe seat where AV will make no difference at all in the foreseeable future, and was hesitating over whether to spoil my ballot paper in protest. You’ve convinced me to vote ‘yes’.

82. Patrick Lee Says:

Fantastic post, Tim! And I loved the style (especially the comments re the BNP!), too.
Those who think the post is too long could always post a link to their own punchier blog …

83. Julian Says:

A very interesting post, although I was rather put off by the initial statement “… 1975, when we voted on whether to remain in the EU, or the Common Market as it was then called.”

The EU was not called the Common Market in 1975 and we did not vote to remain in the EU. The Common Market was just that, a common market. It was changed to the European Community by the Single European Act in 1986 and the European Union by the Maastricht Treaty in 1993. Does Tim Gowers not know that this is the key point of the current arguments about a European in/out referendum (i.e. that we never voted to be in the EU)?

It is also strange that Mr Gowers is so upset at the spurious arguments used by the opponents of AV yet fills his post with many spurious arguments in favour of it, a lot of which boil down to “FPTP is bad because it isn’t proportional” or “FPTP is bad because it doesn’t have a post”. None of this has anything to do with AV.

84. polleetickle Says:

Surprisingly this long drawn out attempt at acedemic elitism simply cannot explain why people should accept that #AV counts least-pref votes more than once.

MultiFPTP/MPTP/TRS is equitable by overcoming the unethical flaw in #AV of multi-instance-counting.

• Ronald Says:

Perhaps I am wrong but I assume, by TRS, you mean a Two Round System. Famously used in the French Presidential elections.

That is almost identical to AV except that, in AV, we cast votes for both rounds at once.

Suppose there is an election between four candidates, A-B-C-D.
In the final round A and D are eliminated, leaving only B and C.

I cast my vote D-A-B-C
what I mean is that – under TRS, in the first round I would cast my vote for D, but on the occasion that only B and C are left in the final round, I prefer to cast my vote for B.

meaning that – under TRS, in the first round you cast your vote for B, and on the occasion that only B and C are left in the final round, you cast your vote (again) for B.

There’s no fundamental difference in counting between AV and a TRS system, except that AV saves everyone from going to the polls twice.

Where TRS is called “runoff voting”; AV is called “instant runoff voting”.
Apart from the timescale and expense in running two polls, they are effectively identical.

[Under AV, because there are multiple rounds instead of 2, there is a tiny chance that the third or lower placed candidate in the first round might end up winning. which is impossible under TRS. This would represent a rare occasion where the top 2 candidates only appealed to a core segment of voters and everyone else absolutely hated them, whereas the third place candidate had less fundamentalist support but more broad appeal]

• Emmanuel Kowalski Says:

The last scenario seems to indicate a great advantage of AV compared with TRS. For instance, in the next French presidential election, it is unlikely, but not entirely impossible in view of the current state of opinion, that the first round would end with : Sarkozy 20%, Extreme Right 20%, Other right 5% and a split of the remaining 55% among center-left, left, and green candidates. In such a case, the second round will be a choice between two candidates who are rejected by a very large majority of the country. (The 2002 case was similar, except that I think the right vs. left total of the first round did favor — slightly — the right.)

• Emmanuel Kowalski Says:

(In my previous comment, it is of course necessary to add the assumption that no left / center-left / green candidate gets more than 20% in the first round; this may happen, though it seems not too likely — to me — at the moment.)

• polleetickle Says:

The call for AV is based on FPTP not being perfect overall. While that may be a valid viewpoint the substantiations offered in support of AV are similarly imperfect, if not more-so – and here’s some points:

# [TRS ... is almost identical to AV except that, in AV, we cast votes for both rounds at once.]

This is not quite the full declaration: Under AV, an electorate least-prefing a candidate dropped after 1st, 2nd or 3rd round has unwittingly wasted their vote.

Under Multi-FPTP elections, least-pref votes are made in the knowledge of who has been dropped.

# [FPTP ... often elects a candidate that most people didnt want]

This is what many in certain trades call ‘smoke & mirrors’: Under AV, the candidate that secured the greatest homogenous vote of support might get supplanted by a hetrogenous vote of support for a candidate that most people *didnt* initially want (and ends up with numerous policy priorities that are unlikely all to be fulfilled).

Under FPTP the electorate return the most-preferred candidate as winner. While I undertsnad the ‘desire’ for 50% majorities, this does not recognise the multi-faceted broad political church of the UK, for which a 40% winning line seems very equitable were AV to succeed.

NO2AV is significantly justified and fairly substantiated with FPTP democratically proven in large numbers of comparable nations across the planet approaching 95+%, whereas AV is at most used in 3% of National elections.

So, instead of change for the sake of it the UK must look toward *evolving* FPTP and invest in; Demoracy Version 2.0

85. Is AV better than FPTP? (via Gowers’s Weblog) « In the Dark Says:

[...] Here’s an interesting discussion of the Alternative Vote versus First Past The Post voting systems. This is the issue to be decided at the Referendum on 5th May in case you didn’t know… On May 5th the UK will vote in a referendum for only the second time ever. (The first time was in 1975, when we voted on whether to remain in the EU, or the Common Market as it was then called.) Now we have a chance to decide whether to retain our current voting system, misleadingly known as First Past The Post, or whether to switch to the Alternative Vote. Let me come clean straight away. Although in this post I shall try to write dispassionatel … Read More [...]

86. R M Chater Says:

A compelling and articulate argument with one critical flaw – you’ve not convinced me that the ‘deficiencies’ of Simple Majority would necessarily be resolved through the introduction of the Alternative Vote. Why bother going to the hassle and expense of substituting one inept system for another?

87. Richard Lubbock Says:

A couple of commenters have raised Arrow’s theorem, which renders the notion of “Will-of-the-People” incoherent. But the criterion to follow is that presented by David Deutsch: The prime object of voting is to cleanly dispose of bad governments without violence. Since FPTP amplfies small voting edges and (usually) produces substantial Commons majorities from small pluralities, it is best for unseating incompetents. All other systems surrender power to splinter parties and crank politicians and so frustrate the voters’ hopes.

88. Tom C Says:

Thanks for this explanation. I’m grateful for the time taken to debunk some of the clearly outrageous claims by the no2av camp.

I’m still not decided on how to vote in this referendum, mainly because I have one objection that’s not (as far as I’ve seen) been dealt with. Under AV, each voter is effectively able to cast a veto as well as a vote. In other words, the tactical element of FPTP is replaced with voting for everyone-but-the-. Your examples were of voters wanting to stop the Conservatives getting in and using their preferences to try to ensure that.

Maybe I’m being naive, but I prefer a system that only allows you to vote positively for the party you want and not simultaneously voting to cancel out other people’s votes.

• gowers Says:

That’s fine under some circumstances, but sometimes there are two fairly similar parties, both of which I like and distinctly prefer to a third party. For example, putting Labour first and Lib Dem second can be a positive choice for progressive politics rather than a negative defeat-the-Tories vote. And at the next election, somebody might vote Conservative first and Lib Dem second because they felt positive about the coalition.

[...] Timothy Gowers: Is Alternate Vote better than First Past The Post? [...]

90. shel Says:

i just wanted to say what an amazing post this is and thank you for taking hours out of your work to submit it. being one of those awful head in sand types when it comes to politics, i was approaching the referendum with very little understanding of what i am actually being asked to vote on. my initial perusal of the internet left me with the gut feeling that av is for me, but i don’t mind admitting that i was a little worried i had been propagandised or had somehow missed the crucial point entirely. i found the link to this post with a warning that i would need to set aside a good half hour to read it. nonetheless, i ploughed on… and what a wonderfully, solidly presented argument for av. i’m no mathematician, but found this completely engrossing and accessible. you had me at “wtf is the post?”!!!!

91. Jonathan Phillips Says:

To Morning Tory:

“But that gives the 2nd preference of one voter the same weight as the first choice of another. You seem to think that’s a fair situation because the 2nd preference voter is happier, but what about the decisive voter who only puts down one choice? Why is it fair that he/she has less of say? It’s not.”

Oh dear. A Green supporter, knowing her candidate has no chance, considers voting Lib Dem, since they appear to have the greenest policies of the larger parties. But she lives in a Tory/Labour marginal and – believing that the Tories are the least environmentally aware – decides to vote Labour. Even though Labour is her third choice she is counted as a Labour supporter – and her vote has exactly the same weight as that of a committed Labour member.

How does that differ from an AV election in which her vote, cast honestly for the Green candidate, is transferred first to the Lib Dems and finally to the “least worst” of the remaining candidates? AV merely makes explicit what FPTP conceals, showing the true pattern of party support.

• MorningTory Says:

I accept than point. Some people consider a vote to that makes a statement but does that is unlikely to influence the outcome of the election (such as vote for the Greens, UKIP, the BNP or the Communists) a “wasted vote”. At the last election a quarter of million Greens didn’t think making a statement was a waste.

Why, I wonder, do you think people should have the right to both a statement vote and a vote that counts. Is it too much to ask that voters make a grown up choice? Electing a government is serious business.

92. Mark Wainwright Says:

Hi Tim: this is a very thorough post which I agree with almost all of except on two points, one of which is mere pedantry. So let’s get that out of the way first. A much more concise and intuitive way to express AV (indeed, you more or less say the same later) would be

1. Assign each vote to the voter’s highest-ranked candidate who hasn’t been eliminated.
2. Eliminate the candidate with fewest votes.
3. Go to 1.

When only one candidate (not ‘party’, as in your account, of course) is left, they are the winner. Your account, besides being more long-winded, doesn’t even quite work – you are at pains to explain that the rank k of subsequent preferences must be diminished by 1 when a candidate is eliminated, but forget to mention that if so, this must happen to other voters’ ballot papers too (in your Step 4).

An additional advantage of the above is that it makes obvious nonsense of the anti-AV claim that supporters of fringe candidates are advantaged by having their vote ‘counted again’ in later rounds. As Step 1 makes clear, EVERY vote is counted again in each round! Yes, even those of the candidate suffering from the crippling handicap of being in the lead.

*

My second point is on this:

“This sounds like a big disadvantage of AV: it gives people a chance to vote BNP without wasting their vote. [...] WE SHOULD NOT LET THE BNP DICTATE HOW WE RUN OUR POLITICS.”

The slogan is true, of course. But the disadvantage, which you seem to accept with qualifications, is not a disadvantage. As someone who in the final battle will man the barricades against the BNP if necessary, I still want to be crystal clear that it is *not* an advantage of a voting system that it somehow conceals the fact that some people support them. We live in a democracy, and what that means is that those people have as much right as me or anyone else to have their voice heard.

As it happens, I think the suspicion that FPTP conceals support for the BNP actually *advantages* the BNP, who can make it look to their supporters as if they are being unfairly victimised. In fact I even agree that they are to a degree, in that I also think the rise of the BNP has been facilitated by the electoral arithmetic meaning that the mainstream parties can marginalise the concerns of a sizeable minority – and I don’t think those concerns are actually to do with foreigners going home; they’re to do with jobs, housing and wages. (Otherwise it would be hard to explain why support for a racist party is overwhelmingly a predictor of a particular economic demographic.) I am generally in favour of allowing high levels of immigration, for reasons of equity rather than of business efficiency like the Tories and some others. I’m not seduced by the silly argument that there’s a fixed number of jobs and when foreigners have come and ‘taken’ these, there’ll be none left for everyone else. But it would be dishonest of me to deny that locally (in time), there is undoubtedly a pressure in that direction, and a lag in the correcting growth in the economy. The rise of the BNP, in my view, was the result of the frustrations of some of those voters when ‘New Labour’ abandoned their core voters’ concerns about jobs and housing.

But even if I didn’t believe any of the previous paragraph, on democratic grounds I would still be saying that we shouldn’t be trying to devise a voting system to sweep inconvenient political views under the carpet.

• gowers Says:

I totally agree with your first point, and have in fact written a second blog post (but not yet posted it) in which I have explained AV in exactly the way you advocate. I haven’t decided when the best moment would be to post it.

In fact, on reading the rest of your comment I find that I agree with all of it.

• MorningTory Says:

“the rise of the BNP has been facilitated by the electoral arithmetic meaning that the mainstream parties can marginalise the concerns of a sizeable minority”

Well, well… there’s always something new to surprise! I thought I’d heard everything in this debate, but I must admit I had never heard anyone blame FPTP for the the “rise of the BNP”.

93. Gil Kalai Says:

This seems like a new ground breaking post on this blog. I like the post although I did not think about it yet to see if I agree or not with Tim’s position (and probably I will try to carefully see where and why I do not agree with Tim…, I can see one reason upfront – overall, keeping the status quo on such mechanisms has a lot of advantages.)

I hope people who study voting methods in economics/and CS/and political sciance will pick up this referendum and see if formal methods or analytical studies or heuristic methods or some insights can be applied. So I will try to spread it around.

Just one clarification question: I suppose that the general principle that the U.K. is divided to constituencies and each constituency leads to one parliament member remains unchanged and the only difference is the rule to chose within a constituency. Is it right?

• gowers Says:

In answer to your last question, yes it is a single-member constituency system, and for that reason is unlikely to be very proportional, though might slightly reduce the unfairness against the third party.

• MorningTory Says:

… and ONLY the third party…

94. Mark Wainwright Says:

(And on the pragmatic side again – surely better to have that support out in the open where we know there’s a problem and a need to do something about it.)

95. Alan Weir Says:

I enjoyed the blog very much though I confess I haven’t worked my way through all the comments so I hope this one worry I have hasn’t already surfaced.

It is this: your argument seems to be directed at voters whose methodology is essentially that of a decision-theorist, someone whose decision at the ballot box is determined by her or his estimation of the expected utility, or the likely consequences, of voting this way or that way. And such an individual, you say, would be less likely to vote tactically under AV. ‘If you are a mathematician, then you will probably toss a coin a few times and make a probabilistic decision’ you write and many of the commenters write in similar fashion about how they are weighing up the likely consequences of their voting this way or that. (Or rather, I imagine they could be weighing up the consequences of lots of people voting in the same way as they, for each possible choice. But how is that relevant to their choice? Not at all as far as I can see, unless they are influential political and media figures, and even then all they have to do is say how they will vote; if nobody will know if they do or not, they needn’t actually vote.)

Moreover you seem to apply this type of thinking to the coming vote too: if you are a Tory whose goal is to maximise the chances of Tory rule, vote no, if you are a supporter of whatever party whose goal is to reduce the chances of the manifest unfairness of previous distributions of seats versus votes, vote yes and so on.

But if that is the methodology your target voter, and you yourself indeed, adopt, isn’t the rational thing to do not to vote at all? (Even if widespread adoption of that will lead to disaster- we are in prisoner’s dilemma territory here.) The probability that in an FPTP election there will be a one vote difference between your candidate and an another is extremely small. Likewise the probability that in an AV election the chance your vote would make the difference between your candidate X staying in and Y, whom you favour less, being eliminated rather than vice versa, must be very very small. It’s worse than that, is it not, because even in such a situation given our actual voting practices- recount followed by recount until everyone wants to go to bed and so on- this might mean it is a random matter who is eventually declared the winner, or drops out. In which case the probability of each result conditional on you voting such and such a way might be the same as that conditioned on you not voting (for each way you might vote). And then, if you have the slightest disinclination to get off the couch and head out to the polling booth (or fill in that envelope, lick that stamp etc), it is irrational for you to vote at all.

All this changes if one does not approach matters by weighing probabilities and utilities but if one thinks one has a civic duty to express one’s political views in a vote. But if that is the rationale, it would be wrong to vote tactically at all. (I’m not saying this an argument for FPTP- if one thinks tactical voting is wrong, perhaps because it is irrational, but acknowledges it is widespread, your argument that it might be less frequent in AV might be attractive.) Unless of course, tactical voting was the, or one of the ways, in our social practice of expressing one’s political opinions.

How such opinions are made manifest will differ of course, in different systems, and I’m not saying we (legislators, pundits, ordinary citizens who feel they have a civic duty to express a preference vis a vis FPTP and AV) can’t use broadly utilitarian reasoning to decide which practice would be the best, or least worst, way to inculcate on the citizenry as the way to carry out one’s civic duty of voting. Here we have to weigh up the probability that AV, in current circumstances, will lead to less of the manifest unfairness you highlight in previous elections, unfairness which leads to disenchantment with the political system, also the probability that AV now will lead to a more proportional, AV plus or STV system in future then there is the probability that AV, in our context, will lead to unstable government, minority parties exercising too much influence in smoke-filled (well perhaps no longer) back rooms and so on. For my part, I’m going to vote for AV, notwithstanding the last worry which I acknowledge is a real one.

A second comment, on the racing FPTP metaphor. What metaphor should AV proponents use? One analogy which would surely be part of the experience of a lot of people, either as interviewers or more likely interviewees, is job selection. I’ve been on a number of job panels, and I’ve never said, A is the best candidate but if she turns it down I don’t care in the least whether we get manifestly competent B or C or any of the palpably incompetent and off their rocker D …. Z. No sane person would think like that. True, voters aren’t an appointment panel and no candidate is going to turn the job down. But people can surely understand the idea of ranking rather than a simple A or nothing from such examples. Or my favourite beer isn’t in this pub: I don’t say, I’ll take any other then (Hey, this is a much better example). Not unless it’s all lager, in which case I might choose at random rather than take the evidently absurd (unless one is driving) option of non-alcoholic drink. But we haven’t quite reached that desperate, only lager, state yet.

Maybe the reason Cameron and Osborne find FPTP so intuitive is that in their very affluent upbringing they never had to settle for 2nd best. It’s Pimms No.1 Cup or nothing for them.

(Only kidding Tories- and apologies to non-UKanians for the somewhat parochial example but the general point should be clear, and I hope plausible)

96. Andy Williamson Says:

Love this post – and have referenced it on Facebook, where some people have already come back having read it, and been strongly influenced – thank you.

Your dialogue with ‘MorningTory’ was even more enlightening – thanks to him (I presume) for his contribution. The later comment from ‘Another Tory’ should give any Tory-No2AVers pause for thought.

I think the comments about the likely anomalies that will occur under AV are interesting – and I hope that these get more widely discussed, as the reasons for accepting them should be heard now, rather than after the event.

On Radio 4′s ‘Any Answers’ today, the first contribution from a bloke in favour of AV included more analogies on the theme of ordering food in a restaurant, which very clearly showed up the nonsense in the claim that AV somehow allows some people to have ‘more than one vote’ (etc). In particular, say you’re part of a group (no veggies), which can only order one dish for everyone, from a choice of Beef/Chicken/Fish. Fish gets fewest votes, so those people are added to Beef or Chicken. I don’t think anyone would argue that their opinions should carry less weight in this ‘run off’.

• MorningTory Says:

Be careful with the restaurant analogies. It’s not especially difficult to construct scenarios where more people actually hate the chosen dish than like it, and in which a sizeable proportion of the people that “voted” for that dish didn’t do so because they particurly like it but because they hated something else; i.e. scenarios in which AV clearly does not represent the will of the electorate.

• Andy Williamson Says:

OK – but are there any that are so likely that they don’t come under the ‘accepted occasional anomalies’ category?

“scenarios where more people actually hate the chosen dish than like it” – much like our current voting system then.

“a sizeable proportion of the people that “voted” for that dish didn’t do so because they particurly like it but because they hated something else; i.e. scenarios in which AV clearly does not represent the will of the electorate.”

Actually, I think the analogy still holds here. With both the current system and AV, we end up with an MP no matter what. In the restaurant, unless you decide to go hungry, avoiding eating something you hate is a much stronger urge than putting up with something you don’t particularly like. I’d say the same about politics.

It’s often claimed that AV will mean that boring candidates, who lack passion and radical ideas will become the most common victors. Actually, I think the opposite may turn out to be the case, with occasional passionate radicals emerging from nowhere, on which the majority of an electorate decide to take a punt. Not a great idea if we’re electing a Prime Minister, perhaps, but could be just the shot in the arm that our tired politics needs. A few more Martin Bells, and that Doctor from the Midlands, to be in Parliament saying the things that currently get left unsaid so often.

• MorningTory Says:

The scenarios I can think of aren’t all that unlikely in the restaurant metaphor. I’ve not event tried mentally applying them the the world of UK politics.

“In the restaurant, unless you decide to go hungry, avoiding eating something you hate is a much stronger urge than putting up with something you don’t particularly like. I’d say the same about politics.”

I suppose it’s this is a perspective thing. But you could have a situation where someone not particularly liking a food ends up forcing you to eat food that you hate. They would have been content with your preferred food, but make you eat something you hate because they like something else a bit more. In the restaurant scenario you’d probably stop going out to dinner with them! That’s not a option when electing an MP.

Martin Bell made precisely zero impact once elected, and neither you nor I can even remember the name of the Honourable Member for Wyre Forest!

• WJ Says:

“It’s not especially difficult to construct scenarios where more people
actually hate the chosen dish than like it, and in which a sizeable proportion of the people that “voted” for that dish didn’t do so because they particurly like it but because they hated something else; i.e. scenarios in which AV clearly does not represent the will of the electorate.”

Replace ‘AV’ with ‘FPTP’ and that statement makes perfect sense. Under FPTP, people are going to vote for one candidate because they feel it has the best chance of keeping out another candidate whom they dislike. Under AV they at least have the oppurtunity to make express the fact that their first choice candidate is someone else, in case that candidate does gain enough support to win the seat.

• MorningTory Says:

“Replace ‘AV’ with ‘FPTP’ and that statement makes perfect sense. ”

I didn’t say it wasn’t also true of FPTP, just that it is not a benefit of AV.

• gowers Says:

This kind of phenomenon exists under both systems. However, under AV it is greatly reduced. That is the benefit.

• MorningTory Says:

You don’t know that it is greatly reduced under AV. All preference under AV have the same , because all preferences have the same weight so it tells you almost nothing about the DEGREE to which a voter approves of a candidate.

• gowers Says:

FPTP tells you nothing about strength of preference either. But it tells you less about the preferences full stop. Under AV it is extremely hard for a candidate to get elected who is strongly disliked by the majority. Under FPTP it is not hard, and happens with great regularity.

You’ve said that AV doesn’t always reflect the will of the people. That’s true of FPTP too. But can you give us a scenario where the outcome of FPTP is quite clearly a more accurate reflection of the will of the people than the outcome of AV?

• MorningTory Says:

“FPTP tells you nothing about strength of preference either.”

Of course it dones’t. Perhaps my criticism would be better aimed at the Yes campaign (who seem to think it does) rather that the voting system itself.

“Under AV it is extremely hard for a candidate to get elected who is strongly disliked by the majority.”

The counter-argument, of course, is that under AV it’s not particulary difficult for a candidate who is not actually stongly favoured by many voters at all to be elected.

“You’ve said that AV doesn’t always reflect the will of the people. That’s true of FPTP too. But can you give us a scenario where the outcome of FPTP is quite clearly a more accurate reflection of the will of the people than the outcome of AV?”

It’s difficult to say, because to the best of my knowledge there is no adequate AV data for any election other than 2010 (for some reason the pollsters asked about 2nd prefs without stopping to think about whether a different system would have resulted in different first preferences! But my gut feeling is that 1992 was more “the will of the people” than it would have been under AV, and 2010 would of course be a fairly obvious example. It’s not clear to me that there are any UK elections in the last where AV would have better reflected the will of the people.

97. Peter Says:

This is a generally well written article, other than the occasional and highly unneccessary attacks on the right. It makes me feel that it has been written from a left-wing bias, and that you have chosen to cite only those election results that support your point of view.

And, as in many pro-AV arguments, you have fallen for the myth that a candidate needs 50% of the vote to win. This is simply not true. They only need 50% of the votes counted. Once you take into account that many ballots will be discarded with each extra round of voting, the eventual winner may have nowhere near 50% of the support of the electorate. By removing votes for the lowest ranked candidate, you artificially inflate the percentages of every other candidate, making them appear more popular than they actually are.

I sympathise with all who have said they are very worried about a No result. I promise you, all of us on the NO2AV are equally worried about a Yes result!!

• gowers Says:

For much of the post, I am putting myself in the position of people who are on the left, trying to persuade them that they should vote yes. That may make me sound more left wing than I actually am.

However you look at it, under AV you have to seek a broader appeal than you do under FPTP. That’s what really matters rather than the 50%, which I agree is of votes in the final round.

• Mark Wainwright Says:

In one way, one could say the 50% target is a bit of a red herring. In my simplified account above, you may notice, I didn’t mention it at all: the winner is the last candidate standing when the others have been eliminated. Having a 50% rule is just a neat optimisation: if there are 3 (or 4, or 20 …) candidates left and one has 50% of the votes still in play, and you are the returning officer, it’s nice to know you needn’t bother with the 19 remaining redistributions rounds since no-one can possibly catch the leader. In this case you could see it as artificially *deflating* the support of the most popular candidates, since we never find out how many more redistributed votes they may have got.

It’s true that voters whose ballots are exhausted before the final round must be dischuffed with the result, since the final runoffs are between candidates so bad (in their view) that none of them seems worth preferring over the others (at least, that’s how they’ve cast their ballot). Of course they would have been equally disenfranchised under FPTP where there is only one round, and their one candidate would almost certainly have been eliminated straight away. The difference under AV is that they were given the option of expressing a preference between the other candidates with broadest support, but chose not to.

It’s funny for an FPTP supporter to use the existence of people casting only partial votes as an argument *against* AV. After all if everyone did it, giving only their first preference, the system would reduce to FPTP! Logically therefore the FPTP supporter ought to see an outcome closer to this as making the system better, not worse.

98. Dom Says:

In a response to Mark Wainwright you said that you are going to post again with a more concise explanation of AV: if so, could you please make it clear that the “magic 50%” winning threshold is 50% of the votes counted IN THE LAST ROUND and NOT of the total votes cast? It is possible to win an AV election of more than two candidates with less than 50% of votes cast. Exhausted votes cause the threshold to drop in successive rounds. Arguments for AV need to be clear about this.

• gowers Says:

In my description of the process, I have indeed said this, though perhaps I could emphasize it more.

I don’t think this significantly weakens the case for AV. Under AV, in a seat where the top-ranked candidate in the first round does not get 50% of the vote, that candidate still has to appeal to voters from other parties, people are still under no pressure to vote tactically, etc. And even if you did have to get 50% of the total vote under AV, there would still be a whole lot of people who hadn’t voted (who we could think of as people who did vote but the number of preferences they wrote down was zero).

If you think of it as an actual multiple-round election, then there are two candidates in the final round. The one who wins is the one that gets 50% of the vote in that round. That means 50% of the votes from people who can be bothered to vote (in that round).

99. Dom Says:

It doesn’t weaken the case for AV, and I didn’t say that, but claiming that 50% of votes is the threshold to win weakens the argument for it because it is wrong. It’s made even worse when some people say that AV victory requires 50% of constituents, which Nick Clegg and others seem to believe.

The Yes campaign rightly castigates the No campaign for telling people that AV is difficult to understand, but then the No campaign fails to explain it properly. The Electoral Reform Society’s explanation is particularly bad. The Electoral Commission’s explanation is very good, but then it is not campaigning and so it is unbiased.

I’m not interested in the tedious drivel spouted by politicians on both sides of this nasty and unprincipled campaign, but I do want AV to be considered fully and properly.

100. Polly Shaw Says:

Thank you for this post: it has made me reconsider my small-c conservative plan to vote No. I’ve just got one paycological point to make about your refutation of the No campaign’s argument that the second-preference votes of the supporters of the least popular parties get taken into account first. When I first read it, I thought ‘ah, but what happens if after round one, there is a party with 50% of the vote?’ Then the least popular party’s supporters have got their preferences taken into account while the second-to-least popular haven’t. It was only when I tried to construct an example that I realised that the result couldn’t be changed by eliminating extra parties after one had reached 50% of the vote. And, because, as you’ve demonstrated, the algorithm is fair after two rounds, and the result is unchanged from the first round by doing a second, it’s also fair after one. This is a simple observation, but I think it shows that it takes some time to develop intuition for AV.

I wonder if it would be less confusing if the algorithm were described without the exit point of a win for a candidate of over 50% of the vote at any step, and instead were described as elimination of the smallest party until only one remained. The 50% rule is just an algorithmic shortcut to this result.

101. Jonathan Phillips Says:

AV is a mechanism, and the Yes campaign was quite wrong to focus initially on the possible results of adopting the mechanism (harder-working MPs & the like – an insult to the many MPs, perhaps particularly on the Labour left, who have very safe seats and work very hard for their constituents).

Neither the voting nor the counting procedure takes long to explain or, if this is done well, difficult to understand: http://bit.ly/fldUMZ, http://bit.ly/g73aDr, http://bit.ly/hctTGk, http://bit.ly/dSMTYV.

Failure to ram home the nature of the mechanism from the very start made it even easier for the No campaign to spew out their lies.

102. RodCrosby Says:

Voting and voting systems are full of paradoxes. When you try to eliminate one problem you often find that the ‘solution’ raises an even worse problem. However, Thinkers for centuries have pretty much arrived at the conclusion that FPTP is the worst system.

Among its worst flaws:-
Majority Loser: – the candidate, who above all, the majority don’t want can win under FPTP.
Condorcet Loser:- the candidate who would lose head-to-head against every other candidate can still win under FPTP
Mutual Majority: – if 59% prefer lemonade, fruit-juice or tea, and 41% prefer whisky or beer, FPTP can elect whisky.
Clone failure: see Bush/Gore 2000

AV removes ALL of these problems.

AV has also been shown by numerous studies to be the most strategy resistant system. It ends the pernicious blackmail of FPTP, which often forces a voter to choose between being a fool or a liar.

AV doesn’t guarantee the election of a Condorcet Winner, however. Paradoxically this might be a GOOD thing. Why? Because every Condorcet compliant system suffers from at least two serious flaws.

i) they fail Later-no-Harm. In other words a second choice can defeat a first, meaning that people will eventually just bullet vote, taking us back to FPTP and square one.
ii) they are vulnerable to the ‘Burying’ strategy. Basically, it pays to rank your major opponent last, and if most people do that, the candidate elected will be a dark-horse, not necessarily the true condorcet winner.

AV doesn’t suffer from these drawbacks, and so in practice, may actually elect more Condorcet winners than Condorcet systems themselves!

And AV, while not an explicitly proportional system, will tend to produce more proportional outcomes than FPTP.

note: cardinal voting systems such as Approval and Range are strictly for the birds, I’m afraid. Why? They fail what might be considered the ‘cornerstone of democracy’ – the Majority Criterion. If 60% want A, and 40% want B, cardinal systems can elect B! [if B's voters' 'intensity of preference' is stronger than A's voters' intensity]
Not likely to be implemented any time soon, then…

AV is the natural replacement for FPTP in a multi-party world. It actually puts ‘the POST’ into First-Past-The-Post.

• gowers Says:

I don’t see why it’s wrong in principle that if 60% mildly prefer A to B and 40% very strongly prefer B to A that a system might choose B. However, I certainly see that such a system would be hard to sell to the public …

It’s not inconceivable that we’re in exactly this position with the current referendum. I suspect that people who plan to vote NO2AV to spite Nick Clegg do so because they don’t care too much about which system we have. So it might be that FPTP will win the referendum, but that AV would win if you took into account the degree of preference. (I’m not saying this is definitely the case — just that it could be.)

• MorningTory Says:

Neither clone failure nor mutual majorirty are real things. In fact, they are the same thing thing, but it only exists as a figment of the imagination. Vote splitting presumes that the votes that were “split”, BELONGED to one party/candidate/faction in the first place.

There’s no such thing as “the left” or “the right”. If there were, there’d be only one “left party” and only one “right party”!

103. Jonathan Phillips Says:

No voting system can take account of the strength of voters’ preferences or indeed for their voting the way they do – you’d have to conduct separate surveys to find out. But AV does at least show the ordering of preferences (“I prefer Ukip to Tory and Tory to any of the others”, for example) which does tell us much more about the patterns of public opinion and party support.

Attitudes could vary widely even in a “straight” fight: did you vote for A (a) because you think A good and B bad, (b) because you think they’re both pretty fair but A is better, or (c) because you think they’re both awful, but A is nevertheless slightly less awful than B?

As CGPGrey’s entertaining videos show, both FPTP and AV can land us with a two-party system in which nobody much likes either of them. http://bit.ly/hRwaAB and http://bit.ly/hRwaAB

Let’s hear it for proportionality and something for everyone!

104. Trev Says:

Why can’t we have just 2 parties then none of this will matter.

In terms of fairness the size and distribution of seats is being overlooked here. Equal sized constituencies are also important, though I would have fewer seats in London – why should such a small geographical area have such a voting pull? We are too Londoncentric as it is…

105. Simon Says:

Allow me to apply AV to the multiple/preference voting system to The Eurovision Song Contest as an example.

As it stands, each country gets ten votes. Preference 1 gets 12 points, preference 2 gets 10 points, then preferences 3-10 get 8-1 points respectively. The winner is the country with the highest score. (Let’s ignore tie-breakers, as it’s unlikely in an election). This year there are 43 countries competing.

FPTP would give each country just one vote, so there would be no 10s, 8s, etc., thereby grant the winner as the one with the most 12s.
(To take the analogy more literally, if there is no country with over 50%, i.e. 22 or more votes, there is no winner, and there would need to be a coalition between countries to total 22 or more to declare a result).

AV would also require the 12 count to be over 50% (22 or more 12s). If not, the countries with the fewest 12s are eliminated, and the count moves to the 10s.
If n(12s) + n(10s)>44, that country is declared winner. If not, those with the fewest 10s are eliminated, and the count moves to the 8s.
If n(12s) + n(10s) + n(8s)>66, that country is declared winner.
Etc.

Have I understood that correctly?

• I_want_FPTP Says:

But it is like saying, you awarded Greece 12, Spain 10, Ireland 8, Netherlands 6 – now Greece didn’t win, so let’s turn your 10 for Spain into a 12, Now Spain didn’t win either, so erm…let’s turn your 8 for Ireland into a 12 – oh hang on Ireland are out now – how much did you give Netherlands – Only 6 – no worries, we’ll turn that into a 12 as well.

Meanwhile the punter that has voted for UK with 12 sits with their 12 as the UK isn’t bottom placed.

One voter gets one vote, the other gets 4 votes counted.

Obviously this post is completely floored as in Eurovision, the UK would have gone out first round!

• polleetickle Says:

[I_want_FPTP Says: Obviously this post is completely floored as in Eurovision, the UK would have gone out first round!]

LOL

But! Mercilessly, Eurovision’s winner doesnt get to run the music industry afterwards. Moreover, electing a less-than-most-preferred candidate as an MP (when many already regard local MP’s as less productive than they’d like) seems utterly devoid of any sense at all.

106. RodCrosby Says:

Simon.
No, Eurovision uses a type of Borda count [arbirary cardinal utilities applied to preferences, then sum the utilities]

AV is an ordinal system [no utilities], outcome determined by elimination.

Borda is a pretty crap system. Even Mr. Borda thought so. Manipulable, and doesn’t pass the majority criterion.
‘my system is intended only for honest men’ – Borda

107. Daniel Meeson Says:

Brilliant article! If only the national debate was this sane and rational.

108. Joseph Malkevitch Says:

Just because one lives in a democracy that does not mean that elections result in the “will of the people” or that the “best” person wins. In the end, it is the choice of election method (function in mathematical terms) that makes for the winner. Here is a simple example that I developed for my students to show them that 5 different popular and, each for different reasons, appealing methods (plurality, run-off, sequential run off, Borda Count, and Condorcet) yield a different winner when used in conjunction with ranked ballots: http://www.york.cuny.edu/~malk/courses/elections/election-one.html

109. Andy JS Says:

I think it’s wrong to suggest that Labour could have formed the government in 1983. The Tories won 43% and the Alliance 25%. That means the Conservatives would have only needed the second preferences of about 1 in 5 Alliance voters to win an absolute majority of votes (when you discount parties winning only a very small percentage of the vote). There’s no doubt that at least 1 in 5 Alliance voters would have given their preferences to the Conservatives over the Alliance.

By the way, I’m a Conservative supporter myself but I’m also strongly in favour of AV. Maybe this is due to the fact that I know a lot of LD supporters who would preference the Conservatives over Labour so I don’t accept the notion that AV would damage the Conservatives.

110. Gil Kalai Says:

Here are some comments to the analysis in the post.

(9). AV leads to more coalitions and hung parliaments.

This claim is dismissed too quickly. Of course, it can happened that the UK will move into 3 (or more) large party system even under FPTP (and this could have happened last elections) but it is much much more likely under AV. In fact if AV will correct even partially “unfairness” of FPTP as claimed in other parts of the post in the underrepresentation of the “third party” then this will also lead to hung multi party partiaments.

(7). AV is complicated

PUT THE CANDIDATES IN ORDER OF PREFERENCE UNTIL YOU DON’T CARE ANY MORE.

Well, AV like any method asking the voter to rank all candidates he cares about is complicated. The input expected from each voter is much more complicated. If there are 10 parties and you favour A and hates B (and dont care about the rest) in order to express these preferences you essentially need to rank all of them. (Of course you should avoid expressing your preferences as 1. A 2. B)

FPTP HELPS EXTREMISTS.

As you claim in other parts of the post AV does give advantage to extremist. Imagine a new party that call for the elimination of income tax that has a campeign “put us second!” Such a party has some chance under AV.

A LABOUR SUPPORTER VOTING FOR FPTP IS A TURKEY VOTING FOR CHRISTMAS.

This is nice!

• gowers Says:

Your response to (7) is an important point that I had not thought of. In fact, it raises another problem that I also hadn’t thought of. Suppose you were voting in an election under AV and you did indeed love one party and hate another and that you had no preferences between the rest. And suppose you were sufficiently clued up to know that you should rank the party you loved top and the party you hated bottom. What would you do then? It would be quite tempting just to number the remaining parties in the order in which they appeared in the ballot paper, which would give an unfair advantage to those who appeared higher up. I’ve no idea how much of an effect this would be in practice — I suspect not great, but I think it could exist.

As for (9), a pretty convincing argument that AV leads to more coalitions is that if the third party is larger, then the first party needs a bigger lead over the second party to get an absolute majority. So if we see the gap between the two main parties as a random variable with mean zero, then it will have more chance of being too small for the party that gets top to form a government on its own.

Against that, it could be that under AV the variance is bigger. When a government gets unpopular, the time-for-a-change sentiment coupled with a more efficient combination of the votes of the opponents could benefit the main opposition party more (in additive terms) than it benefits the third party.

But perhaps all that this is saying is that AV has the potential to amplify the swings when there is a decisive switch away from one of the main parties, but to make coalitions more likely when the mood of the country is more ambivalent.

When I said that FPTP helps extremists, I should not really have used that word (even though I was careful to define it in advance). I think FPTP helps non-lunatic extremists (in this country, the right wing of the Conservative party and the left wing of the Labour party). Less palatable extremists could as you say get some help from AV, though not to the extent of actually winning seats.

111. Joel Says:

I think this is an absolutely superb analysis. You refute the tame arguments of the NO2AV campaign brilliantly, pointing out, correwctly in my opinion, that in many cases their accusations are just plain wrong (ie ‘AV gives some more than one vote’, ‘AV allows parties such as the BNP to do better’ etc…)

However, I’m a little surprised that you did not engage more thoroughly with the objection that AV will lead to more coaltions and thus weaker government. This seems to me to be the primary argument of the NO2AV campaign. It is, again, wrong. I don’t think AV will lead to more coalition govenments. Michael Howard in particular goes on and on about ‘accountability’ but won’t admit the fact that a one party government, whilst apparently more ‘accountable’ is still less representative. And REPRESENTATION is a very important thing in any democracy.

You’re quite right about the main benefit of AV though, which is that it reduces tactical voting. Another slogan perhaps?:

AV allows voters to vote POSITIVELY not negatively!

We can vote FOR what we want, not for the lesser of two evils.

112. Jonathan Phillips Says:

“AV allows voters to vote POSITIVELY not negatively! We can vote FOR what we want, not for the lesser of two evils.”

Better than that – AV lets us vote both positively (honestly, truthfully) and negatively (tactically) on the same ballot paper (http://bit.ly/fgHxR0). We can show what we really think without throwing out vote away – and we can vote tactically (against a party we dislike) without giving the party that gets our tactical vote a mistaken impression about the extent of their real support. AV must be the psephologist’s wet dream.

• MorningTory Says:

One is tempted to suggest that the reason you can vote both positively AND negatively is that you (but not other people) have more than one vote!

“and we can vote tactically (against a party we dislike) without giving the party that gets our tactical vote a mistaken impression about the extent of their real support.”

That, sadly is wrong. I can assure you that after the any AV election, UKIP for example, fringe parties will be trumpeting their level support by quoting the number of people that voted for them in total, not just in the first (real) round.

• WJ Says:

“you (but not other people) have more than one vote”

It is a fallacy to suggest that people have a different number of votes under AV. If you really want to look at it that way – under AV, everyone has the same number of votes (unless they don’t list all their preferences, in which case the result should mean nothing to them anyway). If you vote for a candidate which gets more first-preference votes, however, you are allowed to cast all of them for your favourite candidate. If you vote for a candidate who is eliminated, then you have to cast some of them for your lower preference candidates. As gowers says, GETTING MORE BITES OF THE CHERRY IS A DISADVANTAGE STUPID!

• MorningTory Says:

Getting two bites of the cherry is an ANDVANTAGE in terms of INFLUENCE STUPID! That’s true even if it does mean you are less likely to have got your way in the first place. Imagine a family at the fairground. Daddy gives each of his two sons £1 to try and win a teddybear (or whatever) with the mechanical arm thingy. One son is successful, the other is not. If the Daddy give the son who was unsuccessful another £ in order to try again, then he’s given one of his sons £1 and the other £2. … The third BNP supporting son gets a fiver.

• Mark Wainwright Says:

There are three things wrong with the fairground analogy. First, to make it stick, you’d have to add that each time the kid operates the mechanical arm, he has to try for a different teddy from all the ones he’s tried so far. Primus, an expert on the mechanical arm (and you have to take your hat off to him – they’re bloody difficult those things), had £1 and gets his first choice of teddy, whereas the klutz Tertius, who had £5 and really wanted the big red dog, ended up with his fifth choice, a little yellow duck. True, Primus only played once, but he goes home better off.

The second problem is that the £1 cost of each play doesn’t correspond to anything in AV. A better analogy again would be that the fairground stall allows a child to keep playing for £1 until he or she has won a prize (subject to the different-teddy rule).

The third problem is that it’s quite fun playing the mechanical arm, so you might think Tertius got some compensation or even an advantage from all the enjoyment he had playing again and again. This too doesn’t seem to correspond to anything enjoyed by voters, whose experience of 30 seconds in the polling booth was exactly the same in each case.

• MorningTory Says:

“True, Primus only played once, but he goes home better off.”

Primus comes home better off because he went for the easier teddy, not because he’s better with mechanical arm (unless you think that in the 30 seconds in the voting booth you can be especially “skillful” at voting).

“The second problem is that the £1 cost of each play doesn’t correspond to anything in AV. A better analogy again would be that the fairground stall allows a child to keep playing for £1 until he or she has won a prize (subject to the different-teddy rule).”

Good luck with trying to get the fairground stall to let you keep playing until you win! This is the point I have been making about perspective. I see the the £1 as equating to the vote. You see the time at the machine as equating to the vote.

“The third problem is that it’s quite fun playing the mechanical arm, so you might think Tertius got some compensation or even an advantage from all the enjoyment he had playing again and again.”

Again, perpective. I have never derived any pleaseure from the act of “playing the mechanical arm”. The only pleasure I have experienced has been on the rare occasions I have been successful.

• Mark Wainwright Says:

The reason it’s definitely misleading to see extra preference votes as being worth £1 each is this: the whole point about money is that it’s a limited resource. The more I spend on winning a teddy, the less we all have to spend on fish and chips for dinner. If I start off going for very difficult teddies, you could reasonably feel aggrieved, telling me to just grab the easy little yellow duck before we all have to go hungry. But in the polling booth, there is no such per-preference cost: it does neither of us any harm that before expressing my preference for the duck over the platypus I have tried for the dog and the kangaroo.

True, you went for an easier teddy (you’re right, this is a better analogy than skill with the machine) but that’s because it was your favourite. That’s the sense in which you go home better off – you have your favourite teddy, whereas I have to make do with one I’m not very happy with. How are you harmed by my extra plays?

• MorningTory Says:

“in the polling booth, there is no such per-preference cost: it does neither of us any harm that before expressing my preference for the duck over the platypus I have tried for the dog and the kangaroo.”

The “per-preference cost” is democratic capital. AV doles out more of it to people who want the BNP teddy than it does to the people that want the Labour teddy.

Does it matter to the son who only recieved £1 when his brother receive £2, that the father is infinitely rich?

• Mark Wainwright Says:

I still feel the comparison with money is muddying rather than clarifying the issue. Money is a highly exchangeable resource, but Secundus didn’t get £2 (which he could have spent on more lollipops than his brother); he got a second go on the machine when he failed the first time, paid for by his father. He can’t exchange this for lollipops or anything else, so it is very different from money; nor will he be allowed to win two teddy bears. And since we now learn Daddy is infinitely rich, the relevance of how much he has ‘paid’ for his sons’ gaming seems to fade into nothingness.

If you want to think about ‘democratic capital’, it’s clear to me and others here, I think, that this most closely corresponds in the fable to the ability to get a teddy one likes, not to the number of goes it takes to get it. Primus gets *more* democratic capital because he likes his teddy more, despite (or, in fact, because of) the fact that Secundus took two goes to get his.

Put another way: does it matter to the son clutching his favourite teddy if his brother, whose favourite was inaccessible, also goes home with a consolation prize?

• MorningTory Says:

“If you want to think about ‘democratic capital’, it’s clear to me and others here, I think, that this most closely corresponds in the fable to the ability to get a teddy one likes, not to the number of goes it takes to get it. ”

It’s not at all clear that “democratic capital” most closely corresponds to the ability to get the teddy one wants. But I think you’ve nailed what is at the heart of our differences in perspective.

• Mark Wainwright Says:

I think so too, and it’s interesting to consider how well your nice fairground analogy supports your perspective. You said yourself you derive no pleasure from simply playing the machine – the only value of playing is in the prize you win, if any. Yet you want to argue that Secundus, who has a less-favoured toy, has been advantaged over Primus by his extra unsuccessful plays.

I don’t think of democratic capital as being simply power. If I am a dictator I get my way, which we may call a kind of capital, but there’s clearly nothing democratic about it. Democratic capital is something that accumulates to the whole of society to the extent that everyone has an equal chance to influence the decision-making process.

Going back to AV, it’s clear that besides getting a *less favoured* candidate to vote for in the final run-off, Secundus also had *less influence* in the result. Primus’s vote not only helped his candidate in the final run-off, but *also* helped her in the earlier rounds, by helping ensure she stayed in the contest. Secundus’s vote was unable to secure that for his candidate and so had no effect on who stayed in in the early rounds; he came to the final round, like a man late for breakfast, with less choice about the dishes on offer. But in terms of equal influence, the result is more nearly democratic than one where his vote was thrown away after the first round and he got no breakfast at all.

• WJ Says:

I think that the main problem with the fairground analogy is that the children are not competing with each other, and each leaves with a teddy. In an election, voters are competing with each other to get their candidate through, as only one candidate can win. You also talk about the BNP supporting child getting £5 while Primus is given only £1. Neither is actually better off, though, since they have both spent all the proffered money on the machine, meaning that each leaves with no more capital than they started with. It doesn’t seem particularly unfair to me.

• MorningTory Says:

“I think so too, and it’s interesting to consider how well your nice fairground analogy supports your perspective. You said yourself you derive no pleasure from simply playing the machine – the only value of playing is in the prize you win, if any. Yet you want to argue that Secundus, who has a less-favoured toy, has been advantaged over Primus by his extra unsuccessful plays.”

I think I overstated my case when I said that I derive no pleasure from playing the machine. I was attempting to dismiss your third objection to the analagy. I should have just said that it was irrelevant, as looking at it now it isn’t. I think you were expecting too much from the analagy.

If you think about, it’s my perspective that is actually less motivated by outcome. It’s having the opportunity to secure a teddy that counts. If the 2nd boy is unsuccessful in securing any of the teddies (remember, he can only try for each once) and has spent £5, can you really say he has not had the more opportunity to influence the outcome than the first? True, he goes home without a teddy, but he has had more turns.

• ChrisP Says:

It’s interesting how often proponents of the status-quo analogize voting to a game. There’s the “third horse coming last” advert, the sportsman arguing he’s used to losing but you should just accept it and stop whining, and now comparing chosing a party to rule a major nation for five year with picking teddies. Perhaps that should be a new slogan?

AV: BECAUSE POLITICS IS NOT A GAME.

• ChrisP Says:

I think the best analogy for political capital if want to understand where AV is coming from is: the ability to remove a candidate you don’t like from the running.

Under this analogy, FPTP gives more “bites of the cherry” to supporters of the two main parties: at each round, the least liked gets voted off, and *so do their supporters*. Thus, if you back a niche party, your ability to vote off is severely reduced, because you’ll be “eliminated” early. Of course, this is another gaming analogy — but it does flip the view around. If you’re in the AV worldview, this is the way analogies will be formed, and phrases like “bites of the cherry” mean something quite different.

I believe the correct response to this is not to start arguing “but that view is wrong”, nor to go “yes, that’s exactly why we differ! different worldviews!”. It’s to realise the whole concept of “bites of the cherry” or “dollars given to the son” is flawed reasoning based on an inadequate analogy. That may be enough for the media, but we should be concentrating on other arguments, ones based on facts not analogies.

• gowers Says:

ChrisP, that is a very neat argument. I don’t hold out much hope that it would be widely understood though.

I think I’ll add this argument to a new post I’m writing — with a link to your comment to make clear that it came from you.

• MorningTory Says:

All analagies break down if you try to push them too far, but most people do find they help aid understanding.

“I think the best analogy for political capital if want to understand where AV is coming from is: the ability to remove a candidate you don’t like from the running.”

I know you don’t like gaming analagies, but all you have done here is change the objective of the game. I accept that under your “game” FPTP gives you a larger bite of the cherry (it can’t be more bites since there’s only one round!). But I don’t think the objective of your “game” is the right objective to be setting. I’m sorry, but that does boil down to worldview.

“That may be enough for the media, but we should be concentrating on other arguments, ones based on facts not analogies.”

The trouble with that is, there are very “facts” to argue about.

• ChrisP Says:

“All analogies break down if you try to push them too far, but most people do find they help aid understanding.”

The problem comes when people start arguing based on the analogy, not the facts. Fact is, there is no “cherry” that people are getting “more bites of” in AV. To understand the objection, we therefore need to remove it from the inappropriate analogy. What is the actual argument behind this objection? “Some get more bites/votes than others” = “some are unfairly advantaged”. But in order for something to be “unfair”, it has to be biased in favour of something, and AV is voter-neutral (everyone has a choice among the same set of actions) and party-neutral (no party has different terms). The advantage given by AV is (as said elsewhere) that you can always vote with both your heart and head — a very different spin than “more bites of the cherry for LibDem and BNP voters”, but also closer to a true understanding. We can (again shown elsewhere) still argue about whether this is good/bad/fair/unfair, but without the inappropriate baggage.

This also holds true when deciding what “objective” our “game” should have. The objective is to vote a political party that can do what must be done without doing what shouldn’t be done. No analogy with horses, teddies or boxing will give you any insight into this.

By pursuing false analogies, we only find ourselves further from understanding. POLITICS IS NOT A GAME.

• ChrisP Says:

Sorry, that should have been “establish a political system”, not “vote a political party”.

• MorningTory Says:

There’s not point in just repeating your mantra that “POLITICS IS NOT A GAME”. Nobody thinks it is.

But it does no harm whatsoever to think about electoral systems in terms of game theory. And there’s no point in arguing about which set of rules is “best” if we can’t agree what the rules are supposed to achieve.

Between 15 and 20 years ago, the Rugby Union points system was changed from “4 points for a try” to “5 points for a try”. The idea was to encourage a style a play that focused more on running with the ball than on kicking it. Now, if you prefered the style of the game dominated by kicking, you probably wouldn’t agree that it was a positive change to the rules.

You objective for the game is too imprecise for any meaningful discussion.

• ChrisP Says:

“There’s no point in just repeating your mantra.”

No point? That surely depends on whether I’m aiming just at yourself, or a wider audience.

“But it does no harm whatsoever to think about electoral systems in terms of game theory.”

Using the tools of game theory? Absolutely. Re-expressing it as a game? Very damaging, as I have argued.

“And there’s no point in arguing about which set of rules is “best” if we can’t agree what the rules are supposed to achieve. Your objective is too imprecise for any meaningful discussion.”

I totally agree with both these points. However, my objective leads into and frames the discussion of “power” (do what must be done), “representation” (without doing what shouldn’t be done), and the inevitable trade-off between the two, whereas discussing games leads into discussions of rugby rule changes.

• MorningTory Says:

“whereas discussing games leads into discussions of rugby rule changes.”

I doubt that. At least it got us to the point where we can agree that we need know what the objectives of the system are before we start arguing about which is system is best.

That’s a breakthrough from where we were earlier:

“I believe the correct response to this is not to start arguing “but that view is wrong”, nor to go “yes, that’s exactly why we differ! different worldviews!”. ”

For “different worldviews”, you substitute the words “different objectives”.

• ChrisP Says:

Different objectives, I can get behind. However, they must be expressed in terms of the problem at hand, not analogies: trying to decide what “money” or “influence” meant in the fairground analogy derailed the whole discussion. Are we happy to throw away that analogy completely?

• MorningTory Says:

If it confuses you then I’ll refrain from mentioning it again. Though I do not accept that it is wholly invalid.

• ChrisP Says:

If by “Confuses me”, you mean “Led to a discussion that to me appeared wholly without merit in its latter stages due to being totally divorced from reality”, yes

I agree that, in understanding what the mechanics of FPTP/AV are, games can be a helpful analogy. They also let us express why different objectives feel right/wrong.

113. Idiot’s Guide to AV « Patchwork Dreams Says:

[...] more detailed but thoroughly readable analysis of the various arguments, I suggest that you look here. Like me, the writer Andy is inclined to the ‘Yes’ vote; but like him, I going to try [...]

114. Jonathan Phillips Says:

Please, Morning Tory – under AV (or STV, or the supplementary vote used in mayoral elections) nobody gets more votes than anybody else.

AV is a simpler form of the Single Transferable Vote (the clue is in the name), but used for electing single representatives. That’s why AV is used in Euro, council and Assembly by-elections in NI and in council by-elections in Scotland, where across-the-board elections use STV. (And of course it’s also used by MPs to elect committee chairs and peers to elect the Lord Speaker http://bit.ly/fAmLaU.)

Imagine an exhaustive ballot system. Nobody gets an overall majority in the first round. The lowest-placed candidate drops out. Suppose the rules say you may not alter your vote between rounds unless your previous choice has been excluded. Then EVERYBODY votes again. And so on, until one candidate has an overall majority in the decisive round. Every vote is counted in every round. No one gets more votes than anyone else.

Marking ordered preferences on the original ballot paper does not alter this one jot.

Parties cease accumulating votes once they have been excluded. They are left with the total they had at the point of exclusion. If Ukip (say) is excluded at an early stage it will not have much to trumpet. (And a party which finds it has received votes transferred from BNP supporters will have nothing to trumpet at all.)

Under FPTP there is no “real” round, since it is impossible to tell which of a party’s votes were cast positively for that party and which negatively against that party’s nearest rival.

• MorningTory Says:

Well, that’s a matter of perspective isn’t it. Under an Exhaustive Ballot I get to choose who I vote for in each round. Indeed, each round can be considered as a separate election. Under AV, I do not get to decide (the system decides for me on the basis of the preferences I state at the start of the content). The presence or absence of a candidate might easily affect my preference order. How on earth, then, can I decide up-front who my preferred candidate will be in each round?

Under AV, [some] ballot papers are marked mores than once, are counted more than once, and influence the outcome of the election more than once. It’s pretty difficult to see how that is not more than once vote! Especially, as some ballot papers are marked more than once, but are only counted once, and only influence the outcome of the election once.

The fact that so many Yes campaigner say AV would would allow them the chance to vote with their heart AND their head suggests that deep down, they know it’s more than once vote too.

Parties will quote their support on the basis of the total number of votes they received. Those that go out in the first round are surely entitled to claim that support, are they not? They were first choice votes after all… [Incidentally, I suspect we’ll see a large rise in BNP support as people will no longer see it as a “wasted vote” because they can also put down a vote for a “credible” candidate too (most likely Labour…).

But what of the MPs that get in claiming that more than 50% of the voter voted for them? Well, they are entitled to say that also, are then not?

The problem is that is all adds up to quite a lot more than 50%!

• MorningTory Says:

100% I mean…

• WJ Says:

“Under AV, [some] ballot papers are marked mores [sic] than once, are counted more than once, and influence the outcome of the election more than once.”

That ‘[some]‘ is misplaced. All ballot papers influence the outcome of the election exactly the same number of times. AV is exactly equivalent to recounting every single ballot every round after the supporters of unpopular candidates have had their first choices removed, so the fact that some ballot papers are counted more than once is only a matter of convenience: since we know that the supporters of popular candidates are able to keep supporting their favourite candidate, there is no point in counting them again.

115. Jonathan Phillips Says:

While FPTP distorts results away from overall proportionality in a rather random way, AV has the potential to do it systematically.

If large numbers of voters regard a particular party as leprous and an “anyone but them” attitude sets in, then that party could find itself winning fewer seats than its rivals despite receiving more votes.

Perverse results of this kind can happen with FPTP, of course. But AV does make it easier to punish the unpopular in a systematic way. Nothing wrong with that, of course – helps to make for really decisive results!

• MorningTory Says:

You mean like the 2010 result in which AV could have propped up a deeply unpopular Labour government? Don’t think so…

116. I_want_FPTP Says:

Just a question (and this may have been covered above) – Is it possible (mathematically) for a candidate to go out in round 1, that then has a support in the later preferences that means they would have beaten the eventual successor?

• MorningTory Says:

Of course. A candidate who recieves 1% of first choices and 99% of 2nd preferences could easily go out in the first round. But clearly (assuming the first preferences are split between 3, 4 or 5 cother candidates) he/she is the one that candidate with most overall “support”. Whatever that means….

• Jonathan Phillips Says:

Now that’s an interesting one.

A candidate is the first choice of few but the second choice of many, so that although he/she is eliminated in the first round, subsequent eliminations would somehow feed back and resurrect the corpse?

If I’ve marked as my next choice a candidate who has already been excluded, my ballot paper moves on to my subsequent choice, if I’ve marked one, without stopping on the way. That’s why it does a party no good to be the second choice of many but the first choice of few – and it’s not much better to be the first choice of many but the second choice of few.

This becomes more of a problem, at least in theory, with STV, where winning candidates’ surpluses are transferred as well as the votes of excluded candidates. It is possible for a transferred surplus to push the vote going to an already excluded candidate above the quota required for election. But you really do need computers to operate a recursive count of this type, and in practice “excluded is excluded”.

Quite irrelevant to the matter in hand, of course.

• MorningTory Says:

Interesting, and also quite dammning for AV’s claim to be more representative, is it not?

• WJ Says:

“Interesting, and also quite dammning for AV’s claim to be more representative, is it not?”

Not at all. Since the choice is between AV and FPTP, and the problem you are talking about is much more serious under FPTP, AV is more representative.

You might argue that the problem might be less serious under FPTP, as enough of the 99% of people who put the eliminated candidate second might vote tactically for that candidate, that he/she would win the election. But you would be wrong: there is no reason why voters would cast a tactical vote in favour of a candidate who was only the first choice of 1% of voters.

117. Jonathan Phillips Says:

Please, Morning Tory! I was answering your allegation that AV gives some people more votes than others. I asked you to imagine an exhaustive ballot in which you could n o t change your vote between rounds unless your previous choice had been excluded. That is exactly what an AV election is. And nobody gets more votes than anybody else! I know perfectly well that that isn’t how exhaustive ballots function in fact – it was just a thought experiment.

And how on earth could you influence the outcome of the election more than once, however often your single vote was transferred? If the winning candidate gets in having been your first and my third choice, we have still each influenced the outcome only once! Just the same if the candidate who was your first and my third choice is the runner-up. One person, one vote, one value.

• MorningTory Says:

Yes, I accept that AV simulates an exhaustive ballot where votes who votes for any candidate who wasn’t eliminated get carried over to the next round. In fact, isn’t that the definition of AV?!?! Takes away the good bits from EB…

“how on earth could you influence the outcome of the election more than once, however often your single vote was transferred?”

How do you think they decide which candidate gets eliminated? Do they guess? No, they count the preferences!

The problem is that it is the ORDER in which which preferences are counted that matters, and not the number of them. Some people’s second preferences count, whilst others do not.

And before you write back and say that some people first’s choice don’t count, that’s utter rubbish. There is no such thing as a right to back the winning horse.

• gowers Says:

It’s true that some people’s second preferences count, whilst others do not. Let me illustrate with an example.

You vote Conservative as your first preference and UKIP as your second (say). I vote Lib Dem as my first and Labour as my second (say). At some point it’s down to the Conservatives, Labour and the Lib Dems. The Lib Dems are in third, so are eliminated and I get my second preference, Labour, counted. Meanwhile, you have to stick with your first preference, the Conservatives. In what sense am I better off than you? In what sense have you lost out by not having your preference for UKIP counted?

It’s not obvious that a genuine multiround system might not be better in some respects than AV. But I think most people would prefer to get the voting over and done with in one go, and if you want that then AV is a good approximation to multiple-round voting — it is hard to come up with convincing scenarios where they would lead to different results.

• Mark Wainwright Says:

Tim, I think the kind of situation being referred to is this. Mrs Peacock’s supporters are fairly sure that she is loathed by almost all the partisans of Col. Mustard and Prof. Plum, who will therefore benefit from each other’s second preferences. They themselves dislike the colonel but reserve their special hatred for the professor. In the first round Mrs Peackock is in front with 40%, the other two on about 30% but with Prof Plum slightly ahead, and the Rev. Mr Green is eliminated with an irrelevant 3 votes. Now there will be a second round of voting between the three main contenders.

With multiple rounds, it is open to some or all Peacockites to conclude, *having seen the vote shares from the first round*, that their candidate has no chance of picking up enough votes in later rounds to win, and that one way or another the broad Plum-Mustard consensus is therefore going to win the seat; and thus to switch their vote to Col. Mustard in order to keep out Prof. Plum. Under AV they don’t have that luxury.

I doubt this scenario would play out very often in practice, but I suspect that Morning Tory – and a lot of afternoon and evening Tories, too – fear that it would happen all the time, with the Tory candidate in the villainous role of Mrs Peacock. I don’t have much sympathy for them, but I do have a little. I think the idea of actually running multiple rounds would be a nightmare – annoying to voters and expensive – and am happy that AV does pretty much the right job almost all the time, and a much righter job, even in this case, than FPTP.

• MorningTory Says:

Tim:

“In what sense have you lost out by not having your preference for UKIP counted?”

I haven’t been ABSOLUTELY disadvantaged (in terms of influence) but I have been RELATIVELY disadvantaged by the fact that you have been unfairly advantaged.

There a parable in one of two sons approaches his father to ask for his inheritance early. He goes away, lives the life of Riley and blows the lot. The other son stays at home takes care of the family farm. When the profligate son returns, the father welcomes him back. And when the father dies he gets half of what’s left. Jesus tells us that it is right to welcome back the profligate son. But then Jesus is a was a complete mug – which is probably why he ended getting fvcked over by one of his best mates. I can’t help thinking that the sensible son would be seething with anger at the inheritance situation.

The profligate Green Party/UKIP/Communist/BNP supporter squanders his votes and is rewarded with another.

And yes, a genuine multi-round system would be impractical. The question is whether AV is a good aproximation of a multi-round system.

Mark:

That’s wasn’t what I had in mind. I will repeat what I have said elsewhere – I don’t think the Tories would suffer too bandly under AV. My issue is with the system.

Your scenario probably would happen more than you think, but it would also work against Labour in the Home Counties and in rural area, so I think the net result would probably be approximately. There’s quite a lot of people in this country (including the deputy prime minister and the business secretary) that delude themselves into thinking there’s a “progressive majority” out there. Yet the evidence suggests that 40% of Lib Dems would have put the tories down as their 2nd preference instead of Labour.

118. haim shalom Says:

I just wanted to thank Gower for this highly amusing little rant. He is spot on. I don’t really care, having left Britain for a democracy with no monarchy and proportional representation, but I just find it hilarious some of the things people are pulling out to defend what I will now refuse to call FPTP (after all, wtf is the post?). One thing the writer should have mentioned is that in the current climate, the Lib Dems are the only CURRENT party who will probably benefit. Tories won’t because they never do, Labour won’t because it will help sure up the Lib Dems when they battle to take back the house (to use an americanism). But it is not important whether in the short term it will benefit the stinking Lib Dems (AKA Tory henchmen). In the long term it will bring Britain closer to democracy, and will actually allow for people to get more involved in politics and maybe create a workable multi party system. It is not the best system, but it is the best of a bad bunch at the moment.

119. MorningTory Says:

“AV is a good approximation to multiple-round voting — it is hard to come up with convincing scenarios where they would lead to different results.”

It’s not actually that hard, but it’ll have to wait for another day as the wife doesn’t like me to debate online whilst we’re supposed to be watching moves together.

120. RodCrosby Says:

Condorcet only considers ‘broad’ support, to the exclusion of everything else.
FPTP only considers ‘core’ support, to the exclusion of everything else.

AV considers both – you need enough core support to stay in the race, and enough broad support to carry you over the finishing line.

And you could say AV is intrinsically biased towards first/higher preferences – they are the sine qua non for winning, after all.

121. Andy JS Says:

This has nothing to do with maths so apologies for that, but I think it’s interesting (though perhaps blindingly obvious) to note that university towns/cities such as Cambridge will in my view probably have some of the highest YES votes in the AV referendum. Therefore for the result to be YES overall places such as Cambridge will in my estimation need to register a fairly comfortable YES vote for there to be any hope of an overall YES. So if areas such as Cambridge come through fairly early in the counting process and the result is a NO it would almost certainly mean that the overall result is NO. Of course I personally hope this doesn’t happen because I support a YES vote. In other words I’d be amazed if Cambridge, Oxford, etc. vote NO but YES still wins.

122. Gil Kalai Says:

One aspect of the current system is that there is a huge incentive for a party not to split and for large political forces to form. (In fact, there is strong forces towards a 2-party system where the main incentive for the third party is the hope to become the second.)

This might be very different under AV. There may be direct incentives for parties to split in order that the combined array of parties will appeal to a larger number of voters. The discussion seems to assume that the overall political picture will remain pretty much as it is. Is there strong reasons to believe that AV will not lead to many-parties parliament?

• Jonathan Phillips Says:

Mightn’t AV tend rather to lead to the formation of two blocks or alliances, rather than to a number of parties competing each with all of the others? The electorate would then be able to determine the balance of power within each block.

You can draw only tentative conclusions for one country from another’s experience, but in Australia there is a permanent alliance (which they call the Coalition – I expect that’s what confused Prescott) of the two parties of the right, both of which can stand candidates in the same constituency without splitting the right-wing vote, facing a single party of the left. The two-round system in France has tended to produce a similar result, now threatened by the rise of the FN.

It’s true that a party that splits is less likely to suffer under AV than under FPTP, since under the latter both bits might get squashed, whereas their votes could still cumulate under AV. Would that tend to promote splitting? And would it be a good or a bad thing if it did? Might it not be healthy for there to be two main blocks, each consisting of two (or more) parties committed to working together but putting up their own candidates, so that voters could determine their relative power? But as for parties deliberately splitting with the hope of hoovering up more votes, or of creating “daughter” parties with the same aim – a far-fetched scenario?

Please God we get the opportunity to find out what happens under AV – could it be worse than what we get now?

123. Mark Cobley Says:

Excellent post. I was already voting Yes but this has furnished me with all the arguments I’ll ever need when discussing this with friends and acquaintances who might plan to vote No.

I only have one comment, which is a possible answer to your question “WTF is the post?”

Is it possible that the “Post” in “First Past the Post” refers to the (usual) requirement to get an absolute majority, i.e. more than 50%, of the seats in the House of Commons in order to form a government? As per Jon Snow’s excitingly overcomplicated election-night graphics, the potential Prime Minister who is “First Past the Post” is he whose party gets to this magic number first; hence, that is the winning post referred to in the horse-racing analogy.

I’ve no idea whether this is actually the correct derivation, and it would need to predate Jon Snow obviously, but I can imagine some Victorian coining the term with reference to Gladstone or whoever needing more than half the Commons’ seats.

• gowers Says:

The thing about that is that it applies equally to any system for electing MPs.

• Andy Says:

I think you are correct Mark. Not suggesting such a ‘post’ is the right or even wrong way to form a government, but in the instance of the UK’s FPTP system, the ‘post’ is that number of seats required to form a government, a number that is greater than the total of all the remaining seats. For instance, when I was being taught about the system at A-level, I think there were 659 seats in the HoC, and therefore the ‘post’ was 330.

• Mark Cobley Says:

I should add, though, that it’s still a manifestly stupid name; as you point out, if the “post” is a Parliamentary majority then FPTP is a useless term for distinguishing the system from any other, as democratic governments elected under other voting methods generally also regard a Parliamentary majority as the “winning post”. And it remains a stupid name for the vote-counting method in individual seats, where it’s entirely misleading.

And of course, I may just be entirely wrong about the term’s origin. If anyone actually knows how our voting system acquired this odd name I’d be nerdishly interested…

Until then I’d stick with your slogan. WTF IS the post?

124. RodCrosby Says:

er I guess, under FPTP the “Post” is the number of votes cast for the guy that came second…

Not a very useful definition, I agree.

125. WJ Says:

“you (but not other people) have more than one vote”

It is a fallacy to suggest that people have a different number of votes under AV. If you really want to look at it that way – under AV, everyone has the same number of votes (unless they don’t list all their preferences, in which case the result should mean nothing to them anyway). If you vote for a candidate which gets more first-preference votes, however, you are allowed to cast all of them for your favourite candidate. If you vote for a candidate who is eliminated, then you have to cast some of them for your lower preference candidates. As gowers says, GETTING MORE BITES OF THE CHERRY IS A DISADVANTAGE STUPID!

126. WJ Says:

Comment posted elsewhere: please delete the above post (and this one).

127. tek-monkey Says:

I’ve asked in numerous places, but never had a straight answer. How can the Conservatives say AV is unfair if a variant of that is what they use to elect their own leader? If FPTP was fairer, why not just use that? What is the point in unfairly whittling the candidates down to 2 before having a proper vote (using multiple rounds, to allow rethinking of votes), if just letting the members vote on them all in a single ballot is fairer?

128. RodCrosby Says:

Unsurprising…

If it walks like a duck, quacks like a duck, and has the same mathematical properties as a duck…

It’s NOT a duck, according to the Tories.

If you’d asked an honest Tory a year or two ago why they use their system, whatever they prefer to call it, instead of FPTP…

…the answers would be straight out of the YES2AV manifesto.

I heard a lying little git called George Eustice claiming tonight that “it’s FPTP”

Thank you for taking the time to write such an informative and lucid article – it really has cleared an awful lot up for me!

The one thing I still don’t quite understand is your rebuttal to the charge that ‘AV is unfair because the least popular party gets its second-choice votes counted first’. In your hypothetical situation you show that a BNP voter, whose first choice candidate is eliminated first, would get no more of a say than a Lib Dem voter, whose candidate is eliminated second.

But what about a scenario where two parties are both close to gaining 50% of the votes with first preferences alone. For example – say Conservatives have 42%; Labour 40%; Lib Dem 10%; BNP 8% [obviously these results are unlikely to occur in practice!]. Now if all BNP voters made the Conservative candidate their second preference, then the Tories would win this seat. It seems unfair in this case that the Lib Dem second preferences are not taken into consideration – those who backed the least popular party are in effect the king-makers. Does that make sense?

Apologies for the lengthy question, but, not being a mathematician myself, I do actually find AV rather difficult to get my hear around. But of course that’s not a reason for voting against it – complex things can actually be rather good! Thanks.

• Ken Says:

I think that in the example you give, the Conservatives wouldn’t actually win after eliminating the BNP and counting their second votes as they need more than 50% to win. In your example, the next step would be to eliminate the Lib Dem and count their second votes in which case the Conservatives would have 50% as would Labour (assuming all Lib Dem 2nd votes go to Labour). This is clearly highly unlikely. Since the total number of votes being used is conserved (i.e., if n people have voted, the total number of votes being counted will always be n) once someone has more than 50% of the vote, it can never be the case that eliminating the next party and counting their second vote (or third or whichever is next) could lead to another candidate having more than 50%.

To expand your example slightly. Imagine the Conservatives have 42%, Labour has 40%, Lib Dems have 9.9% and BNP have 8.1%. Eliminating the BNP and counting their 2nd vote gives the Conservatives 50.1. Even if we went on and eliminated the Lib Dems (and assuming all their 2nd votes goes to Labour) Labout would only have 49.9%.

• Tom Says:

Sorry Ken, that’s not quite right. This is a weakness as far as I can see, because once you start to look at second preferences you’re essentially dealing with a second set of votes.

It’s quite possible that the second preference of the Lib Dem and Labour voters all name a fifth party, in which case the order of transfer does matter as between them they can muster 50% (or more, if the first round figures are adjusted slightly). In that case you end up with a different result if you transferred Labour then Lib Dem then BNP than if you transferred in the “correct” order.

Whether this extremely rare situation is a fatal flaw is a different matter, since (as the no campaign seems keen to remind us) everyone has an equal vote regardless (as they seem less keen to remind us) of who they vote for — and the smallest group of voters are the ones least likely to push anyone over 50%.

It’s certainly a downside to the system, but it’s handled in the fairest possible way and I’m not going to give up on the vast improvements AV brings just because of freaky edge cases!

• To the left of centre Says:

Tom, what I was trying to point out was that under the current AV system (proposed) once a candidate (call this person candidate A) has more than 50% of the votes counted, transferring votes from another candidate cannot reduce candidate A’s percentage. What I did get wrong was that the number of votes counted is not strictly conserved. It can get smaller as first (or subsequent) votes are eliminated if some voters did not make additional preferences.

• Tom Says:

Yes, I was mistaken. Pointing out that your vote share can’t decrease unless you’re knocked out makes things much clearer.

130. Hal Says:

This is the first coherent argument I have seen that expands on the reasons why Yes to AV is the correct choice.

I am persuaded to do so by this post – and would add that there is an element of being highly dissatisfied with the current system, and wanting a change of any kind. I hasten to add that this is *not* about sticking two fingers up to the tories, but a genuine attempt to change our political system for the better.

I don’t think AV is the best answer, but it will introduce a new dimension to our politics, and probably force the issue of how to create a more fair system. With luck, we’ll get a further referendum in my lifetime (I was too young to vote in the Common Market referendum).

I’d prefer a PR system that loses the constituency link, personally – I see little value in maintaining the link when so many people wouldn’t use it anyway. I am in a ‘safe’ seat, and can think of nothing worse than talking to the incumbent MP about issues I feel strongly about and which I know he will diametrically oppose in parliament if toeing the party line. Thus I won’t talk to him, and prefer to work on a national picture… however, AV won’t give me that, but it gets me closer to achieving it than FPTP.

Thank you for this article – it is long, but the debate is important enough to merit a detailed discussion, and you can’t get that from a bullet point list. This post was exactly what I needed to help move my thinking along.

131. Daverinio Says:

@Mark Wainwright

“With multiple rounds, it is open to some or all Peacockites to conclude, *having seen the vote shares from the first round*, that their candidate has no chance of picking up enough votes in later rounds to win, and that one way or another the broad Plum-Mustard consensus is therefore going to win the seat; and thus to switch their vote to Col. Mustard in order to keep out Prof. Plum. Under AV they don’t have that luxury.”

Errrm – yes they do. They simply put Professor Plum Lower down the list of preferences than Colonel Mustard, or express no preference for Plum at all. If indeed they hated both Mustard and Plum but Plum more than Mustard it would make sense for the Peacockers to use the system in this to make the Plum victory less likely.

Of course, with FPTP many of those Peacockers may decide to vote Mustard anyway in order to keep Plum out, denying themselves an opportunity to express their support for their desired candidate.

• Mark Wainwright Says:

In the scenario I gave, it doesn’t matter what they put after their first preference, as Mrs Peacock is always going to come second in the election – when she is eliminated it’s all over and it’s too late for their second preferences to be used.

You don’t need to convince me of the inferior qualities of FPTP.

132. Jonathan Phillips Says:

I’ve come to the conclusion than Morning Tory might be either an idiot or slightly insane. How do other people feel?

If boy one actually gets his first choice the election is over. If a mass of people get their first choice the election is over. If a mass of people all direct that their votes be transferred to a candidate who is in a position to win and he/she does win, the election is over.

It is not possible for two people with non-coincident preferences both to get their way in a system with only one winner.

Those who still refuse to understand how AV works and want to see a analogy which is actually meaningful should watch http://bit.ly/g73aDr.

It is of course possible to elect several candidates of different political hues in a system with multi-member constituencies (i.e. for two people with non-coincident preferences both to get what they want), as happens with the Single (note the word!) Transferable Vote introduced by successive Conservative governments for local, Euro and Assembly elections in NI. And by-elections in such a system are conducted by AV. If such forms of voting are so objectionable, why did the Tories introduce them in the first place and why aren’t they campaigning for their abolition now?

133. Jonathan Phillips Says:

If I mark the Green candidate as my first choice and he/she is later excluded, so that my second preference e.g. for the Labour candidate comes into play, and the Labour candidate is subsequently elected, then I have influenced the outcome only once.

And I have not been biting into any cherry: he who gets two bites of the cherry gets two bits of said cherry; he who marks two choices and gets the second is only getting one MP.

• MorningTory Says:

“And I have not been biting into any cherry: he who gets two bites of the cherry gets two bits of said cherry; he who marks two choices and gets the second is only getting one MP.”

No, but you have spent £2 on the mechanical arm thingy at the fairground.

• gowers Says:

But unfortunately, the second time round you are forced to hand over your prize to someone else.

• MorningTory Says:

“But unfortunately, the second time round you are forced to hand over your prize to someone else.”

What’s relevant (to this part of the debate) is the amount of democratic captial you get to spend, not whether you ultimately end up with a prize.

• gowers Says:

We’re all given one ballot paper to do with what we like. That is our democratic capital and it’s the same for everybody.

If you have an alternative definition of the phrase, then you need to say carefully what it is and why it matters.

I suspect that your objection really amounts from an inability to shake off the FPTP mindset: if we held an election under FPTP and the party I supported came third, I couldn’t legitimately ask to change my vote, and if I did get to change my vote then I would have had an unfair advantage over everyone else. But that is not the situation if we have an election under AV. Then everyone plays by the same rules.

• MorningTory Says:

I apologise if there’s an established use of the phrase, though I think my meaning is clear. But in case it isn’t, I mean “opportunities to have my opinion taken account of”. (Not so very different from your definition, I think). I’ll ignore the “one ballot paper” spin (it might be one bit of paper but it can be marked any number times).

Of course everyone is playing by the same rules, but the point is that depending on which candidate you vote for, you end up with a different number of opportunities. Many AV supporters say, “Under AV I would be able vote with my heart AND my head.” They know that depending on how they mark their ballot paper they can engineer more opportunities to have their opinion taken account of.

I don’t know about a “FPTP mindset” but there’s definitiely an AV mindset. AV supporters see a vote that doesn’t directly influence the outcome of an election as wasted, or worse still, they say, “I live in a safe seat, so my vote has never COUNTED”. Of course it counts! A quarter of a million people voted for the Green Party in the last election with no expectation that their candidate would win (with the exception of those in Brighton Pavillion who hoped their candidate might). We now know there’s [at least] a quarter of a million Green party supporters out there. It didn’t help them get many seats, but it does translate in political power.

• gowers Says:

I think you’ve misunderstood the heart/head complaint. If you support one of the two front runners in an FPTP election, you get to vote with your heart and your head, for the simple reason that your heart and head say the same thing. But if you support the third party, you are denied that opportunity.

Under AV, everyone gets to vote both with their heart and their head. You put your heart preference first, and if your head preference is different, then you put it lower down. If it’s the same, then you’re even better off because you’ve got a good chance of getting your heart’s desire.

If you support the leading candidate you get your opinion taken account of in every single round of the counting. It just happens to be the same opinion every time. The people who support less popular candidates also get their opinion taken account of in every single round of the counting, but they have to settle for lower and lower preferences.

When people talk of wasted votes, they refer to votes that have no chance of influencing the outcome of the election. It is possible to use votes to make gestures, but they feel like pretty futile gestures when you support a party like the Greens under FPTP (though I agree that they wouldn’t be that much better off under AV, at least in the short term).

• MorningTory Says:

“I think you’ve misunderstood the heart/head complaint.”

I haven’t misunderstood it at all. If your heart and your head are saying different things it’s because your heart wants a candidate that is unlikely to win. So, as a grown-up, you have to make a choice about what to do. That really shouldn’t be too much to ask.

Under AV you can register your support for a fringe candidate, and still vote for whichever mainstream party you favour most.

“It is possible to use votes to make gestures, but they feel like pretty futile gestures when you support a party like the Greens.”

You have a very different perspective than I. As I have said elesewhere, it seems to me AV is more concerned with maximising each voter’s possible influence (even though it differs depending on which partie(s) you support) whereas FTPT is more concerned with treating each voter the same.

• gowers Says:

“So, as a grown-up, you have to make a choice about what to do. That really shouldn’t be too much to ask.”

Let me try to explain why I think that is unfair by giving an example.

Suppose you support the Lib Dems and at the last election they came third in your constituency, but were not too far behind Labour who came second. Let’s say the figures were something like Conservatives 38%, Labour 30%, Lib Dems 25%, others 7%. Suppose that the Conservatives have been in power and are now very unpopular, and that the Lib Dems have been putting in some strong showings in the polls. Under FPTP there is a very real possibility that (i) enough people have the Lib Dems as their favourite party (the one they would choose if they could make the decision all on their own) to get the Lib Dems elected, but also that (ii) enough of them will judge that the Lib Dems probably won’t win that they end up plumping for Labour or the Conservatives.

One of the great things AV does is remove the need to guess how other voters will vote. In the situation above, if all those people like the Lib Dems they will put them first and the Lib Dems will get elected. If they don’t, then they won’t, and they won’t.

And finally, AV treats all voters the same: it gives them identical ballot papers. The fact that voters use those ballot papers in different ways is up to them.

I would say that AV is concerned with giving voters a chance to express more accurately what they want. That is what makes it more democratic than FPTP.

• Anonymous Says:

“One of the great things AV does is remove the need to guess how other voters will vote.”

It doesn’t do that. The conditions in the scenario you give are exacly those in which AV might throw up a monotonicity failure. The Labour supporter is not sure whether to Labour (and risk Lib Dem 2nd preferences pushing the Tories over the “magic 50%”) or to vote Lib Dem knowing that Labour 2nd preferences will mostly go to the Lib Dem candidate and ensure the Tory candidate cannot win.

“And finally, AV treats all voters the same: it gives them identical ballot papers.”

It’s true that it applies the same set of rules to all voters. But because the algorithm is conditional, it handles the different voting patterns differently.

• gowers Says:

Sorry, I didn’t mean “remove” but rather “greatly reduce”.

FPTP handles different voting patterns differently: if you vote for the candidate who gets the most votes, your candidate gets in; if you don’t, then he/she doesn’t.

• MorningTory Says:

The above was me. No idea why it posted anonymously. I wish to correct myself. It’s true that the condition you outline are not dissimilar to those that might give rise to monotonicity failure (which also requires a bit of guesswork on the part of the voter), but I then proceeded to give an example that wasn’t monotonicity failure all. Ain’t AV complicated?!?!

Nevertheless, my central point was correct; i.e. that it is not true to say AV removes the need to guess how other voters will vote. For that to be the case, you would need to be sure that all Labour & Lib Dem 2nd preferences would go to each other. That’s not a real-world scenario.

• Anonymous Says:

“FPTP handles different voting patterns differently: if you vote for the candidate who gets the most votes, your candidate gets in; if you don’t, then he/she doesn’t.”

Or to put it another way, “Most votes wins”. I think I can live with that difference in handling voting patterns!

• gowers Says:

Similarly, I can live with the differences implied by “If your higher preferences are knocked out, you have to make do with lower preferences.”

• Mark Wainwright Says:

Ok, Morning Tory, let’s put it another way. Let’s imagine there’s an election in your constituency with four candidates and your actual preferences are 1. Tory, 2. UKIP, 3. LD, 4. Labour. The election is being conducted under AV, much to your disgust, but still, you want your voice heard so you cast your ballot accordingly.

Now everyone likes to have an edge, don’t they? If someone’s going to have an unfair advantage, you’d generally hope it was you rather than the other guy. So would you be thinking, ‘Gee, I hope the Tory, UKIP and LD candidates are eliminated, in that order, because then I have a big advantage over those unfortunate Labour voters?’

Wouldn’t you like to have the last laugh by getting four votes where they only get one?

No?

In that case, you can’t seriously believe that AV gives an ‘unfair advantage’ to people in that position.

It seems to me that you have recognised that redistributing someone’s vote compensates them partially, though not fully, for the *disadvantage* of not having their favourite candidate elected. You are already *advantaged* by supporting one of the largest parties. Like the privileged in all times and places, you have become so used to your privilege that you see it as a right, and a modest attempt to redress the balance as giving an unfair advantage to others.

• MorningTory Says:

“If someone’s going to have an unfair advantage, you’d generally hope it was you rather than the other guy.”

I would hope that NOBODY had an unfair advantage. But, yes, obviously I would seek to maximise the effectiveness of my vote under whatever system that the election is being run under.

“It seems to me that you have recognised that redistributing someone’s vote compensates them partially, though not fully, for the *disadvantage* of not having their favourite candidate elected. You are already *advantaged* by supporting one of the largest parties. ”

With repsect backing the three-legged horse in the Grand National and then claiming you were disadvanted by is a bit laughable. I am “advataged” only because I choose to vote for a mainstream party. If I choose the Monster-Raving Loony Party instead, I am going to have to live with the fact I probably wont have voted for the winning candidate. I can either accept that because I want to make a statement, or I can choose to use my vote differently.

“Like the privileged in all times and places, you have become so used to your privilege that you see it as a right, and a modest attempt to redress the balance as giving an unfair advantage to others.”

What?!?!?!

• gowers Says:

OK let me try to give a scenario that illustrates as clearly as possible where AV scores over FPTP. Suppose you are in a seat where for one reason or another there are two credible Conservative candidates, one officially Conservative and the other an independent who promises to vote with the Tories. Perhaps there was some dispute and a number of people felt that the person standing as an independent should have been the official Conservative candidate, or something like that. Under FPTP, the votes might work out like this.

Conservative 30%
Labour 38%
Independent Conservative 18%
Lib Dem 10%
Others 4%

The result would be that Labour slipped in as a result of the splitting of the Conservative vote.

It’s clear that this is basically a Conservative constituency (let’s assume that enough of the Lib Dems and the others vote Conservative as their second choice to tip them over the 50% mark). Those Conservative voters would all prefer a Conservative or an independent Conservative to a Labour MP but because FPTP forces them to choose between two very similar candidates they lose out.

In theory, the interests of the Conservative supporters would be best served by having their own election to decide whether they will all vote for the official candidate or all for the independent candidate. That is, what they would really like to do is coordinate their votes so that their voice can be heard properly. Unfortunately that’s impossible.

Or is it? Oh no, wait a moment. AV allows them to do precisely that.

• Mark Wainwright Says:

“I am “advantaged” only because I choose to vote for a mainstream party.”

No, your advantage is that you actually PREFER a mainstream party; not merely that you choose to vote for one. Someone who does not prefer one of the mainstream parties simply cannot get the same advantage as you, however they vote.

Your claim that your advantage is merely in ‘choosing’ to vote for one is disingenuous. It is identical in structure to the argument, which so many people made for so long, that laws against homosexuality were not really discriminatory since anyone could ‘choose’ to take an opposite-sex partner. In some sense, anyone could (just as anyone can vote for a mainstream party); but the laws (resp. voting system) discriminated against people for whom that choice was unappealing.

You haven’t answered the question: in the 4-way marginal I described, would you hope for your first three choices to be eliminated so that you got the ‘unfair advantage’ of four votes? If not, your claim to believe people are advantaged by ‘extra’ (i.e. transferred) votes is simply incredible.

• MorningTory Says:

@ Gowers:

“That is, what they would really like to do is coordinate their votes so that their voice can be heard properly.”

Isn’t that what the party’s own selection process if for?

“No, your advantage is that you actually PREFER a mainstream party; not merely that you choose to vote for one.”

Do you think I agree with every aspect of every tory policy? Of course not! The Conservative Party is the closest approximation to my views that has a realistic prospect of electoral success. I have to make the same compromise as anyone elses. Admittedly it’s a little easier for me because I have fairly mainstream views.

“Your claim that your advantage is merely in ‘choosing’ to vote for one is disingenuous. It is identical in structure to the argument, which so many people made for so long, that laws against homosexuality were not really discriminatory since anyone could ‘choose’ to take an opposite-sex partner. In some sense, anyone could (just as anyone can vote for a mainstream party); but the laws (resp. voting system) discriminated against people for whom that choice was unappealing.”

That’s absurd.

“You haven’t answered the question: in the 4-way marginal I described, would you hope for your first three choices to be eliminated so that you got the ‘unfair advantage’ of four votes? If not, your claim to believe people are advantaged by ‘extra’ (i.e. transferred) votes is simply incredible.”

No, I didn’t answer it. I think I dismissed it as being daft.

• Mark Wainwright Says:

Admittedly it’s a little easier for me because I have fairly mainstream views.

Well, that’s all I was driving at. I’d like it to be equally easy for other voters.

No, I didn’t answer it. I think I dismissed it as being daft.

Well you’re right – it is daft! It is daft to imagine a voter whose favourite candidates are all eliminated has an advantage over one whose favourite wins. That’s why despite all you say we don’t really believe you think so, being confident, as most of us are, that you aren’t daft

• MorningTory Says:

“Well, that’s all I was driving at. I’d like it to be equally easy for other voters.”

I repeat, the compromise that I have to make under FPTP is EXACTLY THE SAME as the compromise someone who supports a finge party must make. It is a compromise between the degree to which a candidate’s views accord with your, and their likelyhood of electoral success. OF COURSE, if you choose a candidate who has little likelihood of electoral success, then that compromise becomes a harder choice. Why shouldn’t it? On a moral level, why shouldn’t it?

“You haven’t answered the question: in the 4-way marginal I described, would you hope for your first three choices to be eliminated so that you got the ‘unfair advantage’ of four votes? If not, your claim to believe people are advantaged by ‘extra’ (i.e. transferred) votes is simply incredible.”

I suppose I must answer this since you seem to be attempting to claim some kind of “victory” here. The best possible “outcome” for a voter in any election is either:

a) to see a candidate they strongly support win; or (depending on their perspective),

b) to see a candidate they particularly dislike lose, or

c) both of the above.

The voters objective is not “to maximise the number of times their opinion is taken account of.” So, obviously, no I don’t want to see my favoured candidate(s) eliminated. But clearly, having your opinion is taken into account more than once is an advantage in achieving one or more of those objectives.

What many with the AV mindset cannot get their head around is that to support a candidate that didn’t win is not the same thing to be disenfranchised!

• gowers Says:

“What many with the AV mindset cannot get their head around is that to support a candidate that didn’t win is not the same thing to be disenfranchised!”

Well I have the AV mindset and I can get my head round that. However, I think that if a voter feels unable to support their favourite candidate (because that candidate is likely to come third, say) then “disenfranchised” is not a bad word to use. Under AV you can vote for that candidate and express a preference between the other two. And if the candidate you really like still comes third, nobody says that you have been disenfranchised. I also think that if the candidates split between two fairly similar ones, both on 30% and one very different one on 40%, then the inability of the 60% of voters who like candidates of that general kind to have their way over the 40% of voters who like candidates of the other kind is a sort of disenfranchisement. See this poster if you don’t understand what I’m on about here.

• MorningTory Says:

“FEELS unable” [my emphasis]. That more or less sums it up for me. I FEEL that I should have a Ferrari, but life is just not like that.

• Jonathan Phillips Says:

Oh dear.

If I want to show truthfully which party and in particular constituencies that could be a Lab or Con candidate) then my vote and my opinion can go hang for all the difference it will make. One person, one vote, no value.

But it’s perfectly OK for me to *pretend* I support a party I don’t much like because I can’t stand the other lot – that’s real life, that’s just the way things are, and I should be grown up about it, like it or lump it.

It’s also a lie. How can democracy be built on systematic lying? At least AV lets us show what we really think, even if we don’t all get what we really want.

• gowers Says:

If you want a Ferrari analogy, here goes. The father of a lucky 21-year-old boy says, “Son, I’m going to buy you a car, and I think you should have some say in what kind of car.” They go to a dealer, and in the forecourt there is a Ford, a Vauxhall and a Ferrari. The son says, “I’d like the Ferrari please.”

FPTP is like the furious father who says “Right, you’re getting the Ford,” despite the protestations by the son that he prefers the Vauxhall. AV is like the father who says, “It’s a pretty cool car I agree, but you know I can’t possibly afford it. Which would you prefer out of the other two?”

Whenever you say “life is not like that” you ignore the inconvenient fact that under AV life WOULD be like that. (I don’t mean that you would always get the candidate you wanted, but that you would always be able to express your preference for the candidate you wanted.)

I’ve got to the stage where I feel we’re going round and round in circles, so I may have to stop replying to your comments now (even if I think you’ve said something wrong and feel the temptation to point out why). This is your opportunity to have the last word …

• MorningTory Says:

Of course we are going round in circles. We have been for some time! It’s because we are starting from different places.

What frustrates me about this whole discussion is that people in favour of the sinle-member plurality system are often caricatured as being one or more of the following:

a) not able to understand AV;
b) wanting to protect party advantage (for whichever party); or

None of the above are necessarily true. Indeed, it may be equally true of those in favour of AV.

Whenever you say “life is not like that” you ignore the inconvenient fact that under AV life WOULD be like that. (I don’t mean that you would always get the candidate you wanted, but that you would always be able to express your preference for the candidate you wanted.)

You CAN “always… express you preference for the candidate you” want! A quarter of a million people voted Green in the 2010 election knowing that their candidates almost certainly wouldn’t win. Two and half thousand people in Guildford voted Labour knowing that that the Tories would win and the Lib Dems would come second. I have a massive amount of respect for all of them.

• ChrisP Says:

@MorningTory: Is that the same massive amount of respect you showed when you described supporters of minority parties as backing a three-legged horse?

You keep talking about this as making an “adult” decision between head and heart. I’m sure you’ll understand what I mean when I point out that this is simply argumentum ad hominem, as was the three-legged horse reference. I feel it devalues your argument, which is a shame, if only because it makes it less likely you’ll get a reply to the meat of your argument, and more likely you’ll be dismissed as a troll.

• MorningTory Says:

The three-legged horse analagy was merely meant to illustrate the fact that if you vote for a party that is unlikely to achieve electoral success, then you shouldn’t be surprised or put-out when it turns out they don’t win.

“I’m sure you’ll understand what I mean when I point out that this is simply argumentum ad hominem, as was the three-legged horse reference. ”

“I feel it devalues your argument, which is a shame, if only because it makes it less likely you’ll get a reply to the meat of your argument, and more likely you’ll be dismissed as a troll.”

I’m not really sure what a “troll” is. Gowers set out his views and invited others to comment on them… which is what I have done. Is that not the idea?

• ChrisP Says:

Because the implication is that the other option — being allowed to vote both head and heart — is childish, and hence wrong. It’s not a logical or reasoned argument, merely name-calling. Hence, ad hominem.

“Gowers set out his views and invited others to comment on them… which is what I have done. Is that not the idea?”

Yes, and I appreciate fully your contribution, it has been very valuable to me and I hope to engage you further. However, as well as reasoned arguments you also use troll-like tactics (I recommend a quick Google if you have not come across the term before), which serve to detract from the important parts, for a number of reasons.

• MorningTory Says:

“Because the implication is that the other option — being allowed to vote both head and heart — is childish, and hence wrong. It’s not a logical or reasoned argument, merely name-calling. Hence, ad hominem.”

I don’t think it implies that at all. And even if it did, it would be an attack on the system no an individual (or even group of individuals). But I am very sorry if anyone has taken it that way.

134. MorningTory Says:

There’s no need to be impolite. I can actually understand your point of view. You, on the other hand, stubbornly refuse to accept that there’s another way of looking at things.

This is a question of values and perspectives.

“Transferable Vote introduced by successive Conservative governments for local, Euro and Assembly elections in NI. And by-elections in such a system are conducted by AV. If such forms of voting are so objectionable, why did the Tories introduce them in the first place and why aren’t they campaigning for their abolition now?”

Please forget for a moment that I happen to be a Tory supporter! I didn’t personally introduce any such system. I am not campaigning for their abolition.

I am in favour of preseving the existing system for WESTMINSTER elections. Different system are suited to different purposes. One does not use a Phillips screwdriver for a slot screw.

135. Jonathan Phillips Says:

But you have yet to give any explanation of your objections to AV that actually makes sense!

If it’s necessary to counter the “wasted vote” phenomenon in NI why is it ok to allow it for Westminster? If it’s a good idea to preclude the election of candidates who are widely disliked in NI should it be ok to allow this to happen at Westminster?

• MorningTory Says:

They don’t make sense to YOU because you have a particular worldview that you are unable see beyond.

If you can’t see the difference between NI (which was effectively in a state of civil war) and Westminster then there’s not really much point in me even trying to remove your blinkers.

• gowers Says:

I think it’s fair to say that there are indeed relevant differences between Westminster on the one hand and Northern Ireland, or Europe, or mayoral elections. If you believe that FPTP leads to strong government, then you might think that that is a good thing in Westminster and therefore support FPTP. (There are objections to this view, but it’s not nonsensical.) But in a country like Northern Ireland, where there are two groups of people strongly divided along religious or ethnic lines, there is a danger that strong government means that one group gets to walk all over the other one. (This is also a very serious problem under PR if one of the groups has 60% of the population and one has 40%. Devising a system that looks after large minorities is very hard indeed.) In the European elections, the strong-government argument doesn’t apply, since we are electing just a small fraction of the European parliament. And in a mayoral election it doesn’t apply because you’re going to get just one mayor whatever your system. Also, in a mayoral election the vote-splitting problem is worse, because a popular individual standing as an independent has much more chance (as Ken Livingstone demonstrated in London in 2000, though in that particular case he did so well that the split in the Labour vote was not enough to stop him winning, and in fact the outcomes under FPTP or the AV-like system actually used would have been the same).

136. » Dan Snow’s Alternative | Weston-super-Mare East Ward | David Cordingley, Keith Harrison and Mark Johnston – campaigning for you on the issues important to Weston Says:

[...] For a detail look at these issues there are many excellent blogs such as: http://gowers.wordpress.com/2011/04/20/is-av-better-than-fptp/ [...]

137. Gil Kalai Says:

GETTING MORE BITES OF THE CHERRY IS A DISADVANTAGE STUPID!

The question is different: why is it fair that your preferences between the fourth and fifth candidates once your first three candidates were eliminated will have the same weight as the preferences of another voter for the first candidate.

Imagine a devoted conservative supporter who put the conservative candidate first. Suppose that because of he dislikes the left his choices between the labour and social democrate candidate will always be to put the weaker, more stupid, and less competent candidate ahead in order to harm left as much as possible. Why should his preferences between the left candidates get same weight as a person who support the left and prefer the better left candidates win?

• gowers Says:

That’s another good point. I had wondered about whether the best system would be AV but with lower-preference votes having slightly lower weight. This, of course, would not be practical, so one settles for AV as a decent approximation. But another approximation that isn’t obviously worse is a two-round system where all but the top two candidates in the first round go through to the second round and there is then a runoff (unless someone got an absolute majority in the first round). This is, I think, the system in French presidential elections, and it does lead to the occasional strange outcome, such as le Pen making it to the runoff in 2002 with under 17% of the vote (a sort of FPTP-ish problem actually). But I don’t think voters would like going to the polls twice.

The scenario you discuss can happen under FPTP. I might judge that the Conservatives had no chance in my seat and therefore vote for the weaker candidate on the left in order to do as much damage to the left as I could. Should my vote carry equal weight to that of somebody who sincerely votes for the candidate on the left that they judge to be better?

• Mark Wainwright Says:

You could simulate, in one round, a second-round runoff between the top two candidates, using exactly the same ballot papers as for AV, in an obvious way. Considering the drawbacks of running a second round, I do wonder why the French don’t do this.

• Gil Kalai Says:

“The scenario you discuss can happen under FPTP.”

Right, to a much less extent, this is true. But this was not my main point. My main point was that the critique about having several bites at the cherry has some merit: under AV you can express your preference for the conservatives and at the same time also influence which left candidate will be ahead. If there is some obscure movement with no chance that you want to express support for it will be almost a waste not to put this movement on top of your list.

• gowers Says:

I’ve thought quite hard about what you write but haven’t managed to understand it. I still don’t see how AV involves any unfairness.

But let me take one question that arises out of what you say. Suppose you are a Conservative supporter in a Lib/Lab marginal. Under FPTP you have to choose whether to vote Conservative or to influence which of Lib and Lab gets elected. Under AV you can do both. What’s more, having put the Conservatives first your influence on the Lib/Lab battle is equal to that of another voter who supports either Labour or the Liberal Democrats. The question is whether that is fair.

It’s an interesting question because the extent to which the answer appears to be obviously yes depends on the distances between the political parties. If I had the choice between two left-wing candidates, one of whom I slightly prefer but who is likely to come third, and one right-wing candidate, then it seems unfair to make me vote for the “wrong” left-wing candidate or have no influence at all. But if the main battle is between two shades of left and I support a right-wing candidate, then it feels slightly different.

In my opinion, the main drawback with the Conservative voter getting to choose between two fairly similar left-wing candidates is that he/she doesn’t care about the outcome in as genuine a way as a committed supporter of one of the two left-wing parties. But since it is completely impractical (and not obviously a good idea) to have any voting system that gives more weight to people who mind more about the outcome, I don’t see this as a disadvantage of AV.

Going back to the question of fairness, I think it’s important to distinguish two sorts of unfairness. It might be possible to make a case that AV gave some people more of a chance to use their vote to make a gesture without wasting it. But I don’t think it’s unfair if all you are worried about is the outcome.

• Gil Says:

Just to make it clear, my point was not about unfairness. Ranking all candidates give a voter (any voter) an opportunity to promote several agendas at once. It is a bit complicated how to take advantage of this opportunity and it is another complicated matter how the voting method should average out all these rankings (AV seems reasonable in this respect). Things are simpler when the voter has to make a single choice.

Having a right wing supporter that also has a say in the choices of the left wing candidates and vice versa moves us, in some sense, to a sort of a compromize between alternatives faced by voters. We can conjecture that the AV method through the voting method itself and through the parliaments that will be formed will lead to the outcome that on central dividing matters between left and right we will have always some sort of “compromize” and, on the other hand, it will be easier to promote agendas of strong interest to small parts of society. In any case, I do not think AV is unfair (and also I did not understand why the current method is unfair).

• Jonathan Phillips Says:

“Ranking all candidates give a voter (any voter) an opportunity to promote several agendas at once.”

I don’t think this can be true. AV means “If I can’t have this, then I’d like that instead. And if I can’t have that either, then please may I have the other.” In other words, surely, you opt to relinquish (if necessary) any influence over “this” and “that” and are left with influence solely over “the other”.

I have a niggling sense that talk of “ranking” and indeed “preferences” in connection with AV is a little misleading, since it seems to imply something like: “I’d like a lot of this, some of that, and a bit of the other.” What AV offers is a sequence of conditional choices in which *shades* and *strengths* of preference are of no account. Only the order matters.

• Jonathan Phillips Says:

And another thing…

“I do not think AV is unfair (and also I did not understand why the current method is unfair).”

Both are unfair to the parties and to the mass of their supporters across the country, in that there is no relationship between the votes cast by us voters and the seats won by the parties we support.

FPTP is unfair at constituency level to those of us who are forced to choose between:

- showing which party we really and truly support, even if we know it has no chance of winning, and thus seeing our vote go to waste (i.e. we might just as well not have bothered to vote at all for all the difference it made), and
- voting for a party we don’t particularly like in the hope of defeating a party we detest.

(NB in particular constituencies the “no hope” candidate could be Labour or Conservative – it isn’t only minor parties’ supporters that suffer from the wasted- vote syndrome.)

AV ensures that no vote need go to waste and thus puts all voters potentially on an equal footing: one person, one vote, one value.

• MorningTory Says:

“In other words, surely, you opt to relinquish (if necessary) any influence over “this” and “that” and are left with influence solely over “the other”.”

You’ve only relinquished influence over X AFTER you know that the influence was not sufficient to make a difference. Before that vote is counted there a probability that is >0 and <1 that might help take the candidate through next round. After it is counted, the probability is either 0 or 1. Even if it is zero, the voter has still taken some "value" from that vote.

138. whomightyoube Says:

Great article. I am pleased that someone has arrived at very similar conclusions to my own on just about all of the points of argument raised by the “No to AV” campaign. A few points that I would like to add:-

1) Av does not favour the Lib Dems, it does not even fully redress the bias against them that exists under the Furthest Past the Starting Post (FPTP). It does mean that one can safely vote for one’s first choice and in general that will mean an increased Lib Dem vote.

2) If the election staff are paid on an hourly rate then AV would mean an increased cost due to the longer time required to count votes if second and subsequent rounds are required. I have not seen any figures on this and do not know the terms under which they are employed. They could well be doing it for love

3) I am constantly amazed at the general public’s lack of understanding of the AV system, even amongst seemingly educated and intelligent people. I have talked to many people who are adamant that will vote no but are then embarrassed when questioned about how AV works. There are others who do not know the definition of a majority and many who do not understand percentages.

4) Many people, mainly Conservative supporters, will often ignore the rights and wrongs of logical arguments about fairness and representation and see things purely interms of which system will give the result that they want. Such people, I suspect would prefer a dictatorship.

5) An election is not a race. All race analogies are bogus.

139. whomightyoube Says:

Great to see an intelligent and intellectual argument on this subject which should be sent around all academic institutions. There are some seemingly very clever people out there in denial. I have come to very similar conclusions myself on most of the points. The real battle ground however is to be won or lost on a lower intellectual level. An election is not a race in any way shape or form, it is not about fairness to the candidates, but fairness to the electorate.

See many posts that I have made on disqus on the independent website under name whomightyoube.

140. Is AV better than FPTP? (via Gowers’s Weblog) « Verbosity Says:

[...] On May 5th the UK will vote in a referendum for only the second time ever. (The first time was in 1975, when we voted on whether to remain in the EU, or the Common Market as it was then called.) Now we have a chance to decide whether to retain our current voting system, misleadingly known as First Past The Post, or whether to switch to the Alternative Vote. Let me come clean straight away. Although in this post I shall try to write dispassionatel … Read More [...]

141. Dan Says:

Thanks for this article, it’s very useful. Actually the stuff about trying to boil it down into slogans is particularly useful – I’ve turned a couple of them into a flyer/poster design:

http://www.mcld.co.uk/tmp/istoast2.jpg

http://www.mcld.co.uk/tmp/howavworks.png

142. Gil Kalai Says:

A few points:

1) “Please God we get the opportunity to find out what happens under AV – could it be worse than what we get now?”

This is not good sentiment. The UK democracy is a fairly successful one.
And of course it can be worse. The sentiment for changes which are indeed quite strong in all political systems is ususally not justified. The sentiment “it cannot get worse than it is now” is also usually wrong. It is certainly wrong for the UK democratic system.

2) There is indeed a tension between “fairness/the will of the people” with electing a government that can rule coherently. It is well known that this is the case for 3 candidates and more but it is also the case for 2 candidates. When the outcome is 55% labour and 45 % conservative is the “will of the people” (or the fair outcome) that labout will get all the power? This is so obvious to us that we do not question it, but we can very well say that the will of the people is 0.55 labour +0.45 conservative.

3) AV open the door to interesting ways for rather small political movements to have influence which are much stronger than under FPTP. Suppose that there is a national bike lane movement with support of 3-4% of the population in many areas. They can form a party and negotiate with the stronger candadates the second preferences of their supporters. For a social democrate, say, to get extra 2-3% from bike lane people by making a commitement to their cause, can make a huge difference on the outcome. The outcomes will also show quite clearly what the bike lane movement effect was and indicate in how many cases it has a pivotal effect. So the bike lane movement can gain substantial political power without enetering a single person to the parliament. Is it good? I am all for bike lanes but, of course, this was just an example.

• Isaac Says:

In response to point #3…

Whats to stop politicians doing that under the FPTP system? Nothing – other than the same reasons that would stop them doing it under AV.

If you, as a major party, promise things on a similar line to a minority party to secure their voter’s 2nd preferences then you risk alienating your own voters – primarily because the minority parties hold the more extreme views.

Gower illustrated this in part of the original post where he used the example of the Lib Dems and BNP and/or immigration; e.g. Lib Dems appeal to BNP via tougher immigration laws = Lib Dems gain 1 vote from BNP-voters 2nd preferences and lose 10 1st preference votes from would-be Lib Dem voters.

• Gil Says:

Isaac, under FPTP the small interest group can promise support and the politician can promise help. (It is a wonderful think that in political life promises are not binding.) But under AV the small interest group can promise and deliver and prove it. This is a huge difference.

• gowers Says:

Isaac, the actual example I had in mind was that if the Conservatives or Labour tried to woo BNP voters (to get their second preferences) they would probably lose far more than they would gain (because of Lib Dem second preferences).

143. AV vs FPTP | To the left of centre Says:

[...] First Past The Post (FPTP) debate in much detail. Yesterday, however, I read Tim Gower’s post Is AV better than FPTP and found it very interesting and informative (on another note, I found David Broomhead’s [...]

144. Tigger Says:

I would vote tactically under AV at the next election.

My MP is Lib Dem but, all other things being equal, I would probably rather vote Green.

But I would vote 1. Lib Dem 2. Green rather than the reverse, given that I don’t want the main challengers – Labour – to get more than 50% of the vote in the first round.

Given how many people are likely to vote Green, my second preference would (probably) be wasted.

If that isn’t tactical voting, I don’t know what is. :-\

In fact I would probably vote 1. Lib Dem 2. Green 3. Respect 4. SWP 5. Monster Raving Loony 6. Communist 7. Flying Yoga Party 8. Ban Trafic Wardens 9. etc etc… just to make a point.

*Anyone* but the Labatories! (Or BNP/UKIP)

That Nick Griffin, John Reid, David Blunkett, David Cameron, George Osborne, Baroness Warsi et al are lining up together to tell us how thick we all are, and not to worry our pretty little heads over changing a thing, ought to tell any decent person everything they need to know!

(The maths is interesting though.)

Bring on PR, I say. :-\

• Steve Says:

It doesn’t matter if you vote 1.Lib Dem 2.Green or 1.Green 2.Lib Dem, if Labour gets 50% in the first round, they will do so regardless of what your first preference is (unless it is Labour, of coursse).

• Mark Wainwright Says:

Never fear! Whether you vote Lib Dem or Green cannot possibly affect whether Labour get more than 50% in the first round. In fact – I feel a bit like a parrot since this is the third time I’ve said this – you can ignore the 50% threshold, and imagine that the redistributing of votes carries on till there is only one candidate left. It makes no difference to the outcome of AV.

The only circumstance where you could regret putting down your real preferences is where (i) the Lib Dem was eliminated *before* the Green (for want of your vote), and the Green was eliminated later, but (ii) if the Lib Dem had stayed in, they’d have picked up enough second preferences to be the eventual winner. That’s a fairly unlikely scenario. So you can vote with your conscience – in fact AV is designed precisely to allow voters like you to vote for the party they actually want to support.

• gowers Says:

This comment neatly backs up what Gil Kalai said in this comment in response to my point (7) — about the question of whether AV is complicated.

• richard Says:

Love this post – tigger complains that people are telling him he is thick and then wants to vote tactically under AV to ensure Labour doesn’t get 50% in the first round. This is why some people say AV is complicated; they know that some people won’t understand it – and frankly they are right, some people don’t understand it.

• Tigger Says:

LOL – you are quite right of course. And it’s not complicated. *a bit embarrased really wot wiv my MSc an all that innit*

I will add Richard to the list of people who deserve a good kicking along with Nick Griffin etc and vote “Yes” even more happily.

145. jedibeeftrix Says:

Excellent post Gowers, my thanks for taking the (considerable) trouble to put across the description so thoroughly.

146. mypoliticalodyssey Says:

Well this is certainly the longest article I have read on AV. Perhaps it says a lot about what it takes to sell an idea like AV.

As you admit the piece fell far short of neutrality, but I suspect if one is prepared to spend time writing about AV it is unlikely that they will not have fairly strong views either way.

As it happens I have been asked to write an article for OBV.org.uk (should be published tomorrow – and copied to my blog peterboland.com) in order to make a counter argument to OBV’s support of AV.

I suspect that like me you have grown frustrated with the much publicized if less than completely accurate points raised during this campaign. I feel both sides are guilty of what can most generously be described as “over simplifying matters” to further their own cause.

However I think some of the underlying assumptions in your analysis are far from perfect.

I also note that you choose to ignore the fact that in Australia, as a result of tactical voting being too complicated under AV for the average voter to fully grasp, it has become necessary for some parties to issue instructions on how to vote tactically. I find the idea of voters being instructed how to vote in this way deeply abhorrent, and as far removed from democracy as it is possible to get.

My article is also far from perfect, and by necessity far more simplified. It is interesting that both sides of this campaign tend to address the comments of the other side more than their own arguments. But with gems like “miserable little compromise” it’s easy to see why.

• gowers Says:

Is there somewhere where I can find out more details about the instructions parties issue in Australia?

I think AV is a compromise between FPTP and PR (basically because it deals with one major problem with FPTP but not another). I wouldn’t call it miserable or little. Perhaps one could even turn Nick Clegg’s silly statement into a slogan:

VOTING NO WON’T BOTHER NICK CLEGG — HE THINKS AV IS A MISERABLE LITTLE COMPROMISE!

• David Roberts Says:

Hi Tim,

regarding how-to-vote cards in Australia, they are a mixed bag. To recap, they are a copy of the voting form with pre-filled-in numbers reflecting the _party’s_ preferences for how they would like you to vote. It is illegal to hand them out too close to the place of voting, and they need to be registered with the electoral comission.

Here’s a link for the Australian Electoral Comission’s site:

http://www.aec.gov.au/Parties_and_Representatives/forms_handbooks/candidate/handbook/voting.htm#how

but note that at the state level things can be different. Here’s also a bit at wikipedia:

http://en.wikipedia.org/wiki/Australian_electoral_system#The_House_of_Representatives

Before the election parties who have similar views will sometimes come to an agreement to ‘swap preferences’, namely that they will favour each other in the preferences they show on the how-to-vote card. This is not generally secret, but fairly obvious, like smaller left-leaning parties favouring each other. Sometimes the two major parties on opposite sides of the spectrum will favour each other if there is a hugely popular third candidate (I think this is the case when One Nation – an almost BNP-style party – was becoming popular about 10 years ago). That said, the card is just a suggestion, and gives voters an idea of where the policies of the various smaller parties stand with respect to their favoured party.

The how-to-vote card also indicates to the electoral comission how to distribute upper-house preferences where, because of the large number of parties and candidates (over 100 in some recent elections in NSW), people are allowed to put a ’1′ in the box belonging to their party of choice – or number every single candidate as they see fit.

There was a bit of a dingle recently in my state where members of one major party were dressing very similarly to another, smaller, party (blue T-shirts I believe) on the other end of the political spectrum and handing out how-to-vote cards reversing the order of preferences for the two major parties in their favour. This is highly illegal, and raised a hue and cry to the extent that there was a bit of a move to ban how-to-vote cards being handed out outside polling booths and only have them pasted up inside the little cubicle one votes in. This is currently done for all parties that lodge a how-to-vote card with the electoral commission, at least in South Australia.

147. Churlish Mustard Says:

It’s far simpler than it seems, no thanks to the best efforts of the yes and no campaigns.

With all single member seat electoral systems you need to answer the question – “what happens if the majority support someone other than the winner?” FPTP’s answer is “Who cares?”. If the majority end up with an MP that none of them wanted, that is their own fault for not uniting around a single opposition candidate.

AV instead asks: let’s step back and ask who would have won if the last placed candidate had never stood. We eliminate the useless candidates one by one – as you would do under a system of exhaustive ballots – until one candidate emerges victorious with more than 50 per cent of the vote.

It’s not a perfect system. Better systems include Condorcet ranked pairs voting systems which, as its starting point, tries to work out who would have won a head to head contest between every single candidate and then uses various rules to eliminate candidates accordingly. But this comes at the cost of transparency – it has to be counted by computer.

And none of these systems provide an answer if you prefer proportional outcomes. AV may be a useful stepping stone towards STV – it would be unhelpful for supporters of STV if the public rejected preferential voting – but to the supporter of list systems AV offers nothing.

It is a real shame – but not surprising – that neither side is willing to debate electoral reform on the merits. The No campaign likes to pretend that a Yes vote will lead to permanent coalition, while the Yes campaign likes to pretend that a move to AV would be a major positive change to the constitution ( while remaining very vague as to what these positive outcomes would be). David Cameron, meanwhile, says that he does not care about the arguments for and against electoral reform – he just knows it is wrong “in his gut”.

148. András Salamon Says:

MorningTory makes essentially one argument: FPTP is AV where only first preferences are taken into account. This seems mostly a disadvantage to most people commenting here, though MT seems to have decided this is a good thing.

149. R G Hill Says:

Could you please come up with a shortened version majoring on the key stats that will wake people up to the ridiculous inequality of the parties, I would repost this all over Facebook and Tweet if you did but a lot of people can only do soundbites now. I’d do it myself I used to be a sub editor but it’s your material! Thanks

150. links for 2011-04-25 « Embololalia Says:

[...] Is AV better than FPTP? « Gowers's Weblog 1. Under AV the person who comes second or third can win. I find this argument laughable. The truth that the above sentence expresses is that under AV the person who would have come first under FPTP will not always win. Well I’ll be: it turns out that AV and FPTP do not lead to identical results. So that is why we are having a referendum. Duh. (tags: politics uk electoral.reform) [...]

151. Gil Kalai Says:

Moshe Machover pointed my attention to the following interesting link
http://www2.lse.ac.uk/CPNSS/projects/VPP/Home.aspx

152. Mohammed Amin Says:

This is an excellent piece which I enjoyed reading.

I have addressed the referendum on my own website at the link http://www.mohammedamin.com/Politics/Alternative-vote-referendum-2011.html and on my website will now add a link to this blog story.

153. Nikki Says:

This is no doubt pretty pedantic from your POV, but I feel a better phrasing for the first line would be: “On May 5th the UK as a whole will vote in a referendum for only the second time ever.”

I have voted in a UK referendum; I was not born in 1975. (I voted in the Welsh referendum in March 2011.)

• gowers Says:

I actually thought about that when writing (by which I mean that I hadn’t forgotten about the various devolution referendums there have been) and decided that it was OK as written since the UK didn’t vote in those referendums — Scotland and Wales did. I agree that it’s not quite as crystal clear as it might be but I haven’t thought of an alternative I prefer. [PS, and to forestall any comments about this, I quite deliberately wrote "referendums" and not "referenda".]

154. The Stupid Argument Always Seems To Win Out | 1000 Good Intentions Says:

[...] (See here for a superb blog breaking down the numbers why First Past the Post system is so flawed http://gowers.wordpress.com/2011/04/20/is-av-better-than-fptp/). But even the yes campaign has been denominated to this simplistic line of a vote yes is a vote [...]

155. polleetickle Says:

The AV voting system promises much but theres no assurance at always producing a candidate with a majority.

• gowers Says:

True, but it does much better than FPTP in that respect.

• polleetickle Says:

Hang on!…

POLLETICKLE: The AV voting system promises much but theres no assurance at always producing a candidate with a majority.

GOWERS: True, but it does much better than FPTP in that respect.

So, when no candidate reaches a 50% majority under AV no candidate can be elected?

Thats a huge failing.

• David Roberts Says:

@polleetickle – not necessarily a first candidate at the first round, but eventually…. Unless there’s a complete 50-50 split, also possible under FPTP.

• gowers Says:

I’m happy to reassure you on that score. Under AV the candidate who gets over 50% of the votes in the final round gets elected.

When I say that AV does much better, I mean that in a large majority of cases the party that wins under AV actually gets over 50% of the initial vote too. Under FPTP winning a seat without an absolute majority is very much more common.

• polleetickle Says:

I repeat:

POLLEETICKLE: The AV voting system promises much but theres no assurance at always producing a candidate with a majority.

GOWERS-01: True, but it does much better than FPTP in that respect.

POLLEETICKLE: So, when no candidate reaches a 50% majority under AV no candidate can be elected? – Thats a huge failing.

GOWERS-02: I’m happy to reassure you on that score. Under AV the candidate who gets over 50% of the votes in the final round gets elected.

When I say that AV does much better, I mean that in a large majority of cases the party that wins under AV actually gets over 50% of the initial vote too. Under FPTP winning a seat without an absolute majority is very much more common.

POLLEETICKLE: So, pro-AV campaigners are uncomfortable that a third of seats are won with 50+% majority (high credible) and another third won with 40+% majority (very credible)?

What lifestyle panacea’s do these people live in?

156. Albert Freeman Says:

Interestingly, today I had a moment of clarity when I asked myself “hang on, what is the ‘post’ in First Past The Post?!” To which my answer was “There is no post! If there is any post, it is 50%, so in a way anybody arguing in favour of FPTP is in an indirect way making the case for AV”….and then I read your blog, which effectively says the same thing that I was thinking.

• polleetickle Says:

To Albert Freeman: The finishing line in FPTP is – Time.

Proving to be the most credible electable candidate by securing the most votes at the count is utterly democratic.

Its how most meritable people are awarded – the margin of win is essentially unimportant.

• gowers Says:

“Its how most meritable people are awarded”

Suppose you were on an interview panel of nine people, and there were four candidates. After interviewing them, the chairman asks each person in turn who they thought was the best candidate. Three people like candidate A, two people like candidate B, two like candidate C and two like candidate D. And amongst the people who like candidates B, C and D there is a lot of criticism of candidate A.

Would it be sensible for the chairman to say at that point, “Well, candidate A has got the most votes, so that’s who we’re choosing?” Even if you think it would be sensible (which I most certainly don’t), you cannot plausibly claim that that is how most interview panels would operate.

• polleetickle Says:

1/ The hypothetical point above depends on those panelists being validly or invalidly critical of ‘A’ – hence the need for chairpersons.

2/ Exams, commerce, life and politics should remain being about; how much is done well and how much support is mustered – the margin of win remains essentially unimportant but is sometimes recognised. Electorate voting should never be about how little was done wrong or appeasing as many as possible.

157. Will A Says:

IMO AV has a single advantage over FPTP: if people use their lower preferences, then AV avoids the selection of candidates who are dispreferred by a majority to another candidate in a two-way vote. I.e. it won’t select the Tories where Lib and Lab supporters would by a majority support either of those parties over the Tories.

In terms of voting theory, that is it for AV’s advantages. AV is not proportional and it does not always select a Condorcet Winner when there is one. It has the disadvantage of violating monotonicity in rare cases: e.g. a candidate could lose by gaining more votes, and win by gaining fewer.

I am now unsure how to vote.

158. Will A Says:

*dispreferred by a majority to all other remaining candidates

159. RodCrosby Says:

‘does not always select a Condorcet Winner when there is one.’
Good job too.

49 ACB
49 BCA
1 CBA

Are you saying C should ALWAYS be elected?

I think AV passes something called ‘Dominant Mutual Third’ – it always elects a CW with >33.3% of the vote.

160. RodCrosby Says:

‘C is preferred by a majority over A, and over B. So why not?’

What if A and B’s voters have employed the burying strategy, and C is just a huge ?

A Chauncey Gardner, or perhaps the Antichrist in disguise?

161. RodCrosby Says:

And you’re not a LibDem are you?

Condorcet would probably deliver a huge majority of the seats to the LDs [at least the first time it was used]

162. Will A Says:

Not entirely sure what you mean.

Do you mean A and B supporters have insincerely voted B and A last in an attempt at tactical voting? But you can’t do that sort of tactical voting under AV, since second prefs don’t count unless your first pref is knocked out.

“C is just a huge” – a huge??? Not getting the references, what do you mean?

163. RodCrosby Says:

A huge Question Mark! No-one knows sweet FA about him, which is why he only attracts 1% positive support…

Agreed AV can’t do this, since it is immune to the burying strategy.

Condorcet IS vulnerable to the burying strategy, and is why, paradoxically, AV might well elect more CWs than Condorcet itself!

164. Will A Says:

Agree that Condorcet would have helped Lib Dem – until now.

I would expect to see more of a polarisation towards two main parties at the next election, with Lab voters no longer putting Lib as second pref at all.

165. Daverinio Says:

@MarkWainwrite

“In the scenario I gave, it doesn’t matter what they put after their first preference, as Mrs Peacock is always going to come second in the election – when she is eliminated it’s all over and it’s too late for their second preferences to be used.”

You are quite right and I apologise for being such a dunce. Of course, for your scenario to work all of Plum’s supporters would have to choose Mustard (or vice versa) for their second preferences, which is hardly that likely is it?

• Mark Wainwright Says:

They wouldn’t *all* need to, as long as about 2/3 of them did – ie enough to give each other a majority over Mrs P. It’s not hopelessly implausible that some seats are like this with say Labour and Lib Dem candidates getting most of each other’s second preferences, ahead of the Tory.

166. OldBloke Says:

How wonderful to find somewhere on the web where rational argument, essentially devoid of inane expletives, takes place. I have been following this thread for some time now but, like MorningTory, find frowns of disapproval because I should be doing something else. Still, like ‘him’ I believe “Electing a government is a serious matter.” and deserves some thought.
I am a member of the older community whose parents were alive during the Suffragettes period and have been trying for some time to get my contemporaries and acquaintances interested in the coming referendum. No matter who I speak to, young or old, all have inaccurate ideas of how AV works, most have been hypnotised into thinking it is too difficult to waste time on analysis – the focus of the argument starts to narrow with fine tuning so that eventually the main objective is lost in a fog of uncertainty.
Even using the idea of multiple voting to illustrate the effect of AV some still say, ‘what about the second preference …?’ This leads me to believe that the default vote at the referendum is likely to be for the’ Status Quo’.
In trying to look outside the box would I be wrong to advocate ‘change’ because to remain the same offers the possibility of stagnation whilst ‘change’ offers opportunity and is evolutionary? Perhaps I should just toss a coin!
Gowers likes slogans, so, with tongue in cheek, how about this: MY MIND’S MADE UP, DON’T CONFUSE ME WITH FACTS – but keep them coming just in case.
Here’s a question I have not seen discussed before but have an interest in, what happens if two or more candidates get equally lowest votes; more importantly, what happens if the last three candidates get equal votes? Maybe this is a trivial question and not worthy of discussion!

• polleetickle Says:

OldBloke – hopefully you can spend time with BBC’s John Humphrys who displayed some naivety over AV – Telegraph Blogs: http://bit.ly/l2VCYm

• WJ Says:

Yes; I was rather unpleasantly surprised to hear John Humphrys clearly displaying the fact that he didn’t understand AV. It’s particularly sad, since he was replying to David Cameron’s assertion that “under AV some people get more votes than others,” which I’m sure a number of us could easily have refuted on the spot if we had been in Humphrys’s position. It meant that David Cameron came out on top in that interview, despite using a provably invalid argument. If I remember correctly, he spent much of the interview refusing to answer Humphrys’s question as to whether or not he agreed with the NO campaign’s dead babies etc., so it’s a pity it all had to end the way it did.

167. Gil Kalai Says:

Here is an interesting (and fairly realistic) example

We have a labour candidate who is favoured by 40% (or a little less) of the voters, and a conservative and social democrates candidates favoured by 30% (Or alittle more) of the voters. 3 out of every 4 conservatives would prefer a social democrates of a labour and 3 out of every 4 conservatives prefer social democrates over a labour.

Under FTPT the labor candidates will win. A tactical vote by a large number of conservatives for the social democrate is a possibility but a fairly remote one.

Under AV if there are more supporters for the social democrate candidate to the first place than for the conservative candidate the outcome is that the social democrate candidate will win (because of the preferences of the conservative voters). Otherwise, the labor candidate will win.

It is therefore the interest of the labor candidate not only to try to swing voters from SD to conservative but also to swing voters from himself to the conservative candidate in order to guarantee his own victory.

• gowers Says:

Am I mistaken or is that basically the same example as the one I gave in the section “Is tactical voting eliminated under AV?”

• Gil Kalai Says:

Right it is essentially the same example but the main point is different. It is not so much about tactical considerations of voters but about tactical considerations of candidates. (I do not see that much problem with voters making tactical considerations.)

In FTPT every candidate aim is to convince voters to vote for him.
He may also spent some effort against a candidate that thretens him the most.

In such a scenario under AV we have a labor candidate that in order to win he needs to swing some of his own supporters to the conservative candidate (whom they actually prefer the least).

• Gil Says:

BTW in this scenario we still have the “ordinary” tactical votings that a conservative supporter who prefers social democrates over labour will put the social democrate candidate in first place instead the conservative candidate.

• gowers Says:

The fact that candidates may want to behave strangely is also discussed in this comment, and in the video that precedes it. I think it is a genuine drawback of AV, but for reasons I gave in that comment I also think it is a minor drawback.

• Gil Kalai Says:

Let me just summarize the matter regarding tactical voting and specifically the claim “The scope for tactical voting is greatly reduced under AV, because the wasted-vote argument no longer applies” and the example following it. Indeed it is a common claim that tactical voting is reduced under AV and it may well be correct in general.

But lets look again at the example I proposed above (which strangely is not precisely the same as Tim’s). Labor is ahead 40:30:30; Conservative prefers social democrates 3:1. Social democrates are indifferent between labor and conservatives (but this is not so crucial it works under a large range of possible preferences for SD.)

The main aspect of tactical voting under FTPT and under AV is that a voter that realizes that the party he wants to win has no chance will vote in a different way. In this example under AV conservatives has no chance to win and therefore a few conservative voters who put SD first will led to SD winning. This is very similar to tactical voting under FTPT (in other scenarios). It requires the tactical voter to know something about the preferences of other voters but not too much. (This is also the case in Tim’s example where there labor has no chance to win but it is more delicate since SD tends to support labour in that example.) This is standard tactical voting and I dont think it is obvious that it occur under AV less than under FTPT. Under FTPT such tactical voting will tend to harm the SD candidates and under AD it will tend to support the SD candidates (being the party in the “middle”).

So the wasted-vote argument still applies also under AV. We need yet to see a good argument why (and if) it applies considerably less compared to FTPT.

In addition, under AV there are some opportunities for (strange) strategic behavior by candidates which do not exist under FTPT. In my example, labor will gain if they can mobilize some of the voters to vote for the conservatives. Also consider a 40:30:30 situation like the example above (or even a simpler one where the voters supporting one party have no preferences between the other two.) The two 30% parties can reach an agreement on the second candidate which if implemented will simply eliminate the 40% candidates. This strategic opportunity reflect the fact that these two parties are trailing and are in a neck-to-neck fight.

Will such “strange” strategic behaviors be “cancelled out” over many constituencies? Maybe. Will a candidate act strangely in order to win? I tend to think so.

In any case, a party which has “devoted supporter” that will follow the party line not only in their first vote but with their entire voting may have an advantage over a party with just “ordinary” supporters that put her first and apply their own judgement on the other parties. Is this aspect good or bad? I dont know.

• gowers Says:

I think the tactical voting scenarios under AV are a genuine problem in something like a mayoral election where you have just one election rather than several hundred that are aggregated. In a general election, although local campaigning makes some difference, it’s really the TV ads, newspaper columns, billboards, debates between party leaders, etc. that make the difference. And they cannot be sensitive to the peculiarities of a handful of constituencies (which in any case will not be known to any great accuracy). So I incline to the view that the non-monotonicity of AV will balance itself out and will be hard to exploit by game-playing politicians.

• Gil Kalai Says:

Just one more remark about the 40:30:30 scenario.

In any election, under FTPT or under AV when candidate A is leading 40:30:30 against candidates B and C, the result will be that both candidates B and C will attack A. Of course, they will not say “we attack A because he is ahead” they can rather say “we attack A because he is a crook”.

And now comes the difference. Under FTPT, in order to elminate A candidates B and C need to convince some of A’s supporter that A is a crook. Under AV candidates B and C only need to convince their own supporters that A is a crook. This is much easier.

• Gil Says:

Dear Tim, the first 4 paragraphs of my remark were not about “non monotonicity of AV” but about the fact that the wasted vote argument still applies under AV. (And may systematically favour the “central” party.)

168. David R. MacIver Says:

[...] give me the right to disenfranchise them. Also, as Timothy Gowers so eloquently put it, WE SHOULD NOT LET THE BNP DICTATE HOW WE RUN OUR POLITICS. DRMacIver: Ok, fine, but let me make sure I understand: It is possible for this system to elect an [...]

169. mypoliticalodyssey Says:

The article has now been published on OBV.org.uk, and I have copied a link and the text to my blog on here (made a bit of a hash of the formatting though – blogging newbie here).

http://www.obv.org.uk/news-blogs/no-vote-perspective-av

As I said this was written to counter balance OBV’s stance of AV support at the request of Simon Woolley, director at OBV. Therefore I’m not even going to pretend that it is in any way neutral on the subject.

Wrt the Australia thing I will see if I can dig up my source. However as this has not been a contested issue between the two camps (and I believe it may be an agreed upon fact) I have not investigated exhaustively myself.

170. mypoliticalodyssey Says:

ps

I think that slogan has to be one of you best!

171. Andrew Says:

Isn’t your logic in (4) only true in the case where a winner isn’t declared before the Lib Dems’ second preferences have been counted? i.e. if first preferences are Con: 49%, Lab: 30%, Lib: 20%, BNP: 1% and all the BNP voters put the Conservatives down as their second preference, then the Lib Dem voters second preferences are irrelevant.

• gowers Says:

You’re bringing in a situation where there is an exact tie, which is a slightly different issue. (I don’t know how ties are resolved under AV, and I also don’t know how they are resolved under FPTP.) But consider what happens if we adjust the numbers very slightly so that the BNP has 1.1% and the Lib Dems have 19.9%. Then it does indeed look as though the BNP get to decide the election and the Lib Dems are ignored. But think about what would have happened if we had gone on to count the Lib Dem second preferences. Even if they had all gone to Labour, that would have pushed Labour up to 49.9%, which wouldn’t have affected the outcome. The reason we don’t count the Lib Dem second preferences is that we know that if the Conservatives already have 50.1% then it is no longer possible for the Lib Dem votes to make a difference.

• Andrew Says:

Sorry, I didn’t mean to bring up the issue of exact ties (I was incorrectly thinking that getting 50% implied you would win). I was referring to the slightly modified form you bring up, and I agree that you are correct, I hadn’t considered the fact that the Lib Dems’ second preferences would end up being irrelevant. Thanks for the swift response!

172. DBIRKIN Says:

Have used your article to write a ‘revisted’ post.

http://dbirkin.blogspot.com/2011/04/is-av-better-than-fptp-revisited.html

173. Harry Says:

Thanks for your excellent analysis of the maths, but I think the psychology is just as important. The Conservative and Labour parties are very wide coalitions of opinion – Bill Cash to Ken Clarke and Tony Blair to Tony Benn to use the last set of MPs. This is because forming a breakaway party is electoral suicide under FPTP.
If AV makes it less suicidal to form a small party then we will have smaller parties, more coalitions and more cases, as at present, where the manifestos are happily ignored and a new agreement put in place after the election without reference to the electors.
FPTP does have some merits when the effect on party behaviour is considered

174. DBIRKIN Says:

Harry, there is no evidence that AV will encourage smaller parties..in fact in Australia, the smaller parties get a smaller seat % per vote % under AV then they do here under FPTP..no reason to think this wouldn’t happen here.

AV tends to encourage coalition so separate views are even more compartmentalised . You have found symptoms of a bad system, but AV is not the cure.

175. Laurence Says:

Brilliant article. Nuff said.

176. Damien RS Says:

Problem is, IRV/AV is only a marginal improvement over approval, range, or Condorcet voting. As the Australians above note, it doesn’t actually help third parties much, they still have a system dominated by two parties or coalitions. And the case for tactical voting is much simpler. In US parties:
40% Republican
31% Green, Democratic second choice
29% Democratic, splitting into 18% Green second, and 11% Republican second
Democrat gets eliminated, votes redistribute so Green has 49%, and Republican 51%. The Greens would have gotten a better outcome by ranking the Democrat first, exactly the situation IRV is supposed to let you avoid. Truth is, IRV lets you rank Green first safely when it’s insignificant at 5% say, whereas FPTP has no safe zone. But when the third party gets competitive, outcomes become unstable. Cf. http://zesty.ca/voting/sim/

Score voting can be as simple to count as approval or plurality ballots, and a lot simpler than IRV.

Truth is, any single-member district legislature will be unrepresentative and vote-discarding compared to PR.
Also, IRV does not equal STV. Yes, the vote counting is similar, but things which are good in single-winner form are bad in multi-winner, and vice versa.

• gowers Says:

I haven’t checked, but I think this is essentially the same example as Gil Kalai’s above, and it’s one that I hadn’t thought of.

• Jonathan Lundell Says:

The phenomenon is sometimes known as “center squeeze”. Note that while the transition is odd, the result is defensible.

It would be odd—nay, incredible, in the literal sense—if there were no situations in which insincere voting paid off under AV.

The problem with range isn’t that it’s hard to count. Rather, it’s that it makes the entire voting process a tactical endeavor.

• Clay S Says:

Score Voting, including its simplified form called Approval Voting, is actually extremely robust to tactical voting. Jonathan’s “criticism” is a common fallacy.

Tactical voting is actually more problematic with systems like IRV, Condorcet, and Borda.
http://www.electology.org/irv-plurality
http://ScoreVoting.net/DH3.html
http://ScoreVoting.net/CondBurial.html

Score Voting actually obeys to theorems about relatively GOOD behavior when voters use generally sensible strategy.
http://ScoreVoting.net/AppCW.html – elects a Condorcet winner, when one exists
http://ScoreVoting.net/PleasantSurprise.html – maximizes the number of pleasantly surprised voters

• Clay S Says:

“IRV/AV is only a marginal improvement over approval, range, or Condorcet voting”

Actually, it is worse than all three of those other methods. Objectively.
http://ScoreVoting.net/BayRegsFig.html

But it is still better than Plurality Voting, and that’s the most important thing about this whole referendum.

• Damien RS Says:

“IRV/AV is only a marginal improvement over approval, range, or Condorcet voting”

Whoops, I had a big brain error there. I meant to say marginal improvement over plurality voting. Or marginal improvement compared to the others, perhaps.

single vs. plural winner differences:
one vote: plurality (bad), limited voting (half decent, semi-proportional)
vote for all: approval voting (good), bloc voting (very bad, that is majoritarian, US went to single-winner plurality to get away from that, giving at least geographical minorities some representation)
(Though there’s a reweighted range voting possibility, for PR score voting)

177. Andy Says:

One issue is that under AV if you vote for the party that gets a first round count of 40% then your vote is “over” even if you too had second or third preferences. However, the subsequent recounts can then overtake your first vote. Your second choice is lost and cannot contribute to the result fairly.

• Jonathan Phillips Says:

The problem lies partly in the use of the word “preference”: it sounds positive. So you might quite like your second or even third preference. But AV is not about “shades of preference.” “Choice” is a better term (and is used on Scottish STV/AV ballot papers), since what is your “second choice” could be something you don’t actually like much at all.

Your second and subsequent choices are conditional, a sort of insurance which “pays out” only if your first is in a position such that he/she cannot win – because they have been excluded. http://bit.ly/hctTGk

If the candidate who is your first choice gets 40% and leads in the initial tally your second choice will not be counted, since he/she could not be overtaken by two of the lower-placed candidates. However the second etc. choices of supporters of lower- placed candidates could push him/her past the 50% mark in the decisive round. If they don’t, that only goes to show how unpopular your first choice was with the majority of voters. http://bit.ly/fldUMZ http://bit.ly/fgHxR0

178. Andy Says:

btw – an excellent quality debate/discussion

179. AV: a crucial ‘baby step’ if we are to break Britain’s electoral reform taboo | Jonathan Freedland | What Is Hot Now Says:

[...] then I still only get one chocolate bar. As for the claim that AV leads to more coalitions, the number-crunchers say that’s far from clear. Of course this argument would be easier to swallow if it were not coming from Tory ministers [...]

180. missquinnmaths Says:

What a great article, beautifully put – thank you for putting so much time and thought into it. I particularly enjoyed the slogans.

181. Daverinio Says:

@Wainwright

Sure… having thought about it during the day I think this is probably one reason for Tory voters preferring AV less – given that it at least used to be the case that Liberals might by and large prefer Labour as a second best over the Tories… though now – who knows?

Having thought your example was a poor one I can now see how it does indeed accurately reflect the differences between AV (instant runoff) and genuine runoff voting – showing deficiencies with the former.

I guess I’d have to still prefer AV over FPTP in that at least with AV there’s a post, and it’s possible to find out who the majority would settle for should their candidate not get enough votes. What it doesn’t do is allow someone whose candidate is way out front in the first round to change their vote tactically between rounds. But then no-one else can change their votes in that way either – they are simply adjusted automatically once candidates get knocked out.

However, given your scenario I could see why Tories might not prefer it. I can also see how they could legitimately claim a significant difference between AV and the system they use to elect their own representatives – which is I understand it is multiple round runoff voting proper.

182. RodCrosby Says:

I think it was Lewis Carroll, appropriately enough, [as C.L. Dodgson, an early British voting theorist] who first showed that the more a system encourages strategic voting, the greater the chance of it producing a worse result than if everyone had voted honestly…

AV has been shown to be probably the most strategy-resistant voting system there is.

• Clay S Says:

“AV has been shown to be probably the most strategy-resistant voting system there is.”

That is just absolutely ludicrous. It is so much worse than Score Voting, that it behaves as well with 100% sincere voters as Score Voting does with 100% TACTICAL voters.

http://ScoreVoting.net/BayRegsFig.html

But don’t expect anything remotely similar to that hypothetical extreme. Plenty of people will be tactical with IRV.
http://www.electology.org/irv-plurality

In my estimation, one of the biggest things that turns voting theorists AGAINST measures like this recent referendum, is that IRV proponents are so often so totally uneducated about election science.

That being said, I do agree with Warren Smith that IRV would have been a small, but positive, reform over Plurality Voting (aka FPTP). I also believe that most opponents rejected it out of ignorance.

• Chris Purcell Says:

@Clay — Thanks for the links. I hadn’t seen a realistic scenario for a sensible voter changing his first place vote because it can’t win before, but now I’ve seen how that can work, a quick back-of-the-envelope set of numbers suggests AV would have Conservative voters lying about their first preference, in order to vote tactically between Labout and Lib Dem. Whether or not the numbers would match exactly, that’s destroyed the only argument I gave credit to in favour of AV vs FPTP.

In summary, you’ve converted me.

• gowers Says:

Chris, are you basically thinking about the example I gave in the post or do you have a different scenario in mind?

I don’t find the examples or reasoning in Clay S’s second link as convincing as you do. No time to elaborate right now.

• Chris Purcell Says:

Sorry for the very tardy delay. No, I don’t believe the example is the same as the one you gave. Consider the following simple scenario:

40% of voters prefer C > LD > L
35% of voters prefer L > LD > C
25% of voters prefer LD > L > C

Under FPTP, assuming all voters know the above information and vote rationally, Labour wins with 60% of the vote, and 25% of voters (the Lib Dems, of course) lie. The Conservative voters are annoyed, as they get their last preference.

Under AV, assuming all voters vote truthfully, Labour still wins with 60% of the vote, as Lib Dems are knocked out first. The Conservative voters _still_ get their last preference.

However, if again we assume all voters know the above information and vote rationally under AV, the sensible thing for the Conservative 40% to do is lie. By swapping their first and second choices (LD > C > L), they ensure Conservatives are knocked out first, giving a Lib Dem victory with 65% of the vote.

• David North Says:

“assuming all voters know the above information and vote rationally”

How would voters know the underlying preferences when the actual votes do not reflect them?

“25% of voters (the Lib Dems, of course) lie”

It’s interesting that you consider “tactical” voting to be both rational and lying. As far as I am aware, the ballot paper does not ask a question or instruct voters to vote for their most preferred candidate; it merely instructs them to vote for one candidate. If they decide that their vote will be more effective if it goes to someone other than their first preference, they have still followed the instruction precisely, so how is that lying?

“By swapping their first and second choices (LD > C > L), they ensure Conservatives are knocked out first, giving a Lib Dem victory with 65% of the vote.”

In that case, 10% fewer voters get their first preference under AV compared to “FPTP”, but 40% fewer (i.e. none) get their last preference. 65% get a higher preference.

• Chris Purcell Says:

@David – I think you may have missed some context here. I agree with all your responses, but they’re missing the point a bit.

The intent is to address the question of whether AV discourages “rational lying” — yep, by that I mean tactical voting. I believe the conclusion is, alas, no it does not. If you are confident that your party will not get a majority of votes in the last round, you are always better off putting one of the parties in with a chance at the top of your list, as otherwise you may not have your second-choice preference taken into account, as in the scenario under consideration. (The voters having perfect knowledge is therefore just to make the example clear.)

The context: earlier we were fairly confident that tactical voting like this was not rational under AV, which was the main argument in AV’s favour in my mind. The outcome being arguably better under AV in this instance is thus beside the point: the example only needs to disprove an assertion.

I agree the wording I used is biased: it’s only lying if you consider the instructions for FPTP to be “vote for the party you would like to be in power”, and for AV “vote your preferences for whom you would like to be in power”. I note with some amusement that the Government web site about voting specifically does _not_ use any phrasing like that: it just says “put a cross by the party you wish to vote for”.

183. Get out and vote "Yes to AV" in the UK referendum Says:

[...] it. They’re a bit nerdy but hey, this is a kinda nerdy blog! Talking of which, here’s a longish post by Tim Gower, a mathematician at Cambridge, explaining the benefits of [...]

184. kathy Says:

Brilliant! Thankyou : )

185. John O Hart Says:

Excellent article! How can we get all the no voters to read it?

I know hypothetical examples aren’t the best way of making points, but imagine a by-election in Dagenham. A week before polling an opinion poll puts the parties at BNP 28%, Lab 25%. LibDem 25%, Con 22%. All subject to the usual 2-3% error.

What would an anti-AV Tory recommend voters to do, and would he/she be happy if the BNP candidate was elected with 28% of the vote?

186. David R. MacIver Says:

[...] Is AV better than FPTP?, Timothy Gowers writes about the issues around the two systems. It’s very very long, but an [...]

187. EnglishAtheist Says:

Thanks for this post!

http://furtherthoughtsfortheday.blogspot.com/2011/04/im-voting-yes-to-av-and-this-is-why.html

188. A few words on AV « Degrees of Imperfection Says:

[...] dishonest or shabby one, as that has already been done pretty comprehensively elsewhere, such as this fantastic blog explaining the numbers in detail, or Johann Hari’s excellent column comparing the process [...]

189. Jonathan Phillips Says:

Thanks, John O Hart – good scenario.

I’ve blogged and tweeted it (without acknowledgement, I fear): http://bit.ly/g8cQbt. It’s also now on the end of “Ourtown Votes!” http://bit.ly/fldUMZ.

190. R. Moid Says:

Paddy Ashdown gave 4 reasons to prefer AV on Newsnight last night, and all of them were false. (They were that there’d be no wasted votes, no safe seats, no reason for tactical voting, and that no MP would be elected without majority support. He also worded the last one in a different way, claiming that no one would be elected with more voting against them than for them. That version’s less obviously false, because it’s not entirely clear what counts as voting against, but under AV one of the losers could be preferred – using the same preferences – to the winner, which is certainly contrary to the impression he’s giving.)

If he also claimed the Conservatives use AV for their leadership elections (someone claimed it), that would bring his total of falsehoods to 5 (since they use separate rounds of voting rather than a preference list). Someone also started to state the popular claim that AV is like voting in X Factor, which is even less true.

Another frequent false claim is that, under AV, people can put whoever they want as their first choice, secure in the knowledge that, if their 1st choice is eliminated, their vote will transfer to their 2nd choice. That’s false because their 2nd choice might already have been eliminated.

I find it worrying that so fundamental a change could be made on the back of a pack of falsehoods. The one about the winner having majority support is especially troubling, because I’m sure it will be claimed about the MPs who are elected if we adopt AV. If my vote transfers to a Lib Dem, who then wins, for example, I’m sure I’ll be counted as among the “majority” who supports, even though I don’t support them in any real sense at all. I just detest them marginally less than my next choice.

I am less bothered by the falsehoods on the “no” side, because I think the burden of proof ought to be on those advocating a fundamental change, and because the falsehoods on the “yes” side have been circulating for decades.

But I will vote “no” in any case, because I think it’s wrong to make so fundamental a change with only a simple majority in a referendum. It should either require that at least 50% of the electorate participate, or else that the majority be at least 2/3rds.

• gowers Says:

In case you want to make your decision based on the actual arguments for or against rather than on the deficiencies of the official campaigns, let me point out that every one of Paddy Ashdown’s points can be slightly modified so that it becomes true.

1. There would be far fewer wasted votes.

2. There would be fewer safe seats (though many would remain).

3. There would be much less reason to vote tactically.

4. No MP would be elected without majority support in the final round, out of those who could still be bothered to express a preference in that round. In practice, that would usually be over 50% of the initial set of voters, and would always be a larger percentage than you get under FPTP, unless some candidate in FPTP gets an absolute majority in which case AV gives the same result. The main point that the Yes campaign want to make is that under AV parties would be forced, more than they are under FPTP, to take into account the interests of voters for other parties, and that point is correct.

5. The Conservatives used a system for their leadership election that is far closer to AV than it is to FPTP.

6. Under AV you can vote for your party of first choice, secure in the knowledge that you can still have a say in who wins the election out of the front runners if your candidate turns out not to be a front runner.

Thus, as it seems to me, the “false” claims of the Yes campaign are approximations to the truth, even if they aren’t 100% accurate. The false claims of the No campaign, however, seem to be mostly just plain wrong.

• R. Moid Says:

What you say under 4 is seriously wrong, imo. The other cases are less so. But there’s also the question of why, if pro-AV campaigners could make ‘slightly modified’ claims that are true, they don’t make those ‘slightly modified’ claims. Either they don’t understand AV themselves, or they’re trying to pull a fast one.

1. There would be far fewer wasted votes.

That may be true, though it depends on how ‘wasted vote’ is defined. Ashdown defined it in a way (though I’m not sure what the way *was*) that made all but 1.6% of the votes wasted under FPTP. He also seemed to think the only votes that weren’t wasted were ones in marginal seats.

2. There would be fewer safe seats (though many would remain).

That’s not clear at all. There might even be more safe seats under AV. Someone who’s safety was somewhat in doubt under FPTP might be completely safe because of 2nd choice votes. Patterns of voting that persist time after time (which is what makes seats safe) can just as well happen under AV as under FPTP.

3. There would be much less reason to vote tactically.

I agree there’d be less reason, although I think your original post makes the possibilities for tactical voting under AV seem more obscure and ‘ignorable’ than they actually would be.

4. No MP would be elected without majority support in the final round, out of those who could still be bothered to express a preference in that round.

No, no, no! That is fundamentally wrong. That a vote transfers to a candidate does not mean the voter supports that candidate in any real sense. As I pointed out, my vote might well transfer to the local Lib Dem. But I don’t support the guy at all. I just detest him marginally less than the next one on the list. It would be outrageous to claim I supported him.

5. The Conservatives used a system for their leadership election that is far closer to AV than it is to FPTP.

But it’s not AV; it’s significantly different; and it’s false and misleading to claim the Conservatives use AV.

6. Under AV you can vote for your party of first choice, secure in the knowledge that you can still have a say in who wins the election out of the front runners if your candidate turns out not to be a front runner.

You don’t necessarily have any more ‘meaningful’ a say than under FPTP.

The phenomenon of the 2nd choice already having been eliminated is also important for another reason: it’s often overlooked, and sometimes even denied; and that means AV is not the simple thing it is often presented as being. People have a shallow understanding of the basic mechanism, but that’s all.

• Jonathan Phillips Says:

Beams and motes, Mr Moid.

The Yes campaign has been feeble and ill-focused, but at least it hasn’t consisted of downright lies (£250m to introduce AV? AV means some people’s votes are counted more times than others’? AV opens the way to extremists? AV is hard to understand?).

The fact that a voting system doesn’t require you to put numbers on a ballot paper doesn’t necessarily mean that it isn’t a form of Alternative Vote. Two-round systems are used in many countries, for the election of presidents and representative assemblies – if your favourite is knocked out in the first round, you get to vote for an alternative in the second.

With FPTP the candidate with most votes wins, however many people have voted for someone else – and indeed however unpopular that person may be with the majority. Which is of course why the Conservative party doesn’t use it to elect a leader.

What differentiates exhaustive balloting from AV is that (a) anyone can change their vote between rounds, not just those who originally supported the candidate who has been excluded, and (b) candidates can drop out between rounds. But the principle that votes may be transferred is exactly the same.

• gowers Says:

I actually agree with you about point 4 and forgot to mention this. If a Conservative voter dislikes Labour and the Lib Dems in a seat where Labour and the Lib Dems are the main contenders, and if they decide that they dislike the Lib Dems slightly less, and if as a result of that and similar votes the Lib Dem candidate is elected, then that candidate cannot reasonably claim to have the support of over 50% of the electorate. Perhaps “grudging support” would describe it slightly more accurately. But under other circumstances, second preferences can really mean something. For example, a left-wing Lib Dem might be reasonably happy with Labour, and in that case the Labour candidate could claim rather more than grudging support. So I agree that the Yes campaign’s claim that all candidates have to have the support of 50% of the electorate is misleading, but it’s still true that there is more of a need for parties to reach out to voters from other parties.

An interesting case that makes the point rather strongly is the French Presidential election of 2002, which wasn’t held under AV but under the somewhat similar system where there is a runoff between the top two candidates from the first round. The figures in the first round were

Chirac 19.88%
Le Pen 16.86%
Jospin 16.18%

and then a whole host of others ranging from just under 7% to just over 0%. In the second round, those who would naturally vote Socialist (for various reasons some of these didn’t vote for Jospin in the first round to make a statement, but they hadn’t expected him to be beaten into third place by the Front National) held their noses and voted for Chirac. The result was

Chirac 82.21%
Le Pen 17.79%.

Obviously under circumstances like that, Chirac could not go around saying he had the support of over 80% of the country.

If the election had been held under AV, Jospin would have quickly overtaken Le Pen to become the second candidate.

191. Jonathan Lundell Says:

The problem with approval voting (that is, range {0,1}) is that it becomes entirely an exercise in tactical voting. In the simplest non-trvial case, suppose one’s preference order is A>B>C. The only substantive choice is whether to approve B (it makes no sense to vote for all or none, and obviously one votes for A). But the decision to vote for B (or not) is strictly tactical, and moreover can only be made (on more than a coin-toss rationale) on the basis of some degree of prior knowledge of A’s strength relative to B, and presumably one’s degree of liking (or distaste) for B & C. Voting for B can help B to beat C (good), but it can also help B to beat A (bad). Like any voting system, AV has its perversities, but it’s generally a good “tactic” to vote sincerely.

• R. Moid Says:

I don’t agree. For me, approval voting would not be tactical. I would ‘approve’ the candidates I think would be ok, and not approve the rest. Voters don’t necessarily even have a totally ordered preference list.

I think it’s largely because you see it in terms of preferences that you think approval voting is tactical. Seem from an approval voting point of view, it’s preference lists that seem ‘entirely an exercise in tactical voting.’

• Jonathan Lundell Says:

I’d say that you’re in a very small minority in not have a preference over your “approved” candidates.

It’s easy (and wrong) to be misled by the name “approval” or potential voting instructions to “vote for all the candidate you approve” (whatever that might mean). But the counting rule makes no such judgements: it simply elects the candidate with the most votes. The voter’s task is to cast a ballot that maximizes the outcome. If your preference is truly A=B>C or A>B=C, then approval is easy and non-tactical. But I suggest that such a preference is seldom the case.

192. Dan G Says:

This is not a good argument to replace one system with another. It is a good argument for having both systems working together. Lose the peerage and the House of Lords and replace it with a proportional House.

193. Kieron Gillen’s Workblog » Uncanny X-men 536 Out Says:

[...] That’ll do for now, except I’ll link to this extremely long piece on the AV with a slight maths slant. [...]

194. Gil Kalai Says:

A crucial question one can ask is the following: Is the vast under-representation in the parliament of the third largest party in the U.K. system expresses bias of FPTP against the “third powerful party” or specifically against “a party in the political center”.

The liberal democrates has much smaller parliament representation compared to their popular support. This may just reflect the fact that the two larger parties have more political power that they can exploit to optimize their showings according to the current system. (which is not based on general popular support.) And it can also reflects the current system leading systematically to drastically smaller representation of the third party (and also of smaller representation for the second party) compared to the popular support.

So one possibility is that the present situation reflects a bias towards a 2-party system of the current method but it is possible that gradually the liberal democrates will replace, say, the labor as one of these two large parties. (In which case we will have a center and right large parties and an underrepresented left party.)

Another possibility is that FPTP has specific bias built in against a central party.

AV seems to give a specific advantage to a politically central party (because we can expect this party to be in high places on voters’ list from both sides.) If AV corrects a specific bias of FPTP then it makes more sense to support it.

• Jonathan Phillips Says:

“So one possibility is that the present situation reflects a bias towards a 2-party system of the current method but it is possible that gradually the liberal democrates will replace, say, the labor as one of these two large parties. (In which case we will have a center and right large parties and an underrepresented left party.)”

It has sometimes seemed that the LDs might displace Labour as the main centre-left(ish) party, but it’s a bit like trying to turn an oil tanker – too much inertia. There is no doubt a bias in the system but it is not so much against a centre party as against any third party – in different parts of the country (well, England) there are effectively three different two-party systems (Con/LD, LD/Lab and Lab/Con).

In Scotland and Wales there are potentially four parties in contention, making for an even messier situation. In 1992 the Inverness result was LD 26.05%, Lab 25.15%, SNP 24.68, Con 22.63%, Green 1.50%. And if that doesn’t make the case for reform I don’t know what does.

The situation you mention (“a center and right large parties and an underrepresented left party”) already exists in Canada (“first past the post”) and Ireland (STV). (The Canadian situation is complicated by the presence of the large Bloc Québecois, which helps explain the succession of minority governments.) History, culture and electoral system interact to produce particular patterns of representation.

• Jonathan Phillips Says:

… and AV could well tend to accelerate the creation of different two-party systems in different parts of the country, since it makes tactical voting (with second and later choices) more systematic and more effective. What that would do to the overall pattern of party representation is a moot point. Could it be that more (and more varied) two-party systems at local level would spell the end of the two-party system at Westminster? Let’s hope we get to find out…

But as for AV giving “a specific advantage to a politically central party, because we can expect this party to be in high places on voters’ list from both sides” – there’s no benefit in being everybody’s second choice if you’re nobody’s first, (There’s also no great benefit in being quite a lot of people’s first choice if everybody else hates you – which is why Cameron and his rich backers want to keep FPTP).

195. dexmac Says:

Hi Tim,

Great article, though you might find this interesting: http://zesty.ca/voting/sim/

It compares simulations of various voting system, including Instant Run-off Voting (which is basically identical to what you’re promoting, except that all of the candidates are ranked). It does seem to have a couple problems that you wouldn’t necessarily anticipate from first principles. Approval Voting may be a better option.

196. Warren D Smith (PhD) Says:

Hi, I’m a math PhD who co-founded the voting-system reform group
ragnevoting.org and am a founding member of the center for election science.
(Recommend that you join.)

It is not often I get to educate a Fields winner about voting. A lot of people
think voting is simple hence they “automatically” understand it.
That kind of instinctual arrogance goes double for Fields medalists.
The truth: voting is very counterintuitive, and you at the time you posted, did not know
While voting is not nearly as hard a subject as your Fields medal mathematics work,
it is not peanuts either! I now correct you item by item.

Hopefully this will have a salutory effect on you.
I would love it if you came round to supporting “range voting”
and endorsed it. The world and http://rangevoting.org both
could use a prominent endorser like you.

>Gowers: Let me repeat how to vote under AV:
PUT THE CANDIDATES IN ORDER OF PREFERENCE UNTIL YOU DON’T CARE ANY MORE.
That is not complicated.

–Unfortunately this advice can be (and frequently is) just wrong.
This has been known for over 100 years.
E.g. see
http://rangevoting.org/Burlington.html
http://rangevoting.org/Frome2009.html
http://rangevoting.org/Ireland1990.html
http://rangevoting.org/IRVcs.html
http://rangevoting.org/CoreSuppPocket.html
http://rangevoting.org/IrvRevFail.html
etc etc.

>AV is unfair because the least popular party gets its second-choice votes counted first?
Oh dear…
I have already explained why it is nonsense to suppose that AV gives
“more” votes to supporters of unsuccessful parties…

–IRV (instant runoff voting; the USA terminology, unusually, here is superior to British)
can indeed be unfair, and the reason is that some votes are counted while others are not
counted. Which? It can seem arbitary and whimsical.
For example in the Burlington Vermont 2009 election (URL above) Kiss won even though a
majority of IRV voters said on their ballots they preferred Montroll over Kiss.
In fact moderate to large voter majorities preferred Montroll over X for every X.
The reason is that IRV did not count some votes that said “Montroll>Kiss”.
(More precisely, it ignored the fact those ballots ranked Montroll ahead of Kiss.)
IRV counted a higher percentage of Kiss>Montroll ballots, than Montroll>Kiss ballots.
I think it is safe to say that some of th latter kind of voters would regard
this as “unfair”!
However in a different election situation IRV would have counted more of the latter
than the former… Who gets their opinion counted at the crucial juncture? It can
seem arbitrary and whimsical and depends in a complicated way on the exact election
situation.
You may enjoy the following puzzle: create an election example where candidate A
is preferred versus each opponent by a 99% supermajority, but with instant runoff voting A
does not win (indeed finishes in last place). Your example should have fewer than
20 candidates.

Also, Burlington and Frome 2009 both exhibited “non-monotonicity” where, e.g.

How would you feel if it was your anti-Kiss vote that was the crux that directly caused
Kiss’s victory? Would you feel that was “fair”?
These perverse and unfair phenomena are not rare, as the probabilities link above shows.

>A quick slogan:
AV IS MULTIPLE-ROUND VOTING MINUS TACTICAL GAME PLAYING.

–Sorry, slogan false. There is plenty of tactical game playing. Indeed, you here
are just flat out contradicting the single most important theorem in voting theory, see
http://rangevoting.org/GibbSat.html
Here is an amusing puzzle re that:
How can you vote, with IRV, in such a way as to be absolutely sure that your vote
will not help candidate Hitler to win? (Answer: there is no answer! Also no
answer with FPTP.) However with range voting, there is a way to thus safely-vote…

I happen to think that two-round plurality voting (top 2 move on to 2nd round if no
majority winner; call this “T2R”) is a superior system to IRV. The reasons are subtle, see
http://www.rangevoting.org/HonestRunoff.html
http://www.rangevoting.org/TTRvIRVstats.html
http://www.rangevoting.org/TTRvsIRVrevdata.html
democracy, and improved voting systems are not of much interest if you have permanent
1- or 2-party domination. IRV will thus yield the diametric opposite
of proportional representation (I point out since
you seem to like proportional representation).
Meanwhile T2R often yields countries with more than 2 parties in power.
If you want a single-winner voting system that will allow third parties to
win reasonably often, consider range voting. One reason why is outlined here:
http://www.rangevoting.org/NaiveExagSumm.html

>AV is complicated/obscure/perverse.
I’ve just dealt with this objection. My basic answer to it is, “No it isn’t.”

–Re “no it isn’t” perverse, the authors of the paper
“Single Transferable Vote: An Example of a Perverse Social Choice Function,”
American Journal of Political Science 21 (1977) 301-311
might disagree with you!

Here’s a sample simple IRV election demonstrating many paradoxes simultaneously:
http://www.rangevoting.org/CompleteIdioticIRV.html
If you don’t think this is “perverse” you’re nuts.

Non-monotonicity is just one example. IRV exhibits more such perverse paradoxes than any
other commonly proposed voting system, and see URL above demonstrating this is common,
not rare.

–Re complexity:
Sorry: there is actual evidence on the complexity question and it contradicts your
non-evidence-based intuition. Voters “spoil” their ballots more
frequently with IRV than any other common voting system. So we know that voters
find it more complicated. The best systems by that measure are approval and (surprisingly)
range voting, both of which do better than FPTP and much better than IRV:
http://rangevoting.org/SPRatesSumm.html
Another evidence is, IRV has greater Kolmogorov complexity than range, approval, or FPTP.
Another probkem is, even when you think something is simple, lawmakers will
make it complicated. Don’t believe me? See
http://www.rangevoting.org/NCIRVrules.html
for actual verbatim text of the instructions North Carolina gave to election workers
(most of whom are minimum-wage workers without a PhD…) about IRV.

>AV leads to the election of mediocre candidates?
The argument here is that under AV you often end up electing the candidate
who is least disliked rather than the candidate who is most liked. This is supposedly
a recipe for mediocrity…
To sum this up in a slogan:
FPTP HELPS EXTREMISTS.

–I do not know about “mediocre,” but I can tell you that
IRV does tend to elect “extremists” and is biased
against “centrists.” I think FPTP does not have such a bias, or it is smaller.
See
http://www.rangevoting.org/IrvExtreme.html

>In fact, I can feel a slogan coming on.
UNDER FPTP A CANDIDATE IS OFTEN ELECTED EVEN THOUGH MOST PEOPLE PREFER A DIFFERENT CANDIDATE.

–But you forgot to say:
under IRV, A CANDIDATE IS OFTEN ELECTED EVEN THOUGH MOST PEOPLE PREFER A DIFFERENT
CANDIDATE. This is the “Thwarted majority paradox” and it happened in Burlington 2009,
see URL above. It indeed happens in about 25% of IRV elections in the 2D spatial model
here
http://www.rangevoting.org/IrvExtreme.html
as you can see almost immediately from the pictures.

>AV benefits the Lib Dems and nobody else.
This is false. It benefits any party that is small but large enough…
The Greens are an example.

–Actually IRV has little or no benefit for any third party. The Australian House, elected via
IRV, elected exactly one member of a third party over the last 4 election cycles (600=4*150
seats in all) combined. IRV leads to 2-party domination. It is a standard misleading piece
of pro-IRV propaganda, that IRV benefits third parties. Every IRV-using country has
gotten 2-party domination in IRV seats. This is not disputed in Australia.
The Australian third parties, including the Greens, all are against IRV for this reason:
http://www.rangevoting.org/AusIRV.html
Also, a recent poll of 1202 random Australian adults
found that they prefer plain-plurality (FPTP) voting versus the preferential (instant runoff)
system they presently use (if forced to choose one) — i.e. they’d like to abandon IRV
despite having used it 80+ years to elect House — the poll result was 57% to 37%
(with 5% don’t know/refuse). I conjecture that the reason was some combination of
(i) greater complexity for IRV
(ii) since the IRV seats are 2-party dominated, you might as well use FPTP since you are going
to get the same result more simply. (This is not really true because of “spoilers” but it is
true to a good approximation. With IRV the same winner as FPTP happens (95+-1)% of
the time in the real world. With T2R, it is (84+-2)%, and I think about the same will
be true with range voting (but with only 1 not two elections needed).

–SUMMARY.
Many pro-IRV arguments out there are bogus (as are many anti-IRV arguments).
I happen to agree with you that IRV probably is a net improvement for Britain versus FPTP.
But it is a pathetically _small_ improvement.
It will probably still yield 2-party domination for Britain and
won’t change much. There will be some slight advantages (such as solving the “spoiler” problem
in “2 and a half candidate” races, although not in “3 candidate” races) as well as some
disadvantages (such as greater complexity and voter error rates, embarrassing
failures, and more near-ties).

Britain, the LibDems, and the world missed a great opportunity for genuine reform here.
“bayesian Regret” analysis of voting systems (which I am the world’s foremost expert on)
indicates switching to range voting will cause comparable or larger benefit to the invention
of democracy in the first place.
http://rangevoting.org/BayRegDum.html
Since you are into simplified “slogans” I suggest you consider this graphic:
http://rangevoting.org/BayRegsFig.html

Warren D. Smith (PhD)
and
math.temple.edu/~wds/homepage/works.html

• gowers Says:

A few small points.

Gowers: Let me repeat how to vote under AV:
PUT THE CANDIDATES IN ORDER OF PREFERENCE UNTIL YOU DON’T CARE ANY MORE.
That is not complicated.

–Unfortunately this advice can be (and frequently is) just wrong.

… as I made clear in the post and in subsequent comments. I’m going to be
posting again soon and will discuss this point in more detail.

Also, Burlington and Frome 2009 both exhibited “non-monotonicity” where, e.g.

I gave a non-monotonicity example in the post. My main point here is
that general elections tend to be national campaigns, so the main
result is unlikely to be affected by the (admittedly undesirable)
non-monotonicity in a handful of constituencies.

A quick slogan:
AV IS MULTIPLE-ROUND VOTING MINUS TACTICAL GAME PLAYING.

That was a slogan, and as such an exaggeration of what I think. But if
you look at the surrounding discussion you’ll see that what I’m actually
saying is that the opportunities for tactical game-playing are limited
under AV (mainly because voters don’t have enough information
about the intentions of other voters — that is why multiple-round
voting makes tactical voting easier). The theorems you refer to
assume perfect information (or at least, I imagine they do).

I happen to think that two-round plurality voting (top 2 move on to 2nd round if no majority winner; call this “T2R”) is a superior system to IRV.

I’d be happy with that system, but it’s not on offer.

The reasons are subtle, see
http://www.rangevoting.org/HonestRunoff.html
http://www.rangevoting.org/TTRvIRVstats.html
http://www.rangevoting.org/TTRvsIRVrevdata.html
Essentially, IRV will lead your country into 2-party domination sterility, crucifying democracy,

I’d need some pretty good argument before accepting that.

AV is complicated/obscure/perverse.
I’ve just dealt with this objection. My basic answer to it is, “No it isn’t.”

–Re “no it isn’t” perverse, the authors of the paper
“Single Transferable Vote: An Example of a Perverse Social Choice Function,”
American Journal of Political Science 21 (1977) 301-311 might disagree with you!

Here’s a sample simple IRV election demonstrating many paradoxes simultaneously:
http://www.rangevoting.org/CompleteIdioticIRV.html
If you don’t think this is “perverse” you’re nuts.

It’s a nice example, but the sniff test didn’t tell me which candidate should
win. I agree that the results are perverse in this case, but because the
electorate doesn’t (in my view) express a clear preference I am less
bothered than I am in FPTP situations where the electorate expresses
a clear preference that is ignored. I mean this kind of situation:

http://i.imgur.com/Zb9tJ.png

–Re complexity:
Sorry: there is actual evidence on the complexity question and it contradicts your non-evidence-based intuition. Voters “spoil” their ballots more
frequently with IRV than any other common voting system. So we know that voters find it more complicated. The best systems by that measure are approval and (surprisingly) range voting, both of which do better than FPTP and much better than IRV:
http://rangevoting.org/SPRatesSumm.html

Thanks for this — I didn’t know about it.

AV leads to the election of mediocre candidates?
The argument here is that under AV you often end up electing the candidate
who is least disliked rather than the candidate who is most liked. This is supposedly a recipe for mediocrity… To sum this up in a slogan:
FPTP HELPS EXTREMISTS.

–I do not know about “mediocre,” but I can tell you that
IRV does tend to elect “extremists” and is biased
against “centrists.” I’m not sure what FPTP’s bias is on that, but suspect
it is smaller.
See
http://www.rangevoting.org/IrvExtreme.html

Your examples have lots of candidates with a realistic chance. In UK general elections there are usually at most three and just occasionally four such candidates. I know there are problems with putting political views on a one-dimensional scale, but if you do, then I don’t see what’s wrong with the argument that AV will provide a pressure towards the centre (if there are only three parties, that is).

In fact, I can feel a slogan coming on.
UNDER FPTP A CANDIDATE IS OFTEN ELECTED EVEN THOUGH MOST PEOPLE PREFER A DIFFERENT CANDIDATE.

–But you forgot to say:
under IRV, A CANDIDATE IS OFTEN ELECTED EVEN THOUGH MOST PEOPLE PREFER A DIFFERENT CANDIDATE.

What I really meant, but couldn’t express concisely in a slogan, is that under
FPTP the Condorcet loser can win, but under AV this is impossible. I think the Condorcet winner probably has a better chance under AV than under FPTP too.

IRV leads to 2-party domination. It is a standard misleading piece of pro-IRV propaganda, that IRV benefits third parties. Every
IRV-using country has gotten 2-party domination in IRV seats.

I thought there were only three IRV using countries. Are there examples where IRV has taken a multiparty system and converted it into a two-party system?

–SUMMARY.
Many pro-IRV arguments out there are bogus (as are many anti-IRV arguments). I happen to agree with you that IRV probably is a net improvement for Britain versus FPTP. But it is a pathetically _small_ improvement. It will probably still yield 2-party domination for Britain and won’t change much. There will be some slight advantages (such as solving the “spoiler” problem in “2 and a half candidate” races, although not in “3 candidate” races) as well as some disadvantages (such as greater complexity and voter error rates, embarrassing failures, and more near-ties).

Britain, the LibDems, and the world missed a great opportunity for genuine reform here. “Bayesian Regret” analysis of voting systems (which I am the world’s foremost expert on) indicates switching to range voting will cause comparable or larger benefit to the invention of democracy in the first place:
http://rangevoting.org/BayRegDum.html
Since you are into simplified “slogans” I suggest you consider this graphic:
http://rangevoting.org/BayRegsFig.html

Having said all that, I like range voting, though I’m worried that it’s a bit
too tactical. What I mean by that is that if I had a ballot paper in front of
me, I wouldn’t find it at all obvious what I should do. For example, should
I maximize my influence by putting all candidates at one end or the other
(of the range)? Does that maximize my influence? I just don’t know. I’m
sure you’ve got plenty of thoughts on this question …

[PS To all NO-ists, note that despite all the criticisms Warren Smith has of AV, he still thinks it's better than FPTP.]

197. Atreic Says:

I came up with (what I think is) an interesting thought experiment about the AV/FPTP debate.

Parallel run the next set of elections, letting people vote twice, once under AV and once under FPTP. Announce the results under AV, and the results under FPTP. Then in every constituency where the outcome was different, let everyone vote for whether or not they wanted the candidate elected under FPTP, or the candidate elected under AV, in a straight fight between the two candidates.

I think, trivially,[1] that the majority would vote for the candidate elected under AV over the candidate elected under FPTP when these were different, because that’s what AV does better at finding. Which suggests to me AV is a better system for finding the people we want to represent us.

[Not to mention that it's better for increasing information on voter preferences, avoiding tactical voting, etc etc etc. Let me encourage you all once again to read Prof Gowers' fabulous article above ;-)]

[1] assuming conservation of voters – if you suddenly got lots of people turning up to vote the second time who were too apathetic to vote the first time then things might jump around a bit. Or if everyone changed their minds about who they liked in the intervening 2 days…

• Mark Wainwright Says:

I think this is a very nice thought experiment. In other words, if people voted between AV and FPTP according to the results it gave in their constituency in a real election, practically every constituency where it made a difference would show a majority for AV. That seems like a pretty compelling distillation of many of the reasons to prefer it.

I know people may say other systems will find a Condorcet winner more reliably than AV – which may or may not be true, it doesn’t seem to be clear-cut in practice – but we’re not being offered other systems; the choice is between these two.

198. Jonathan Phillips Says:

Suppose you were to ask a representative sample of voters to rank the various political parties on this scale:

a. like a lot
b. like a bit
c. no opinion
d. dislike a bit
e. dislike a lot

Which parties would tend to score most a’s, b’s and c’s, and which most d’s and e’s? Which parties tend to be widely liked (or at worst to leave people indifferent), and which to be widely disliked?

It is clear, from the hysterical intensity of the anti-AV campaign run by the Tory party and its wealthy backers that they fear that their party is the most widely disliked and that it can therefore only hope to win against a divided opposition. AV enables us to unite against those we strongly dislike, and that is what has really spooked the Tories.

Of course there was a time when the Conservatives could win comfortably against a fully united opposition – but that was in the days of Macmillan…

• MorningTory Says:

Jonathan

There are, of course, Tories that fear AV for the very reasons you set out. But most I have spoken to (and I’m guessing I know more of them than you do) are not particularly worried that AV would harm the electoral chances of the Conservative Party. They simply don’t believe that Vince Cable’s “progressive majority” is a reality. If there were a “unified opposition” there would be only one opposition party.

No, the reason Tories tend to oppose AV is that they don’t believe that it would be right for one person’s 5th preference to count for as much as another person’s first choice. It’s a simple as that.

• Jonathan Phillips Says:

Please note that I supported AV as an improvement on “first past the post” *long* before I began to loathe the Tory party (which was in the mid-80s – I felt no great hostility towards the party of Macmillan and Heath, and there were certainly times when I would have preferred them to Labour).

If I really support the Greens and quite like the LDs, but see that in my constituency the only two that could possibly win are a right-wing Tory and a moderate Labour candidate I would very likely vote Labour. Labour would be my THIRD choice – but you would have no objection to that counting as the equivalent of your first-choice vote for the Tories. AV simply makes explicit what “first past the post” hides.

It could, of course, be worse. If I lived in Scotland, Wales or Cornwall (where I come from) I might well rank the respective national parties higher than the LDs. But again, if the only two candidates with a chance of winning were right-wing Tory and moderate Labour I would most likely vote Labour – my fourth choice. And you would be happy to regard that as the equivalent of your first choice – wouldn’t you?

And finally, it’s one thing to oppose AV, it’s quite another to keep spewing out lies about it – remember that £250 million?

• MorningTory Says:

“Labour would be my THIRD choice – but you would have no objection to that counting as the equivalent of your first-choice vote for the Tories.”

That’s correct. It is your first choice VOTE, given the political landscape you are presented with. I accept that you would prefer a political landscape that is more favourable to the “acceptable” candidate you actually prefer.

“remember that £250 million?”

I do not represent the No campaign, and it’s not an argument I use. But the £250 million is not a lie as such, but an estimate [I agree that the cost of the referendum should not be included in the estimate, and it is regrettable that estimate does so.]. Voting machines may or may not be used (there are good reasons to expect that they might) but either way, I don’t actually see the £250million as a wild estimate. It works out at <£60k per local authority. Having worked in the public sector for my entire career (and spent millions of pounds of taxpayers money myself) I don't think that's particularly unrealistic.

But the real reason I would never use that argument is that, if AV genuinely were fairer, £250m that wouldn't be an unreasonable price to pay.

And finally, the Yes campaign has not exactly shied away from "stretching the truth" either!

• John O Hart Says:

Trust MorningTory to come up with a stupid idea. Under FPTP you have no way of telling if my single vote is for my first preference or my 5th preference, yet it’s counted equally with your single vote.

In the end any election comes down to a contest between two candidates. In a democracy I have as much right as MorningTory to decide which should be elected.

Any intelligent voter will vote for the one of the two leading candidates whom he prefers. But under FPTP you’ll sometimes not know who the leading candidates are. Under AV you’ve got far more chance.

• gowers Says:

“Any intelligent voter will vote for the one of the two leading candidates whom he prefers.”

I almost agree with that. However, I think it applies to one-off elections and not quite so strongly to elections that come in a series. For instance, in the past I have voted Lib Dem in Cambridge when they were trailing third in the polls. That is because I wanted to maximize their vote share, so that, just perhaps, they would come to seem credible candidates at some point in the future. Amazingly, this actually happened, and I have seen the seat change from fairly safe Conservative to three-way marginal (but with the Alliance third, if I remember correctly) to fairly safe Labour with Lib Dems second, to Lib Dem with the Conservatives second, closely followed by Labour. My guess is that we will go back to Labour at the next election, but a lot could happen between now and then.

This is the kind of use of a vote that Morning Tory very much likes. I myself regard voting as part of an extremely uncertain 20-year strategy as second-class voting.

• MorningTory Says:

“Under FPTP you have no way of telling if my single vote is for my first preference or my 5th preference, yet it’s counted equally with your single vote.”

I suppose that may be true. The system forces you to decide. I don’t
see a big problem with that. Electing a parliament is a serious matter and should be taken seriously.

“This is the kind of use of a vote that Morning Tory very much likes. I myself regard voting as part of an extremely uncertain 20-year strategy as second-class voting.”

I think “very much likes” is overstating it a bit. But yes, I do think it is better to vote for the candidate you most sincerely support than vote tactically or simply pass up your right to have you voice heard because you might not “win”.

• Chris Purcell Says:

“I do think it is better to vote for the candidate you most sincerely support than vote tactically or simply pass up your right to have you voice heard because you might not “win””

It’s not about “winning”, though — it’s about your life for the next 4/5 years. If you believe Conservatives will make the best decisions, but the papers are telling you your area is split between Lib Dems and Labour, voting blue because they’re the party you most sincerely support may be worth less to you than having a say between bad and worse (whichever way around you believe that to be!). As you say, an adult decision, but one that makes it very difficult to tell what people actually want, and hence represent them.

AV doesn’t make tactical voting impossible, but my understanding is that it does make it _much_ harder to do _accurately_. Any significant level of noise in your predictions about first and second choices are likely to wipe out any benefit, and indeed shoot you in the foot. Without the smokescreen of tactical voting, there is the opportunity to see what everyone actually wanted. Maybe the seats where Conservatives are a distant third will turn out to be blue strongholds.

If FPTP and tactical voting was the only option, I would agree everyone should just get on with the serious adult decision of whether to vote head or heart. But AV is a credible alternative, and I think it’s more important to find out what people actually want than to worry about whether staunch mainstream single-party voters will have less “influence” than BNP five-bites-of-the-cherry voters (or, as mentioned above, whether it’s the other way around).

• MorningTory Says:

Well, it’s true that AV would (more or less) expose the genuine first-preferences of the electorate. The trouble is, it doesn’t end there. If you view any vote that is not for your sincere first preference as “tactical” (and I do) then it is difficult not to conclude that AV is nothing more than institutionalised tactical voting.

• Chris Purcell Says:

It may not be institutionalised, but I think it’s fair to say tactical voting is already a British tradition. Whether you like it or hate it, under AV at least you can identify it.

199. Fnord Edsel Says:

I’ve seen the assertion in that under AV you can’t tell if someone was elected by enthusiasm or by a dislike for someone else.

Here in Australia, that information is available in exhaustive detail through the Australian Electoral Commission. For instance, consider these results for one electorate in our 2007 Federal Election:
http://results.aec.gov.au/13745/Website/HouseDivisionDop-13745-193.htm

Smart candidates can study these and find where their preferences came from, and where they went. I chose this particular electorate because it shows preferences meaning something. If you want to see some other electorate, start here, click on an electorate, then click on ‘Full Distribution of Preferences’.
http://results.aec.gov.au/13745/Website/HouseSeatsDecidedOnPrefs-13745-NAT.htm

http://results.aec.gov.au/13745/Website/HouseInformalByDivision-13745-NAT.htm

200. JPP Says:

I’m a poor Frenchman quite far from this fierce debate. As interesting as this post may be (and it certainly is!), I don’t see how the counting can be done in a reasonable amount of time without electronic machines. Can someone enlighten me?

• Jonathan Phillips Says:

Mon cher JPP-

There are more complex preferential voting systems than AV. For all elections in Ireland, all but Westminster elections in Northern Ireland, and local elections in Scotland the system used is STV, where several representatives are elected for a single constituency or ward. This involves transferring not just the votes of candidates who are excluded but also the votes cast for successful candidates who have exceeded the quota required for election. It can take quite a few rounds of counting (google up some information on Irish elections) but it is all done by hand.

AV is altogether simpler. In some constituencies (a third?) only one count is needed because one candidate has an overall majority (premier tour); in others (another third?) only a small proportion of votes would need to be recounted to give one candidate an overall majority; in the remainder more transfers and counts would be needed. In the very “worst” case the process might require maybe 50-60% more person-hours to complete (and that’s every four or five years.) So employ sufficient counting agents and the result will be out as quickly as it is now – or you just wait until the next day.

• Fnord Edsel Says:

@JPP:

That’s another thing we have in Australia – paper ballots. Since we don’t vote for a President (we elect someone to the House of Representatives from each Electorate, and they choose a Prime Minister), there are 150 elections to count. There were 12,930,814 votes cast, 117,561 of those in the single densest electorate.
http://results.aec.gov.au/13745/Website/HouseTurnoutByDivision-13745-NAT.htm

Estimates based on first preferences are announced on the evening of the election, and the preference breakdown is announced for most electorates in a couple of weeks. A few electorates will have really close results (within 100 votes of a different outcome) and have recounts, taking a few weeks longer. Candidates seem to trust the process – legal challenges to the count are very rare.

201. JPP Says:

I’m quite lost, but I guess it’s because I assume something false.

In France, for each election, volunteer citizens gather at each polling place, open all the envelopes, and transfer the list of the results. The results are then summed over the relevant region (which can be the whole country for the presidential election or much smaller for the various local elections).

If this system is used for an AV vote, that means that the guys opening the envelope have to note the whole ordered list of candidates instead of just putting a tick in front of the candidate’s name. And that is much longer (in France, with the current system, the counting of the votes at each polling place takes one hour, two tops), probably too long to be done.

So I guess that something works differently in Australia or Ireland, and that allows AV to be apply by hand. Do you send the whole bunch of envelopes to the center of the constituency, where they are counted by civil servants or something to the effect?

202. Jonathan Phillips Says:

The ballot papers aren’t in envelopes, just folded, so that speeds things up a bit. There’s no question of trying to count all the preferences at once.

First all the 1′s are counted – just as if we were counting X’s. If any candidate gets more than half of the total valid vote that’s it (the outcome in perhaps two of the nine Norfolk constituencies). If not, the last-placed candidate drops out and the ballot papers which originally went to him/her are reexamined and, where a second choice is indicated, transferred to the appropriate candidate. If any candidate now has more than half of the remaining votes that’s it.

On the whole the lowest-placed candidates do not get very many votes, so the initial stages are over over quite quickly – and in some cases will produce a result. (That would probably have happened in five Norfolk constituencies.)

Elsewhere larger piles of votes will need to be transferred, perhaps several thousand, before a clear winner emerges; particular ballot papers may have to be transferred a second or even third time before the process is completed. In one of the Norfolk seats (which was won by the LDs with less than 30%) quite a few thousand ballot papers would have had to be reexamined and transferred before any candidate emerged victorious in the decisive round.

The process can be speeded up, e.g. by starting to count the second preferences marked on the ballot papers accumulated by candidates who obviously can’t win before the initial tally has been completed; or by transferring the votes of several of the lowest-placed candidates at once, where their total vote would not be enough to affect the ordering of the higher-placed candidates.

Sounds worse than it is – and at least we don’t have to go through the whole thing twice…

203. Gil Kalai Says:

At some point in the discussion Tim said “In UK general elections there are usually at most three and just occasionally four such candidates” and I would like to take it as an opportunity to make some point. This, and also parts of Tim analysis in the post study the different voting methods based on the current political structure and former election outcomes. This is a reasonable thing to do, but we have to take into account that the political system is pretty much based on the current voting mechanism. (And so are the previous election outcomes.) If the current method gives a huge disadvantage to a third party this may explain why we have only three parties and this may change under AV.

In israel there was a strong popular movement 15 years ago (which led to much enthusiasm and support and was very successful) aimed at changing the election system. The new system (pretty much similar to the method of electing mayors in Israel) was based on separating the parliament votes and the votes for the post of prime minister.

Part of the rational was that small parties have too much power when they can determine who is going to be the large party forming the coalition. When it was implemented indeed small parties had less power but on the other hand they became larger. (And the large two parties had become smaller.) There was, for example, even a specific campeign under the slogan “VOTING THE SAME PARTY FOR PM AND FOR THE PARLIAMENT IS LIKE EATING A PITA FILLED WITH BREAD.” Overall, the influence of smaller parties (now medium-small) had become larger.

After several years, because of various difficulties in the new method the voting system was reversed back to (more-or-less) the old system. This particular change was not reversed and the large parties turned into medium-large and the old small parties remained medium small.

204. obryant Says:

Not that I’ve read every post above, of course, but there’s one point I’d like to make that is almost always omitted from these discussions.

National Elections are not just about who gets the title, they also determine the nature of the winner’s mandate. There is some reason to hope that AV could lead not only to winners that more accurately reflect the electorate, but also that those winners will more accurately understand why the electorate prefers them.

By mandate, I refer to those aspects of the winner’s platform that the opposition is afraid to go against. In the US right now, for example, the Tea party (a branch of the Republican party) has a mandate for cost cutting; the mandate isn’t so strong that the Democrats will vote for it, but it is strong enough that the Democrat and Republican leaderships will not block such votes (this year) from taking place.

In the US (sorry, I don’t know British politics), there are usually only two choices: Economic freedom & social restrictions, and Economic restrictions & social freedom. The role (and only role in the US) of third parties is to allow voters to express some other combination of interests, such as Economic freedom & social freedom. Concrete examples are rare; Ross Perot’s 20% in 1992 for campaigning exclusively on deficit reduction led directly to this actually happening over the next 8 years. A vote for the libertarian party first, republicans second, would amount to (after elimination rounds) a vote for the republican, but that republican, his rivals, and the public would all know that votes such as mine were *not* an endorsement of republican social policies.

• MorningTory Says:

Fotunately, in the UK social freedoms and economic freedoms are not [usually] tied together in the way that they are in the US. Matters like abortion, stem cell reearch, etc. are reeagrded as “quenstions of consience” and play no part in party politics. If anything, social freedoms and economic freedoms go hand-in-hand because the larger state, the larger in interference in people lives.

Incidentally, my wife is American, so she naturally assumed when she came to the UK that Democrat supporter would equate to Labour supporter, but she quickly realised that it’s not a simple as that…

• Gil Says:

Kevin, this is an interesting point. But when we have several serious candidates and the winner is the person who got the largest numbers of votes isnt it clearer for the winner why he (or she) was elected compared to a system where his victory expresses a complicated combination of voter’s preferences?

• obryant Says:

I think not so many, Gil. With 3 candidates, there are only 10 possible ballots (including the no-preference ballot), and probably some of those would occur with miniscule frequency. The winning candidate A will have only 5 substantively different types of ballots in his/her pocket: (A), (A>B>C), (A>C>B), (B>A>C), (C>A>B). If A would not have won without the B>A>C ballots, then B’s platform should rightly influence A’s in-office actions, while if the A-first ballots were enough, then A can rightly claim an unmitigated victory.

Four candidates lead to a somewhat messier situation, but again most of the types of ballots would occur with nearly 0 frequency.

• Chris Purcell Says:

Gil, not really. Did he get those votes because his promises are the best fit of all the candidates for his constituency, or only because he was preferable to his main opposition and lots of people voted tactically? (And how many of those tactical votes were down to his quietly bribing the local press to publish studies showing him neck-and-neck in the polls with the hated Not From Round Here party?)

• Jonathan Phillips Says:

Gil – what is chiefly objectionable about “first past the post” is precisely that it >does< hand victory to the candidate with most votes, however many people have voted for someone else and however unpopular he/she may be with the mass of voters. http://bit.ly/fldUMZ http://bit.ly/fldUMZ

The second key objection is that, on account of tactical voting, we cannot know how his/her win was achieved – with positive votes from genuine supporters or with tactical votes from those X supporters who decide they must vote for the just-about-acceptable Y as the best way of defeating the appalling Z?

The LD MP for Norwich South got in with less than 30% of the vote, a handful ahead of the Labour MP he defeated (incidentally a supporter of AV). It could well be that Charles Clarke had more "genuine" supporters than Simon Wright; it could also be that Simon would have won under AV anyway.

AV brings out into the open what "first past the post" conceals, revealing far more about voters' political preferences – surely to goodness that must be better for democracy!

205. There is no post | Timble.me.uk Says:

[...] post comes courtesy of possibly the most famous clip from The Matrix and this brilliant and very detailed analysis by a fellow mathematician. This entry was posted in In the news, Politics. Bookmark the permalink. ← Fairer Votes [...]

206. Anonymous Says:

Braindump: I was pondering the idea that you could view any voting system as some form of data compression. So the ultimate democracy would be something like having a referendum on every single issue decided by government, and the worst possible democracy (just 1 step from complete dictatorship) would be having 2 candidates that you can vote on but are then dictators for life. Then perhaps you can imagine adding in stages that take you closer to the ultimate democracy like having more candidates, having shorter periods between elections, having ranking preference on the candidates, electing more than one candidate etc…. as having progressively less data compression compared to the completely uncompressed ultimate democracy. So it seems to me that as you add in more complexity along each of these axes, you kind of oscillate around some imaginary line of “complete fairness” in this multi-dimensional space.
Anyway, it kind of feels like both FPTP and AV are sufficiently close to the original choice between two lifetime dictators that you ought to be able to enumerate all possible voting systems up to their level of complexity. And then calculate their deviation in some way from this line of ultimate fairness. And maybe by doing that you could mathematically demonstrate which system was fairer.
I think the ultimate democracy situation converges on this line. I also think having a single lifetime dictator is on the line. Perhaps this contradicts Arrow’s Theorem (I haven’t understood that completely yet). Hmmm….
It certainly feels to me like AV is closer to this line of fairness than FPTP, and it is also less compressed. It sort of feels like as things become less compressed, the systems have more degrees of freedom available to them so you can find ones that get closer to the line of fairness.
Anyway, glad I posted that relatively anonymously!

• gowers Says:

What you call the best form of democracy can run into problems. Suppose, for instance, that you take a country with two very distinct ethnic or religious groups, and that they have very different interests. Suppose also that one group consists of 60% of the population and the other one 40%. Then if you have referendums on every single issue, the larger group can have everything its own way.

Unfortunately, there are several countries that have this feature, and it often leads to serious problems. A good democratic system that is sufficiently simple to be accepted and that protects the interests of large minorities is very hard to devise. (I would advocate some kind of credit system, so that if you get your way on one thing then you expect to yield on another, rather like siblings dividing up the possessions of their parents when they die, but getting that to work in practice could be extremely hard.)

• Anonymous Says:

I meant fair in some abstract sense, thats why I said “ultimate” democracy rather than “best”. In the situation you describe, it still feels to me that you could describe the result that 60% of the population dictates to the other 40% as “fair” in some abstract sense. I think the “ultimate” democracy I described is almost by definition completely fair in some sense, every person having the exact detail of their view taken account of on every issue.
In the situation you describe, well I think the basic problem there is outside the realms of democracy – I mean there are some things that it should not be up to a democracy to decide; that is why there are things like the Geneva convention etc… A democracy shouldn’t be able to vote to exterminate a particular ethnic group for example. Actually defining what all these rules are and getting every country into a position where they were implemented and respected is of course, virtually impossible.

207. AV vs FPTP — a supplementary post « Gowers's Weblog Says:

[...] was pointed out to me in this comment of Gil Kalai on my previous post (and also another comment that I can no longer find) that there was another [...]

208. OldBloke Says:

Please forgive me if I am speaking nonsense but I fear these esoteric discussions are leading to symptoms of the ‘Tail Wagging The Dog’. The original objective, ‘…. to persuade somebody to vote yes …’ seems to have been lost and the discussion is degenerating into one that appears to be more and more about less and less. Perhaps all the NO camp needs to do to ensure success is to direct the ‘average’ person to this site and they will probably throw their hands up in horror and say “leave it as it is” – if one of the NO claims is demonstrably true, what of the others?
Could gowers add a summary of the postings (over 400) to the original paper so that ordinary people, like me, can have an honest chance of making a reasoned choice and précising the salient points to present to others who will not, or cannot, give the time to understand the issues?

209. Jamie Says:

Hi, I just wanted to comment saying that I found this blog-post really informative and explained things well, especially what I came to find out.

I have received about 3 or 4 Anti-AV leaflets all spouting the illogical and poor arguments you address in your post, yet I have not received any leaflets from the Pro-AV campaigners, despite the clearly more logical arguments for AV. This annoyed me so I went on a 1 minute search before I found your blogpost and it’s exactly what I was looking for.

While I searched to understand the issue, many people that are undecided will not take the time to read all of your reasoning. I am worried that if I have not received any YES campaign leaflets, what are the chances anyone else in my area has? And these undecided, less informed voters will make a poor decision based on the lies of the NO campaign.

Does anyone know of any site that I may use to summarise the points made against the NO campaigns lies, and the points of comparison between FTPT and AV ?

-Jamie.

• Jonathan Phillips Says:

The best explanatory video I’ve seen so far is “Is your cat confused by the referendum?” @ http://youtu.be/HiHuiDD_oTk. I know cats can’t vote (really I do), but at least it is about voting and not about going to the pub and suchlike.

A neat exposition of the fundamental problem with “first past the post” (that it can let the >least< popular candidate) win is "Ourtown Votes!" (by me) @ http://bit.ly/fldUMZ – there's a lot more stuff in my blog too, what with me being an electoral-systems anorak: try "NO" lies, The Voter's Dilemma & A better Choice. The various blog posts also include loads of links to other sites.

There's loads of explanatory and pro-AV stuff out there. Problem is, what's dropping onto our doormats consists of irrelevances, baseless assertions, misrepresentations, half-truths and lies, all funded by rich Tory backers. Dirtiest campaign by far in British political history.

210. AV vs FPTP — the short(er) version « Gowers's Weblog Says:

[...] this nice comment for a convincing argument that this 50% question is perhaps not all that [...]

211. Anonymous Says:

What do you say to the evidence suggesting that the majorities under Thatcher and Blair would have been even larger under AV?

• MorningTory Says:

I would say that all of the “evidence” is based on the assumption that 1st choice votes would not have changed under AV (Isn’t AV supposed to get rid of tactical voting). No data are availabloe for first preferences under AV for any election prior to 2010 (or none that I am aware of anyway). That means the model used to generate the “evidence” could not have have projected a Lib Dem win in any seat which they finished third. Therefore, the model systematically, over-estimates Labour and Tory seat shares.

212. gowers Says:

Here’s a thought that I now wish I’d put in the post. I think it’s unarguably a very serious defect of FPTP.

In 2000, it is widely accepted that Ralph Nader, by standing for the presidency, took votes away from Al Gore that lost him Florida and with Florida the presidency. Ralph Nader was standing on green issues, but the result was eight years of George W. Bush, possibly the least green president in living memory, and certainly MUCH less green than Al Gore. So by standing on an issue about which he felt passionately, Ralph Nader did huge harm to his cause. Do we want a political system where to campaign for a cause risks harming that very cause? Under AV, the Nader votes would have almost all transferred to Al Gore and Gore would have won in 2002.

This is not a partisan point I’m making. I think it’s also accepted that Ross Perot gave the presidency to Clinton eight years earlier.

• MorningTory Says:

“took votes away from Al Gore”

If I may say so, that’s a totally spurious argument!

• Fnord Edsel Says:

MorningTory:
“If I may say so, that’s a totally spurious argument!”

If it’s spurious, it’s widely believed. Every single brochure like the “Cambridge is a two-horse race” cited in this very post shows that the major parties believe that third parties are “taking votes away from” them. If your own party has ever produced such a brochure, in any election, your own party believes this “spurious argument”.

The sheer number of those brochures I see is the strongest argument I know for AV.

• Chris Purcell Says:

I believe the assertion was clear. Had Nader not stood, all else being equal, the vote would have gone to Al Gore. Thus, had Nader not stood, his green agenda would have been better off. True or false, this is not “pre-assigning” anything. A voter voting for a green candidate would most likely, in his absence, have voted for the greenest alternative, yes?

• MorningTory Says:

It should be plainly obvious that those people that voted for Nader DID NOT WANT GORE TO WIN!!!! If they did, they would have voted for him. The were not Gore’s votes for Nader to “take away”.

• Lesser Whark Says:

MorningTory appears to live in a world where all candidates bar the one he/she favours are equally evil and deserving of contempt. I wish the world I lived in were that simple.

I can see only two explanations:
(1) MorningTory is a strawman, trying to convince us of the benefits of plurality voting by advancing artificially foolish arguments against it.
(2) MorningTory is David Cameron.

For those who still favour plurality, here’s yet another thought experiment. Would you be happy if the referendum had the follow options (tick one only):
(1) Instant Run-Off Voting (AV)
(2) Plurality Voting where you tick the box for the candidate you favour
(3) Plurality Voting where you X the box for the candidate you favour
(4) Plurality Voting where you fill a circle for the candidate you favour

If there’s nothing wrong with plurality voting, there’s nothing wrong with this referendum, right?

• gowers Says:

Morning Tory, you’ve missed the point I was making. I’m not talking about the voters here but about Ralph Nader. By campaigning for the presidency on a green platform, he won votes that would have gone to Al Gore. (This is widely accepted.) And if he had not stood at all, Gore would have won. (This too is widely accepted.) And Gore is much greener than Bush. (Only a complete weirdo could deny that.) Conclusion: by campaigning for the presidency, Nader harmed the cause he passionately believed in.

Under AV he would not have harmed his cause. To me it seems wrong that under certain circumstances the more successful you are at getting people to support your cause, the more you damage that cause. It kinda discourages people from going out and trying to do some good in the world.

• Anonymous Says:

Mr. Gore still won the popular vote by more 500.000, so perhaps the problem is with the US Electoral College.

• MorningTory Says:

Fascinating. I don’t think I have misunderstood at all. I just have a different way of looking at things.

“he won votes that would have gone to Al Gore. (This is widely accepted.)”

This really does baffle me: “would have gone to”. On what authority do you say this?

“And if he had not stood at all, Gore would have won. (This too is widely accepted.)”

Who knows whether Gore would of won, but the point is he did. Why do pro-AV people want to reduce every election to a 2 horse race? There were three “horses” in that election. What is the problem with that?

“To me it seems wrong that under certain circumstances the more successful you are at getting people to support your cause, the more you damage that cause.”

That sounds like an argument against monotonicity failure to me… and that would be an argument against AV, if I am not much mistaken.

• MorningTory Says:

Lesser Whark

This is the argument made in the daft “cats explain AV” video, where three “cat parties” compete against one “dog party”. Or Vince Cable’s “progressive majority”. In reality the three cat aprties are one cat party, a rabbit party, and a gerbil party. The idea that these parties are “the same, but different” is ludicrous.

Oh… and I’m not actually David Cameron, my name is Neal.

• Lesser Whark Says:

@MorningTory:
The first part of my previous message amounted to a personal attack, and I apologise for typing it.

However, I think we are getting somewhere here. I don’t favour AV because of any perceived change in how people would vote with current parties in place, either in my country or yours.

I favour AV because of how it will perform in the future, no matter which parties campaign. There may not be two cat parties today, but what if there are two cat parties tomorrow? What if someone founds a clone of your own favoured party, with the exact same policies, and starts siphoning votes? Yes, it would be pretty silly to do so – but politicians do silly things all time. In the US, I see accusations of financial support being provided to third parties with the explicit purpose of splitting the vote. AV remains robust when this happens, while FPTP breaks.

• obryant Says:

The Gore/Nader issue is more subtle (and interesting) than just “Gore would have won”. In Spring 2000, most people assumed that Buchanon (running to the right of Bush) was the third-party problem. To combat this, Bush tacked from the right-center (from whence he had governed Texas) to decidely-right-of-center (from whence he governed the US). This shift to the right opened the center, and Gore correspondingly shifted his campaign away from green/populist rhetoric. This created an opening for Nader, who is oft-cited as giving us Bush. But actually, Bush took care of his wing problem, while Gore exacerbated his; that’s how it ended up.

So this is a case not only of FPTP giving us a slightly less-popular politician, but of FPTP affecting the nature of the campaign and quite plausibly leading to less popular governance.

Under AV, I would think that politicians would tend to be less acerbic towards their rivals (in the hopes of getting some #2 votes), but also feel less compelled to adjust their opinions to get votes. Could all this lead to more cooperative and thoughtful governance?

• gowers Says:

“That sounds like an argument against monotonicity failure.”

It was indeed such an argument. I think that monotonicity failure exists in both systems and is more of a problem under FPTP, for the reason that the Bush/Gore battle illustrates.

“Why do you want to reduce everything to a two-horse race?”

If you focus on policies rather than parties or politicians, you may come to understand my point of view. Some of us care about the policies that are enacted, and care much less about who enacts them. If you take that attitude, then the splitting of the left/green vote in 2002 was a tragedy because it gave us Bush. AV gives you a way to vote for policies rather than politicians.

• WJ Says:

MorningTory: “It should be plainly obvious that those people that voted for Nader DID NOT WANT GORE TO WIN!!!!”

Yes, but the point is that a majority of people at the Florida election would have preferred Al Gore to the winner under FPTP (George W. Bush). How is it fair that the election should have gone to Bush when more than half the electorate would have voted for Al Gore if it had been a two-way election between the two candidates?

• Ronald Says:

“It should be plainly obvious that those people that voted for Nader DID NOT WANT GORE TO WIN!!!!”

Now, that’s actually a ridiculous statement.

The Republicans had presidential primaries in 2000, which were between various candidates but mostly Bush and McCain.
Plenty of Republicans voted for McCain in the primaries. It should be plainly obvious that they did not want Bush to win.
Nonetheless, Bush went on to win the primaries and was selected as the Republican candidate.

In fact – the electoral system up to that point IS the alternative vote.
If I don’t get to vote McCain like I wanted to, then I’ll vote Bush.

It’s just a shame that the last step, where the people get to vote on the important bit, is not run that way.

It’s stupid to claim that AV is not a better system.
It’s used by Republicans (and, every other political party) because it’s sensible and necessary aspect of one-member constituency voting.

213. Explaining The Alternative Vote | Odd: Says:

[...] those who are interested there is a great in-depth examination of both the AV and FPTP systems on Gowers’s Weblog, it does have a bit of a mathematical slant but between his post and the numerous well thought out [...]

214. Simon Owen Says:

I’ve drawn up an infographic to illustrate the AV system (disclosure: I favour the AV system) – hopefully someone will find it useful.
http://www.odd-uk.com/cool/explaining-the-alternative-vote/

215. Best post ever on “Is AV better than FPTP?” by Timothy Gowers | starshaped Says:

[...] The full original post is at: http://gowers.wordpress.com/2011/04/20/is-av-better-than-fptp/ [...]

216. Julian Woodward Says:

Very good post. Thank you. I’ve not read previous comments – only the post – but wanted to thank you for taking the time to do this.

217. Why I will say ‘Yes’ at the referendum « This is my chaos Says:

[...] the current system), and usually do so in a greater fashion.  For an in-depth examination, this post is informative, although extremely long and technical.  It’s worth taking the time to understand though, [...]

218. Quietzapple Says:

My son and elder daughter would have liked to have voted for Labour and the Green candidates respectively in the 2010 General Election

They voted Lib Dem and Labour respectively in a seat where they weigh the Tory votes but the Lib Dem claimed to have a chance The vote for Labour is counted in the national total as is that for the LIb Dem

My son is now radicalised by the way the Lib Dems have treacherously betrayed his intention: electoral politics will die if too many more take to that road

With AV they could have cast their preferences naturally: the result would have been the same most likely but they would have some hope for their votes making a difference and would be asking rather more questions of the Lib Dem and the others

219. John Shepherd Says:

As I understand it, the electoral system we shall have if the yes vote wins on Thursday is IRV (Instant Rerun Voting) with OPV (Optional Preferential Voting), as used in Queensland state general elections. (In the Australian national general elections, on the other hand, it is compulsory to rank all the candidates if one doesn’t want one’s ballot paper deemed to be spoilt.) So it might improve (but possibly reduce the motivating power of) the history section of your excellent blog, Tim, if you were to add in the results for a real AV election — the Queensland 2009 election:
Australian Labour Party, 42.3% of the first-preference votes, 51 seats
Liberal National Party, 41.6% of the first-preference votes, 34 seats
Greens, 8.4% of the first-preference votes, 0 seats
Other parties, 2.0% of the first-preference votes, 0 seats
Independents 5.7% of the first-preference votes, 4 seats
This AV result is as dramatically nonproportional as most of the UK results given in your essay. In fact, it is even more disproportional that it would have been if no transfers of votes had taken place in subsequent AV counts. There were three constituencies where the candidate leading on the first-preference count was overtaken in the final result (Barron River and Chatsworth, in both of which the ALP overtook the LNP, and Nanango, where an Independent overtook the LNP). It is therefore clear that without the transfers of lower-preference votes the 89 seats in the parliament would have been distributed more proportionally (49 ALP, 37 LNP, 3 Independents), but still in a far from “fair” manner. It is also clear that a tiny swing of 0.4% from ALP to LNP could have led to a situation in which the ALP came second to the LNP but received overwhelmingly the most seats, and that even a much larger swing to the LNP, giving them a substantial lead over the ALP in the popular vote, would still have left the ALP with the most seats – a situation far more extreme than the UK’s 1951 result.
The reason for this extreme disproportionality, of course, and as acknowledged by Tim, is not AV (just as it is not FPTP in the case of the UK, by the way) but the single-member constituency system combined with the differences in the parties’ geographic spread of support. The ALP has its support concentrated, but not too concentrated for its own good, in particular constituencies, while LNP support (and, even more so, Green support) is more uniformly spread. Thus, is clear that this feature of UK FPTP elections is also present (and apparently even enhanced!) in real AV elections.
Another feature revealed by the 2009 Queensland AV with OPV result is that in five constituencies (Chatsworth, Cleveland, Gaven, Mirani and Redlands) the winner took the seat with less than 50% of the votes cast, contradicting the continuing public claims of yes-campaigning politicians (not mathematicians, I hasten to add) that, to win under AV a candidate has to get over 50% of the votes cast.
Similarly, in the 2006 Queensland state elections, of the 28 (out of 89) winning candidates who received less than 50% of the first-preference votes, after the final count nine still had less than 50% of the votes cast. [The constituencies where this was the case were Bundaberg, Chatsworth, Clayfield, Cleveland, Hervey Bay, Lockyer, Mudgeerabe, Nanango and Noosa. In Noosa, after the final count the winning candidate still had only 42.4% (12,324 out of 29,087) of the total votes cast.]
One reassuring thing about the Queensland 2006 and 2009 results, however, is that there is only one instance [Chatsworth 2009] where the candidate with most first-preference votes was overtaken by a candidate who nevertheless failed to get 50% of the votes cast. The only other instance I know of such an outcome happens to be the Labour leadership election of 2010, in which Ed (with the help of my own first-preference vote in the members’ section!) overtook his brother David while still failing in the final count to get 50% of the votes cast. (The final percentages were: votes for Ed 48.84%, votes for David 47.76%, votes ranking neither of the Milibands 3.40%.)

• David N Says:

I don’t think anyone is claiming that AV is proportional, and there is nothing intrinsic in it that should make it more or less proportional than FPTP.

It’s a minor point, but I don’t think I have personally heard anyone on the Yes campaign claiming that a candidate needs to get over 50% of the votes CAST to win. They have certainly said things to the effect of “over 50% of the votes” without being clear about what votes they are talking about, which effectively boils down to those that express a preference between the candidates finishing first and second. I agree that they need to try to be clearer on this point.

• John Shepherd Says:

David N, you say “It’s a minor point, but I don’t think I have personally heard anyone on the Yes campaign claiming that a candidate needs to get over 50% of the votes CAST to win.”

Could I perhaps refer you to the Guardian newspaper? The Vice-chair of Yes to Fairer Votes and (so it was claimed, though the claim was later withdrawn) 59 others wrote (Letters 28 April) that AV means that “MPs need the support of 50% of their constituents [sic: not just votes, but constituents!!] to get elected”. Similarly, ten London pro-AV London Assembly members wrote (Letters, 22 April) that “Under AV MPs will need to secure at least 50% of the vote to be certain of winning”.

It doesn’t seem adequate to say that what is really meant here is “50% of the sum of the votes of the first and second candidates after the final count”. That reduces the statement to a truism, and, moreover, one that applies to FPTP as well!

To give another example, Nick Clegg on the Today programme this morning refers to “a system like AV where you have to try to get majority support”. This modified formulation of the same claim, because it contains the words “try to”, is clearly more defensible in strict semantic terms. (We will ignore the fact that candidates in all systems, including FPTP, generally try to get as many votes as possible, and majority support would be just great!)

The “50% needed to win under” claim has been much the most telling point for several friends of mine who intend(ed) to vote yes, so I don’t expect the yes campaign to make themselves clearer on this point, as David N would wish, before Thursday!

• David N Says:

John, regarding the first letter, all I can say is that whoever actually wrote it is a blithering idiot, and the rest need to be more careful what they put their signatures to.

The second quote is a similar to what I already acknowledged had been said, although this version is true (but is also true of “FPTP”), though somewhat misleading.

I take your point about the 50%, when correctly defined for AV, also applying to FPTP, although under AV this will probably be 50% of a significantly larger proportion of the total votes cast.

Of course, if all electors did as I would do under AV, which is to use all of my preferences, then gaining support, to some degree, of 50% of the electorate (but not of constituents, of course – that’s just silly) would be necessary to win, so we have the opportunity to force that requirement.

While candidates do not need to gain 50% of the total votes to win under AV, at least they cannot win if they are the least-favoured candidate of well over half of the voters, as can happen under FPTP.

220. Alternative Voting System? Says:

[...] B3TA: Alternative Vote Explained – The Crime Studio Here is AV, explained by a mathematician: Is AV better than FPTP? Gowers's Weblog Reply With Quote [...]

221. Matt Says:

In the section:
“AV is unfair because the least popular party gets its second-choice votes counted first.”

I’m afraid that your “proof” is flawed. In your example, you ignore the fact that if the BNP supporters’ second choices were to take one of the other parties above 50%, then the process would end and the Lib Dem second choices will not be taken into account. This breaks the symmetry between the BNP and Lib Dem votes and demonstrates the logic behind the statement that you are trying to disprove.

You also take the fallacy that many in the “yes” camp make, which is to assume (or, at least, imply) that AV will prevent many of the anomalies observed historically with FPTP. Without knowing the distribution of second, third etc choices, it is impossible to say what would have happened.

Much of the choice between AV or FPTP comes down to one’s definition of “fair”, which will make it pretty impervious to any meaningfully rigorous mathematical analysis. Besides, there are other factors to take into account, such as the strength of the resulting government, the existence of constituencies etc, so the most “fair” system may not be the best for the country.

• Chris Purcell Says:

“I’m afraid that your “proof” is flawed.”

I’m afraid your proof is itself flawed. The 50% rule is just an optimisation. Consider a version of AV where you continue to knock out candidates until only one is left. The only second choices ignored in this system are those of voters who put the winning party first (which seems fair, as their primary vote has not been discarded). Now notice that, if in any round one party holds more than 50% of the vote, they _must_ win, since nobody can now outstrip them; thus, we can save ourselves some wasted work and stop early. Voila: AV. (This has been stated more elegantly elsewhere in these comments, but I don’t blame you for not having absorbed them all: the only thing scarier than the scroll bar on this post is how small it looks in comparison with the scroll bar on the comments.)

You make a good point that we have no solid data to back up many AV claims. However, unless we adopt AV we will never be able to get that data. This is, in fact, my own chosen argument for AV: only by eliminating the noise signals introduced by tactical voting can we can hope to understand what people are voting for. Alas, this argument has not been made by the AV campaign.

• gowers Says:

If you don’t believe what Chris said, try to find an example where it would make a difference to the outcome if you counted the Lib Dem second preferences before those of the BNP. You’ll find you can’t.

In the case you describe, if the BNP would have pushed the Conservatives over 50%, then it’s impossible that the Lib Dems would have pushed Labour over 50% (since then we’d get the number of voters adding up to over 100%). So the result would be that the Lib Dems pushed Labour up to somewhere less than 50% and then after that the BNP pushed the Conservatives over 50% (unless the Lib Dems had done that for them).

It makes a difference to the process (since once one party gets over 50% there is no need to continue counting) but not to the outcome.

• John Shepherd Says:

Matt says: “In your example, you ignore the fact that if the BNP supporters’ second choices were to take one of the other parties above 50%, then the process would end and the Lib Dem second choices will not be taken into account.”

Actually, as has been pointed out by Chris Purcell and others, in this example the Lib Dem second choices could not alter who wins the seat.

You are right in one particular respect, however. Namely, if Tim Gowers’ algorithm were used for the counting process, it would be halted before the Lib Dems’ second choices could be ascertained. In real AV elections, I am glad to say, such as the Queensland ones, the counting process used is one in which, even if the winning candidate gets over 50% of first preferences, the elimination of candidates and redistribution of their second, third choices, etc continues until only two candidates remain in the count. The winner’s percentage (and that of the eventual second-placed candidate) increases as the process continues. (This continuation of the process is as it should be: to maintain the symmetry that Matt mentions, the statistics on the lower preferences of Lib Dem voters in your example should be just as public as those of the BNP voters.)

To summarise, Tim’s algorithm ascertains the winner, but the algorithm for the full count should read:

1. Count all first-preference votes not yet counted.
2. If there are two parties, then HALT. (The party with the most votes then wins.)
3. If there are more than two parties, take the party with the smallest number of first-preference votes and change each vote for that party by removing the first-preference votes and turning k-th-preference votes into (k-1)-th-preference votes for each.
4. Remove that party from the list of preferences of all other voters.
5. GOTO 1.

• Matt Says:

“If you don’t believe what Chris said, try to find an example where it would make a difference to the outcome if you counted the Lib Dem second preferences before those of the BNP. You’ll find you can’t. ”

Sure, it doesn’t appear possible for a 3 party example, but it isn’t difficult to find a 4 party example where the order does make a difference, e.g. if we have 4 parties, A,B,C,D

27 % vote A,B,C,D (order of preference)
26 % B,C,D,A
24 % C,D,A,B
23 % D,A,B,C

Under both FPTP and AV, party A would win. However, if we had decided to eliminate C in the first round, rather than D, then we will end up with D winning. Hence, the order in which the eliminations occur can be critically important to the outcome.

Moreover, considering that 73% preferred D to A, I wonder whether the AV/FPTP result would be considered “fair”.

Personally, I think all the “fairness” arguments can be boiled down to a simple example: We have 5 people, 2 are Conservative, 1 Labour, 1 Lib Dem and 1 Green. All the non-Conservatives would prefer Labour to govern over the conservatives. Which party should get the seat?

I can sympathise with both points of view, but myself, I am inclined to go with the Conservatives, as their position in this example demonstrates a better chance of providing strong leadership. Hence, I will be voting no to AV.

• Chris Purcell Says:

“27 % vote A,B,C,D (order of preference)
26 % B,C,D,A
24 % C,D,A,B
23 % D,A,B,C”

This kind of example is where Arrow’s Theorem bites: there is no right answer. After all, 74% prefer A to B, 76% B to C, 77% C to D and 73% D to A. Everyone loses.

” 5 people, 2 are Conservative, 1 Labour, 1 Lib Dem and 1 Green”.

Very neat example. But what if LD and Green believe it’s a two-horse race and vote Labour under FPTP? (1) They are both right. (2) Labour wins despite your choice of voting system. (3) You now have no way of telling that Conservatives would have won but for tactical voting.

• gowers Says:

OK I take back the assertion that the order makes no difference. But I think that in practice it makes no difference. (If I had time, I might try to come up with sufficient conditions for it to make no difference and then argue that these almost always occur.)

• Flatfrog Says:

I agree that this is a flaw (in fact the biggest flaw of AV). But I think that it’s very rare that this is a flaw that produces a worse result than FPTP. In the case where a minority party’s second pref votes takes another party over 50% before a larger minority is taken into account, it’s almost certainly going to be the leading party that is pushed over the mark, which is the party that would have won under FPTP anyway.

Having said that, personally I think it would be a better system to eliminate all but the two leading parties in the first round, then reallocate all eliminated voters’ remaining preferences. It brings back some tactical voting, but I think you’d see fewer anomalies.

• Andy Williamson Says:

People frequently talk about the ‘votes for minority parties’ as if they somehow ‘belong’ to those parties. They then draw the conclusion that those parties are somehow having the strongest influence on the outcome, because the smallest parties are those whose votes are redistributed first.

This is, I believe, flawed logic. The votes don’t belong to the parties, they belong to individual voters, who should be free to express such a preference, whether for the BNP (if they really must) or for the Green Party, or for, say, an independent candidate with particular local, or radical policies.

All that the redistribution does, is to show who those voters would have voted for, if their first choice candidate hadn’t been on the slate, or if, as under ‘FPTP’, they felt it necessary to vote tactically in the hope of preventing a bad outcome.

There may be a small case for the argument that AV encourages bigger parties to adopt policies that attract voters for some larger minority parties, in the hope of securing their 2nd prefs. Anyone who does this in a cynical way, is, I believe, likely to do themselves more harm than good.

222. The straw-man referendum: how the AV debate misses the point « The Dolphin's Blowhole Says:

[...] is FPTP alright in comparison with the problems of AV then?  Hardly – FPTP has consistently returned results and governments that don’t accurately represent the position of …(for example, last year the tories got 57% more of the popular vote than the lib dems but got 439% [...]

223. Travels in a Mathematical World Says:

Maths of AV: a reading list…

looks at, and provides some commentary over, two blog posts: ‘Two cheers for AV’ by economist Dennis Leech and ‘Is AV better than FPTP?’ by mathematician Tim Gowers. Both look at some misconceptions of the whole debate and…

224. Alternatives « Notes from a small field Says:

[...] vs FPTP — the short(er) version (A follow on from Is AV better than FPTP? and AV vs FPTP — a supplementary [...]

225. David N Says:

In the list of claims by the No campaign in the article, we have “3. Under AV, some people get more votes than others.”

I would like to add a variant of this, which is “Under AV, some people get their votes counted more times than others.” The clever thing about this is that, unlike the first statement, it is actually true – technically. If a candidate is not eliminated, the votes of the voters who voted for them will not be counted again in the next round – but that’s only because we already know how many of them there are. This version of the claim may not be untrue, but it is clearly designed to deceive, and I suspect that many of those who have repeated it have been fooled into believing the untrue version.

Yes, under AV, some people’s votes are counted more times than others, but EVERY VOTER’S VOTE COUNTS EQUALLY IN EVERY ROUND (provided that they have expressed some preference between the candidates who remain in the contest).

If you care about abstract properties like “representativeness”, “proportionality” etc then AV is obviously better than FPTP.

What about if you care about real-life outcomes like lower unemployment, longer life-expectancy, better health outcomes, greater GDP per capita etc?

To me (and count me as a contrarian), the entire debate has missed the central issue of politics. The point of a political system is to make our lives better, not to have some irrelevant abstract property like “degree of proportionality”.

Off the top of my head, it seems plausible that FPTP puts just enough of a barrier between people’s wrong-headed amateurish ideas about politics and election outcomes to let the establishment run the country in a sane way, but not *too much* of a barrier. If the barrier between what people want and political decisions gets too wide then we would degenerate into dictatorship.

I think that Thatcher is a perfect example of this. We needed to get rid of the coal miners’ excessive union power; imagine if we were still mining coal at an economic loss, subsidised by the government to “protect our miners” in 2011, an outcome which seems likely had the coal miners not been moved along with the times. Popular opposition to nuclear power seems a better example, as does popular support for punitive taxes on Bankers to the extent that if the will of the people was enacted London’s financial sector would relocate to Switzerland overnight.

In summary, I am sceptical of a “total democracy” because I have more trust in a combination of the UK elite and the people than the people alone.

• gowers Says:

There’s a part of me that has sympathy for your view, since I think the country is about to reject an improvement to the voting system for reasons that are clearly wrong. But your view runs into serious problems. What if, for instance, there is genuine room for debate about what is best for the country? Or what if the same system that made tackling the miners possible also makes it possible for a government to look after the interests of one (minority) sector of society at the expense of those of another? Also, under any system we elect representatives, and at least to begin with (when there isn’t an election on the horizon) they get a chance to do things that the majority of the country doesn’t like.

• Chris Purcell Says:

“I have more trust in a combination of the UK elite and the people than the people alone.”

In the past, FPTP has delivered both. But is that because it oscillates between right-wing “elite” (when left is divided) and left-wing “people” (when left is united)? If so, that’s merely an artifact and may not last going forwards, now the Lib Dems appear to be moving to split the right rather than the left.

What you say may be true going forwards as well as looking back. Just be careful not to confuse correlation with causation.

• WJ Says:

“I think the country is about to reject an improvement to the voting system for reasons that are clearly wrong.”

That brings me to something which has been in the back of my mind for a while, namely the paradox of voting for a new voting system. If AV is a more democratic system, wouldn’t the most democratic thing be to impose it on the electorate rather than holding a referendum?

• gowers Says:

I actually think it would. And one of the reasons is that the system is so heavily stacked against change (because the party in power stands to lose from any change). For that reason, if by some miracle AV is passed on a very low turnout, I think it will be entirely OK to adopt it.

• Chris Purcell Says:

“If AV is a more democratic system, wouldn’t the most democratic thing be to impose it on the electorate rather than holding a referendum?”

Ah, irony. You forgot the markup. Someone might take you seriously.

The referendum seems entirely “representative”, though: commission a review, ignore its conclusions, wait a few years, offer only the options it discarded, insult your opposition for a few months over an issue that no longer matters, and finally let The Mail decide the whole thing.

@Gowers: “What if, for instance, there is genuine room for debate about what is best for the country? ”

Absolutely, I think there is genuine room for debate, so I wouldn’t put myself in the “No” camp. But since nobody has made an argument of the form “AV ==> better health/happiness/GDP”, I refuse to be in the “Yes” camp.

Perhaps my perspective comes from reading “The myth of the rational voter” http://en.wikipedia.org/wiki/The_Myth_of_the_Rational_Voter:_Why_Democracies_Choose_Bad_Policies

• gowers Says:

That’s not quite what I meant. What I meant was, what if there is a genuine debate about some policy, such as, say, whether to intervene in other countries when their leaders are behaving badly? Then the notion that the politicians that FPTP lets in despite representing a minority of the country know what is best becomes less tenable.

I look forward to reading that Wikipedia article though.

227. Why you should vote Yes to AV - Jonathan's Blog Says:

[...] to find that time), Andrew Gowers, a Cambridge (I’ll forgive him :P) mathematician, has a very good essay, taking a slightly mathematically-oriented look at AV vs. FPTP. His supplementary post deals with a [...]

228. Liberal Democrats can’t win here « Notes from a small field Says:

[...] appears they like this kind of graph in Cambridge as well. Perhaps the Alternative Vote would help. (3 May [...]

229. ianji Says:

My own blog post in favour of AV was perhaps equally technical but not nearly as long, referring instead to external sources for the details http://ianji.wordpress.com/2011/04/17/voting-about-voting/

230. m_sissons@hotmail.com Says:

People outside the chattering classes just aren’t going to wade through all this crap. One person one vote has a nice ring to it. That’s why it’ll be a no on Thursday.

231. Flatfrog Says:

Your ‘WTF is the post’ slogan echoes a picture I made a week or so ago – linked here since it includes swears: http://www2.b3ta.com/host/creative/47536/1303258091/fptp.jpg

Thanks for a very clear and thorough post. I don’t think any person could examine the issue rationally and think FPTP is superior to AV (although there are other systems that are better still). But as it turns out we aren’t supposed to be rational – David tells us we’re supposed to think with our guts instead.

232. Virgopunk Says:

Shame we’re so bloody minded in this country. We’ll vote ‘No’ just because the AV system seems too complicated to understand (mind you we seem to be able to figure out how to fill in a Euro Millions Lottery ticket). It was once a place of radical political thought and scientific advancement now it’s a place of superstition and apathy.

We have the chance to try something completely new and we’ll probably avoid it, the sa,e way my Gran avoid eating anything except meat and two veg her whole life, “Ooh, I’m not eating any of that foreign muck!”

Welcome to the 21st century…bah!

233. Maggie E Says:

I lived in Australia for 30 years and have recently returned to the UK in retirement. Summing up my Australian experience, just a few points:

1. Australians are happy with AV. It has been said that Australia is thinking changing their system. I am not aware of this but, if it were, it would not be to return to FPTP.

2. I find voting in Australia much more empowering than in the UK. You can vote for the person you want without any feeling of wasting a vote. It works best when you do express your preferences fully. In that case, when the election comes down to two candidates you know that your vote is still in the hunt and is sitting on the pile of the person you prefer of those two.

3. It should not be much more expensive or slow to count than FPTP. In most consituencies little redistribution is needed.

4. The information acquired from the statistics after the election are very useful in understanding trends in public opinion. For example the Greens are gaining votes in Australia. The ALP candidate won in this electorate because of Green preferences despite losing the first round (http://results.aec.gov.au/13745/Website/HouseDivisionDop-13745-193.htm – thanks to the poster above who gave this link). This means the Liberals need to do more to be green in order to do better in future. Under FPTP the Liberal would just have won.

5. AV makes tactical voting difficult for individual voters but it is worth the while of a party to influence the preferences of the voters as a whole. So distribution of how-to-vote cards should be disallowed.

I voted (legitimately!) in both the UK and Australian elections last year. The second was a much better experience. But I am not at all hopeful for this referendum.

234. John B Says:

I think one of the principal buttresses of the philosophical argument for “Yes” – that voting for an ultimately losing candidate represents a “wasted” vote – is frankly hooey. Of course this is not the only element of the argument, and of course some of the proponents of FPTP also deploy this deeply flawed argument.

Nonetheless “I didn’t bother voting because my vote would never count” seems to crop-up time and time again. I would maintain that one’s vote ALWAYS counts. Representative democracy doesn’t mean everyone has a divine right to “back a winner” and to think that they do is frankly childish.

• Flatfrog Says:

The argument isn’t that voting for a losing candidate is wasted, it’s that voting for anyone other than the two main candidates is wasted. So in order for your vote to make a difference under FPTP, you have to guess which two candidates are most likely to win, and cast your vote in favour of one of them.

AV *is* FPTP tactical voting, with less guesswork.

• gowers Says:

It’s surprising (or perhaps not surprising) how many people are confused by this point. Just to repeat, when people talk about wasted votes, they are NOT talking about votes for a candidate who ended up not winning. Such votes exist under any system, including AV. Of course they do. The point is that FPTP forces many people to choose between expressing their genuine preference for a smaller party and thereby giving up on any chance of affecting the outcome of the election, or backing a lower-preference candidate who actually has a chance of winning. Perhaps “wasted vote” is not quite the right term (since one might argue that expressing your support for a small party sends out some kind of message even if it doesn’t affect who gets elected). But I think of it as a technical term and I can’t think of a better word.

• John B Says:

Unfortunately, your assertion about what (at least some) people mean when they talk about “wasted votes” is demonstrably false. Just to pick the nearest example at hand, Maggie E’s point (2) just a few posts above bears this out. There are no doubt countless others, in the responses here and elsewhere. YOU might not be talking about “wasted votes” in that way, but a significant proportion of the electorate undoubtedly are.

• Stephen Johnson Says:

The term ‘wasted vote’ in respect of a single vote is used in different ways and is usually misleading. Arguably a vote that, by itself, does not change the result of an election can be considered a ‘wasted’ vote. The vote changed nothing. The result would be unchanged if that single vote had not been cast.
This applies to most votes for most electoral systems including FPTP, AV, and STV, when judged in hindsight.

This is not a purely theoretical concept, since the thoughts in many voters minds before they go out to vote may be along the lines of ‘will my vote make any difference?’ The answer for a single vote is ‘probably not’, in which case the question for the individual arises ‘why bother to vote?’

If every vote makes a difference to the result of the election, then it is fair to argue that there are no wasted votes.

An example of an electoral system where every vote makes a difference to the election result is Direct Party and Representative Voting because the party votes are aggregated nationwide and this determines each party’s share of voting power in the parliament.

• gowers Says:

“YOU might not be talking about “wasted votes” in that way, but a significant proportion of the electorate undoubtedly are.”

You’re right. I tried to indicate in the post what I meant by the term. Since the post was aimed at mathematicians, who are used to careful definitions of terms before they are used, and to the phenomenon that the mathematical meaning of a word can be quite different from its ordinary meaning, this felt like a reasonable thing to do. But in the light of the much wider readership, it was a mistake.

235. Referendum on AV - Page 3 - London Fixed-gear and Single-speed Says:

[...] anyone who thinks AV is a poor system this comment may be interesting. It may not be RP, but it's definitely worth [...]

236. gowers Says:

It turns out I’m not the only Gowers to have written in support of AV. Try this from Luke Gowers. Gowers isn’t a particularly common surname and Luke is no relation of mine, or acquaintance of any kind.

I have to admit that David Gower (even less of a relation — the surnames are in fact not connected, despite their similarity) is in the no camp, however.

Even so, my informal poll of people with Gowery names indicates a resounding win for yes2av tomorrow.

237. Simon Lacoste-Julien Says:

Thanks Tim for a (long but) illuminating post!

Another great example of poor democracy is the (disastrous) result of the election in Canada of this Monday:

238. Milton Says:

AV and FPTP are different voting systems. Consequently, in some instances the same candidate will be elected by AV and FPTP, but in other cases different victors will emerge from the shadows. This much is, as far as I can tell, common ground.

However, the majority of assertions, both on this blog and elsewhere, pertaining to the alleged “fairness” of either system are tainted by blatant political bias.

It is quite unsurprising that the views of the various political parties have fallen the way that they have – quite naturally each political party will champion the system it considers will serve the party in question best.

Similarly, those left wing/centrist voters who have a deep hatred of the Conservative party will naturally champion AV. They think it will keep the Tories out. This has nothing to do with “fairness” in its purest sense; it is pure self-interest. Similar conclusions can be drawn in respect of the support for FPTP by right wing or purely left wing voters.

On that note, few contributors to this blog have hidden their political motivation for adopting the positions they do.

But surely a fundamental issue is the idea of “fairness” that is invoked in so many of these arguments? What does this even mean? Few have dared to tackle this becaus it leads on to unpleasant questions. We (well most of us) can vote once, and only once, in a general election. That seems fair, but is it?

But, dare I say it, are some more equal than others?

Why, for example, should a single mother with five children (who cannot vote but who manifestly have interests in the outcome of an election) only have a single vote? Surely when she votes, she is voting on behalf of her children too, and perhaps ought to have six votes (or at least more than one)?

And why should a CEO of a FTSE 100 company, who pays more in taxes than the total paid by scores of his employees, have the same voting power as those employees? Surely the CEO should have more of a say in how his taxes are spent than each of his employees?

What about a private in an infantry regiment of the Army? He has a quite pressing interest in the actions and decisions of his overall employer, the State (or government of the day). The State can send him to war in a foreign land, and thus to death or infirmity. Yet he, the solider, has the same “vote” as, for example, that seemingly worthless entity, the premiership footballer.

Simplistic examples, perhaps, but the point stands. The idea of “fairness” is not as simple as being “fair or unfair”, or even as simple as “X is fairer than Y”.

But I digress. I have a better solution.

Surely we should have (a) a House of Commons elected by FPTP, and (b) a (fully elected) House of Lords (with proper powers) elected by PR.

The House of Commons thereby has the potential for a achieving the much maligned “strong government”, while the House of Lords (with a much vaunted “mandate” from the electorate) can oversee, monitor and if necessary veto the actions of the lower house.

Of course such a drastic change is not what any of the political parties are after. They wish to retain power in the Commons, so have fobbed us of with a meaningless “choice” of which Sir Humphrey would be proud.

It is all too depressing for words.

• Stephen Johnson Says:

Fairness:
Some issues of fairness are constitutional rather than a function of the electoral system. eg who has a vote.

A fair party based electoral system delivers pure PR – no bias towards any one party. Power (voting power in the Parliament) is distributed according to the votes cast, without distortion.
Secondly, every voter should make an equal difference to the result of the election.

On this basis DPR Voting is closer to ‘fair’ than most other electoral systems.

FPTP favours a two party system. In a multi party state it is difficult to see how this can be judged as fair by any criteria.

Re FPTP for the Commons and PR for the Lords

At present the Commons has primacy over the Lords, which is an advisory, revising chamber but has no veto. A Lords veto would result in stalemate.

239. Alex Selby Says:

There is lots of talk about unfairly wasted votes, unfairly many votes, losers unfairly overtaking winners, Condorcet criteria, and the rest. The trouble is obviously that there are different more-or-less reasonable, but contradictory, versions of fairness.

A slightly different approach might be to judge the voting system in terms of how much benefit/favour/resources/attention each voter receives, by modelling the effect of the voting system on politicians’ motives. This gives the possibility of making a somewhat more objective definition of “fairness”: a fairer system would be one where voters get more equal benefit. It’s a kind of operational definition.

For example, as a politician you could regard each constituency as including some unknown proportion, p, of your voters, where each p has a known distribution. Suppose you can allocate resources to each constituency, up to some overall total, which we could say for simplicity has the effect of buying votes. If you are unscrupulous then you’re going to want to allocate these extra resources (effectively votes) to maximise the total number of seats you win. Naturally you don’t need to pay attention to already-won constituencies, and it is wasteful to spend a lot on hopeless ones, so you are going to concentrate on those in the middle. Though it is fun to play with various models and see numbers coming out, the details of the model won’t really matter and we’re going to end up concluding, unsurprisingly, that safe seats are monstrously unfair in this sense.

I think this is more than just a thought experiment, because governments really do make policies in this cynical way (at least, to some extent), and people in safe seats are in a practical sense disenfranchised.

I think some kind of multi-member STV would pretty much fix this problem since even in safe seats relatively modest swings could still change the outcome, so every vote is valuable to politicians. AV is harder to evaluate in the above terms, but I think it would very likely be a big improvement. According to the NoToAV literature I’ve received, there are >200 seats where the sitting MP has 50%+ of the vote. They think that means that AV wouldn’t make a difference, but I think AV would make a huge difference in these cases. E.g., a 52% – 25% – 23% distribution under the present system means a pretty solid seat, but if the 52% candidate had to worry about the others ganging up then it would only take a very small swing to unseat him. (And this kind of ganging up would be quite common I think, because people often want to case antivotes for incumbents.)

240. Josh Says:

“Under AV the person who comes second or third can win.”

“The NO2AV campaign has a TV advertisement involving a horse race. At the end of the race, to everyone’s bemusement, the horse that comes in third is deemed to have won. This is supposed to be an argument against AV.”

My response (because I like sharing it, not because you did a bad job of explaining it):

There is a simple problem with this: nobody votes on horse races. Bet on, maybe, but not vote for or against, and it is a flawed analogy.

A much better analogy would be to say:

19 people are in a room and they’re trying to decide what to have for lunch. The options are chinese, indian and pizza. 8 people want indian takeaway, 7 people want chinese and 4 people want pizza.

In First Past The Post, you get indian, as that’s what ‘most people want’. And for a long time this has seemed to many people like a fair way to do things.

In AV, people realise that there are 4 people who might want pizza, but of those 4 people, 3 of them would like chinese more than indian, and one of them wouldn’t mind indian.

As pizza is the least popular choice, they get asked about what they’d like instead, and the numbers are added up again. Now 9 people want Indian and 10 people want Chinese, so they get Chinese.

In this second scenario it’s obvious that “The people’s choice” is better represented by AV as more people wanted Chinese than wanted Indian, it’s just that their first choice was pizza.

241. Any question answered... - Page 223 - London Fixed-gear and Single-speed Says:

[...] worried about the technical merits of AV versus other systems, but this comment sums up my understanding after a week of obsessive reading. Or just immerse your self in [...]

242. Sophie Dennis Says:

“In my wildest dreams, I wonder whether some people might consider tweeting them” – just tweeted one of them!

And yes, if there’s £26 million to explain AV to voters, you should definitely get some of it.

243. Sean Lew Says:

I have a criticism of AV which I don’t believe you’ve addressed: results can be decided by kth order preferences (k>1) which may not be very well ‘considered’.

You assume that voters are rational and reveal their preferences accordingly. There are empirical studies which suggest this might not be the case but even without going into those, let me just go through my own thought process when faced with an AV ballot sheet.

I know who amongst the major candidates I strongly support and who I am against. (Having been brought up with FPTP, I have little incentive to learn about the minor candidates.) So I know who to put first and who to put last but have very little information to go on to form a preference ordering for the other candidates. I also have not thought about them very much. What write down is actually a poor signal of my real preferences.

Do we really want the most closely run elections to be decided by the afterthoughts of the minority voters?

• gowers Says:

Gil Kalai brought up this problem. But by and large the parties you don’t know about will be minor parties, so it’s unlikely that the ordering you place on them will make much difference. It would certainly be possible to construct examples where it made a difference, but I don’t think this would be a serious problem in practice.

In general, it seems to me that the problems with AV, while real, are dwarfed by the problems with FPTP.

244. Alex Says:

“FPTP HELPS EXTREMISTS”

I don’t think there is much evidence for that “slogan”. How many MPs do the BNP or Communists have and have had since the war?

There is actually a lot of evidence that European countries, with their preferential or even proportional voting systems, have far more extremists. The far right/National Socialists in Europe often get 20-30% of the seats in Parliament. I appreciate this might reflect different politics and circumstance but even still these voting systems don’t seem to harm their prospects. It is inconceivable that in the UK under FPTP such extremists would get anywhere like 30% of the number of seats in the House of Commons.

And the argument that because AV is opposed by the BNP then this is a good reason for having it ignores the fact that the BNP are opposed to AV only because they support full blown PR. It also ignores the fact that UKIP and the Greens support AV.

And regarding coalitions/hung parliaments, regardless of whether AV will increase or decrease their occurrence (and I think, on balance, they will probably become more common) I don’t see them as desirable. Manifestos would become worthless as they would inevitably have to be ripped up in the horse trading that follows each election. FPTP allows a party to implement a manifesto which got more votes than anything else. In contrast, who voted for the “Coalition Agreement” that we now have as a result of shady back room deals (one of which of course was to have this complete waste of money referendum which no one apart from us political nerds is interested in). The answer, no one voted for it! The polticians cobbled it together out of sight. So coalitions and voting systems that encourage them don’t give more say to voters, but more power to politicians. And why is it democratic that the Lib Dems with 21% of the vote should now be in government, whilst Labour with 29% of the vote? How is that democratic? And how is it democratic that a third party could continually hold the balance of power and be in government for perpetuity (like the Greens and other small parties in Germany)? I would suggest that is less democratic than having the party with most votes being able to form a majority government in the House of Commons.

• gowers Says:

Please reread that part of the post: the slogan is not referring to BNP-type extremists but to the left of the Labour party and the right of the Tory party. It was a bit cheeky to call them extremists, I admit. I don’t think either AV or FPTP is much use to the BNP.

• David N Says:

‘In contrast, who voted for the “Coalition Agreement” that we now have as a result of shady back room deals (one of which of course was to have this complete waste of money referendum which no one apart from us political nerds is interested in). The answer, no one voted for it!’

Few may be interested in the referendum (we will soon find out how many), but 29% of voters voted for a party whose manifesto included it.

“And the argument that because AV is opposed by the BNP then this is a good reason for having it ignores the fact that the BNP are opposed to AV only because they support full blown PR.”

I don’t think so. Firstly, AV would give them even less chance of winning than FPTP (though their chances would seem to be very small under FPTP for the foreseeable future as long as other voters turn out to stop them). Secondly, if AV was introduced for Parliament, that might well lead to it being used for local elections as well in time, which would wipe out most, if not all, of their council seats. If they are in favour of PR (and I accept that it would be in their interest – see the last European election), then ISTM that their best chance of getting it in the future is to vote for AV now. So voting against AV because they are in favour of PR makes little sense. I’m sure that they are loving the attention though.

• David N Says:

“this complete waste of money referendum which no one apart from us political nerds is interested in”

41% of the electorate were interested enough to vote, which I think is similar to the typical turnout in local elections (in my district, the referendum turnout was 48.7%, 8.8% higher than in the last DC elections), and only a bit lower than in the Leicester South by-election. Maybe there are more political nerds than you think!

245. David N Says:

I put a “1″ against Yes, and an “X” against No. Is that right? ;o)

246. Ian Sanders Says:

We found your examples rather more complex than your maths talk last Saturday, which our son Edward took us to listen to

Some years back Ed said that another mathematician had advocated another system and being simpler and less costly, basically, first past the post, but rather than having just one vote, you can vote for as many as you like. Personally, I quite like the sound of this, it would perhaps give more chances to independent candidates with a strong local base, and reduce the stranglehold of the party system a bit. Perhaps I am too much of an individualist! Like AV, it would also tend to make candidates less extreme, since they would have to get the majority vote, which will tend to be in the middle of the bell shaped curve of opinion.

• gowers Says:

That system has some strong adherents in the comments above (and is known as approval voting if you want to search for discussions of it), but you can be forgiven for not having trawled through all of them …

247. Ian Sanders Says:

Sorry for not having read it all,

I have a brother-in-law who does not like change, and was unpersuaded by your blog, on the ground that AV was too complicated, and the arguments put for it too confused, also he said he preferred to vote yes after there had been a better consulation as to alternatives. Hence he voted no. He preferred PR, but being a bookie person, was unable to grasp why this would lead to the loss of the constituency MP. The approval voting is easier to grasp conceptually, and has the same simple counting process we now have, plus the continuation of the local MP. The no compaigners would not have been able to run such a successful campaign based on making it look excessively complicated, or more expensive.

248. Pertinax Says:

On point that has been missed is that the proposed system is optional AV.

In Australia the Federal system has compulsory preferencing where you have to number all the boxes, which creates a much higher informal vote but makes preferences more important.

In NSW they introduced a system like the proposed UK one in 1981. In 96% of seats the result is the same as FPTP. Only in a small number of seats has the result been different, and it has only effect which party formed government one. The reason for this is that half of the votes expired because people either didn’t bother to preference or only preferenced one or two other candidates who were eliminated.

AV with optional preferences will improve FPTP in three cornered contests but the difference won’t be that big.

249. AV referendum and local elections: May 5 as it happened | IlNeurone International UK Says:

[...] system. However, Timothy Gowers, a mathematician during a University of Cambridge, argues that many of a claims used by a No to AV organisation have been mathematically wrong. “I find it unequivocally dispiriting to live in a nation where it can advantage a politician [...]

250. Patrick Lindon Says:

Reading your belief that the 1983 election would have resulted in a hung parliament does make me wonder whether AV is such a great system.

This post is clearly mathematically sound and one cannot fault that (the writer is a mathematician after all). What it cannot do however is produce a universally accepted definition of fairness. And I also think some of the political judgements in here are questionable. I would deny that the Thatcher government was unpopular in the 1980s (it may have been in certain parts) but the approval ratings of the government were positive ahead of both the 1983 and 1987 elections. Similarly, I would also deny that the Blair government was unpopular in 2005. Again, his government’s approval ratings were positive at that time.

I take issue with your contention that the mid-1990s was a period of instability (farce, maybe) and that the Labour party traditionally buggers up the economy whilst the Tories then, although fixing it, create social problems. Whilst true, it is the same in virtually any other country, especially the election in Australia a couple of years ago that defeated the Liberals. So that is not a cycle common to FPTP exclusively.

I also think that David Owen was a rather strange example to use as a notable politician (!).

• gowers Says:

I have to say that most of the statements you criticize are ones I no longer feel as confident about as I did when writing them (largely as a result of comments by other people). My take on the popularity of the Conservatives in the 1980s and Blair in 2005 is that they were genuinely unpopular but that the opposition just didn’t feel electable. But from what you say about approval ratings, perhaps I am wrong.

I admitted before I said it that the thing about Labour messing up the economy was a caricature: one has only to think of the three-day week and Black Wednesday (which may have accidentally helped the economy by allowing the pound to sink to a more beneficial level but which wasn’t exactly an example of economic competence). I think this country might have been different from Australia in that the Lib Dems get a higher share of the vote — except that that no longer seems to be the case …

And finally, I have a soft spot for David Owen because he used to answer the question he was asked rather than being boringly evasive in the way of most politicians. But he’s not exactly flawless: I wonder if he honestly thinks that the result of the referendum is good for those hoping for PR.

• David N Says:

“I would deny that the Thatcher government was unpopular in the 1980s (it may have been in certain parts) but the approval ratings of the government were positive ahead of both the 1983 and 1987 elections. Similarly, I would also deny that the Blair government was unpopular in 2005. Again, his government’s approval ratings were positive at that time.”

http://www1.politicalbetting.com/index.php/archives/2011/03/17/hows-the-government-comparing-with-its-predecessors/

The graph on the page linked above seems to show that the Tories’ approval rating was slightly negative in 1983, but slightly positive in 1987, while Labour’s was clearly negative in 2005. In 1987 and 2005, the ratings seem to have peaked around the time of election, and in all three cases they fell away soon afterwards. Something tells me that the 1997 graph isn’t quite right, though.

251. No to AV wins! | To the left of centre Says:

[...] only example I could find where AV does not satisfy the Condorcet condition is from a comment on Gower’s Weblog and considers the following [...]

252. David N Says:

I note that the region with clearly the highest Yes vote (44%) was Northern Ireland, where they already use a preferential system regularly, though I don’t know whether this result is because of their experience of such a system, or because of the totally different political landscape.

253. Gil Kalai Says:

“4. AV is unfair because the least popular party gets its second-choice votes counted first.

Oh dear. There was even an article published in the Guardian that made this completely wrong point.”

Lets put fairness aside. What is curiously true for AV is that it is always better for a voter if he the candidate he supports most is the third most popular candidate rather than the second most popular candidate. So when there are 3 candidates perhaps this is what 4) speaks about.

When there are more than three candidates it seems that under certain assumptions at least you are better off if you support a candidate in an odd place in popularity compared to a candidate in an even place in popularity. (I.e. if your candidate is #4 your preferences will play a role in determining candidate in place #2 but it is worse being #2 than #3…

In short: It is not the least popular party, it is the popularity-parity that counts.

• gowers Says:

“What is curiously true for AV is that it is always better for a voter if he the candidate he supports most is the third most popular candidate rather than the second most popular candidate.”

Can you explain what you mean by this? I don’t follow.

• David N Says:

“What is curiously true for AV is that it is always better for a voter if he the candidate he supports most is the third most popular candidate rather than the second most popular candidate.”

I’m not sure that I understand that claim either. It might help if you clarified what you mean by “third most popular candidate”. However, if there are three candidates in the order A, B, C on first preferences, I will assume that you mean C (even though they may actually be more popular than both of the others). Now if C is eliminated and their votes redistributed such B wins, then who is the “second most popular” candidate. The only way your claim makes any sense is if this means A, as the first-preference voters for B have obviously got what they wanted. However, a voter who voted C1 A2 is probably worse off than one voted A1 B2, as the former has got their least favourite, whereas the latter has got their second favourite, contrary to your claim.

• Gil Kalai Says:

What I meant to say is this: If you rank the candidates according to the AV method it is better for a voter that his top candidate comes third rather than second.

In other words, given that your candidate will not win it is better that he comes third than second.

If there are only three candidates, given that your top candidate does not win, your vote “counts more,” in a sense, if he is the least popular.

• gowers Says:

OK. I think it is very important in that case to say precisely what you mean by the second candidate. It seems that you mean the candidate who ends up second after the whole process, rather than about the candidate who is second just before the third candidate is eliminated.

The strange thing about this is that if the second choices of those who voted for the second candidate did make a difference, it would have to be to elect the third candidate instead of the first. So in some sense it seems that this disadvantage you talk about is even more of a disadvantage for the third candidate.

• Gil Kalai Says:

This was just offered as a curiosity not necessarily as a disadvantage. I was a bit careless to say how we rank the candidates. Lets suppose that we rank the candidates according to the AV method. (An also, for simplicity, that in the last rounds 2 candidates remain.)

Of course it is best for you if your candidate is the winner. In terms of your influence it is worse for you if your candidate ends up second. In this vase your other preferences has no influence. Being the third seems the second best. Being the fourth is a tricky matter. You have as much influence as the third in terms of the final round. But you also have influence to determine who comes second which the third guy does not have. And this influence is likely negative.

I mention it since it says that point 4 in the no points mentioned is not entirely wrong. The problem I find with most of the points and counter points is not their strength but their relevance.

254. Gil Kalai Says:

if your most preferred candidate is in number 2 then your other preferences are not counted and do not influence the identity of the winner; if your most preferred candidate comes number 3 then your other preferences do count.

(If your most preferred candidate is in number 4 then your preferences
play a role in the identity of the candidate that comes second and assuming that the preferences of people higher up in your own list are closers to yours, the disadvantage is having your most preferred candidate coming second also means it is a disadvantage to have him 4th.)

• David N Says:

“if your most preferred candidate is in number 2 then your other preferences are not counted and do not influence the identity of the winner; if your most preferred candidate comes number 3 then your other preferences do count.”

If #3 is eliminated, that is correct. However, while #3′s voters’ second preferences now count, #2′s voters’ first preferences still count. I don’t know about you, but I would rather have my first preference counting than my second, and I would rather my first preference got to the final two and still had a chance of winning than for them to be eliminated, assuming that I thought they had a chance of winning. If I didn’t think they had a chance of winning, then there is a case for voting tactically.

• gowers Says:

The people who vote for #3 would have achieved the same result if they had not voted for #3 and instead put their second choice first. So one could argue that the first preferences of those voters have no influence on the result. In my book that makes them worse off than those who voted for #2.

• Gil Kalai Says:

I am not sure what you mean. Here is a way to say what I mean.

Suppose you are told that your first choice came under AV second. And somebody suggests to you to add votes the the guy on third place (without further ranking of other candidates) so as to push your candidate from second to third place. Then this move that sems harmful to your candidate can only be beneficial for you in terms of the elections outcomes.

If you are told that your first choice came third and sombody offers to add votes to the guy making hin second then this can only change matters for the worse for you.

• gowers Says:

I think my feeling is that you are conditioning on a slightly strange event. If your first choice comes third, then it is possible (though by no means guaranteed) that your first choice would have done better with more votes, because that might have pushed them into second place, and the next round might have made them first. (This would be the case, for instance, if the Lib Dems are the third party but they are the second choice of all Labour and Conservative voters.)

It also seems to me that if your party is third and your second choice differs from the second choice of most other people who vote for your party, then you would rather not be third. In that situation, even if you have some abstract thing called “influence”, it doesn’t help you much.

• David N Says:

OK, so if you believe that your first choice cannot win but may finish second, there may be a case for voting tactically IF you think that most voters who share your first choice will also share your second choice (of the other main candidates).

One problem with that tactic, though, is that it reduces your first choice’s apparent support. This means that, in the next election, even if your first choice’s actual support may have increased to the point where they could win, it may appear that this is not the case, causing voters to continue to vote tactically and your first choice not to win.

255. gowers Says:

Let me try to get some clarity on the question of tactical voting under AV by looking at a couple of scenarios that, in this country at least, are reasonably realistic. Since assuming any kind of support for the Lib Dems doesn’t feel all that realistic, let’s imagine that I’m talking about the situation five years ago.

In many constituencies, the two main rivals would be Conservative and Labour candidates, with the Lib Dems in third place. Moreover, by and large Conservatives would prefer Lib Dems to Labour and Labour would prefer Lib Dems to the Conservatives. As for the Lib Dems, they would probably lean towards Labour but a reasonable proportion of them would prefer the Conservatives. (These people might be natural Conservatives voting Lib Dem as a kind of protest.)

In such a constituency, the Lib Dem votes get redistributed, and Labour wins unless the Conservatives have a fairly good margin over Labour in the previous round.

Let’s suppose that in the first round the Conservatives and Labour are very close, with the Conservatives very slightly ahead, so that it is the Lib Dem second preferences that decide the election for Labour. Then Labour voters get their first preference, most Lib Dem voters get their second preference, and Conservative voters get their third preference.

Now let’s suppose that the Conservatives had volunteered to be eliminated after the first round, despite coming top. Then if almost all Conservative second choices were for the Lib Dems, this would be enough to hand the election to the Lib Dems. The result would be that Labour and Conservative voters got their second choice and Lib Dems got their first choice.

So in the second situation, the Conservatives and the Lib Dems would be better off and Labour would be worse off. So it seems that it’s not the Lib Dems who gain from being eliminated — rather, Labour gains from their being eliminated, and both the Lib Dems and the Conservatives lose out.

It’s a hard situation to analyse. It’s certainly true that in some sense the Lib Dems get a chance to influence the fight between Labour and the Conservatives, whereas the Conservatives don’t get a chance to influence the fight between Labour and the Lib Dems. And yet if you look at the results, it seems as though it is Labour who gains rather than the Lib Dems. So what do we mean by “influence” here?

• David N Says:

“As for the Lib Dems, they would probably lean towards Labour but a reasonable proportion of them would prefer the Conservatives.”

The BES data that MorningTory linked to previously (http://www.oxfordjournals.org/our_journals/parlij/gsq042.pdf) suggests that, in 2010, voters whose first preference would have been LibDem would have favoured Lab over Con by a ratio of about 3:2), so in a Con-Lab marginal, the Con lead at the three-party stage would generally have had to be less than 1/5 of the LibDem vote for the LibDems voters to swing it. Given that the LibDems are in third, that is a maximum of about of about 6% of the total votes still in play, and usually rather less. Going back five years, the ratio in favour of Labour might have been higher.

“Now let’s suppose that the Conservatives had volunteered to be eliminated after the first round, despite coming top. Then if almost all Conservative second choices were for the Lib Dems, this would be enough to hand the election to the Lib Dems. The result would be that Labour and Conservative voters got their second choice and Lib Dems got their third choice.”

You obviously meant “first”, not “third”. [Thanks -- changed now.]

• David N Says:

Following your argument through, it was likely to be only either Lab or Con who gained from LD being third, depending on whether Con was far enough ahead, because the 2nd preferences of Con and Lab voters were so heavily in favour of LD that if LD got into the final two, they would usually win. In other words, there were very few seats where LD would naturally have come second under AV without someone getting 50% before it got to the head-to-head stage. Even where this was the case, the leader would have to be so far ahead that it is highly unlikely that LD voters would gain from voting tactically to try to move the LD into third place. Therefore it would only have been Lab and Con voters who might, in the right circumstances, have had an incentive to vote tactically in that way, although it would have been the LDs who stood to gain most from their doing so.

• Gil Kalai Says:

There is some measure of “manipulation” (or tactical voting) for choice functions that is studied in http://www.ma.huji.ac.il/~ehudf/docs/FKKN.pdf .

256. Harry Says:

I think we are still missing the effect that the system has on how the voter chooses who to vote for. Many voters are just as certain who they do not want as who they do. Let’s take someone from the extreme left, his main concern is that he does not want the Conservatives. Under FPTP, if he votes for the Socialist Workers party he thinks he is wasting his vote and might let the Conservatives win so he votes Labour. Under AV he can show his true preferences so the smaller party gets more votes, and, if enough people think that way, could win a seat.

257. Denis Mollison Says:

Thanks for the excellent post, and many interesting comments, on AV vs. FPTP: but I am left agreeing with Samuel Johnson – “Sir, there is no settling the point of precedency between a louse and a flea.”

Can we forget this appalling referendum – appalling in its abysmal level of public debate – and do something to put proper PR back on the agenda?

I must declare an interest here, as author of the STV scheme voted down in parliament in February 2010 – see http://www.ma.hw.ac.uk/~denis/stv4uk/
- an attempt to show that PR can have many other advantages, including stable, natural constituencies.

Perhaps a next step might be for Engand to follow Northern ireland and Scotland in using STV for local council elections?

258. David N Says:

“Can we forget this appalling referendum – appalling in its abysmal level of public debate”

I was against referenda before this one, and my fears have been confirmed. The whole thing was dominated by slogans and disinformation, drowning out what little clear information was being provided. If that happens with a fairly simple issue like the voting system, what chance would we have of being well informed on a complex issue like those concerning the EU?

259. Here's why Says:

You are completely missing the point and getting carried away, in my opinion. The reason why most people oppose AV isn’t because they are worse at maths than you are. It’s because they don’t like the Liberals.

Opposing AV is then reasonable. People suss that the Liberals promote AV out of cynical self-interest, presented as selfless support for ‘changing the system’ so that it more accurately expresses the popular will. “Yeah, right”, people go – correctly. Under AV the Liberals would be in government almost all the time. People don’t want that.

• David North Says:

“People suss that the Liberals promote AV out of cynical self-interest”

… while, of course, the Tories’ promotion of “FPTP” had nothing to do with cynical self-interest, and Labour’s divided position had nothing to do with being divided on whether AV was in their self-interest or not (and it was their manifesto that included the referendum on AV, not that of the “Liberals”).

If most people “don’t like the Liberals”, and don’t want them in government, they could put them low down in their preferences under AV (or any other preferential voting system, for that matter), in which case they would be unlikely to get into government. If the “Liberals” got into government under AV, it would be because most people preferred them to either the Tories or Labour (and because either the Tories or Labour invited them into coalition, as David Cameron did last year).

260. when is spring break Says:

when is spring break…

[...]Is AV better than FPTP? « Gowers's Weblog[...]…

261. Must Polls be Plurality-Based, Too? « The Leisure of the Theory Class Says:

[...] wins. If you are unfamiliar with the deficiencies of plurality voting, one place to look is this excellent blog post, written by mathematician Tim Gowers in the context of Britain’s recent (sadly unsuccessful) [...]

262. yes@yes.com Says:

@D North – I wasn’t suggesting that any party is more cynical than any others. The point is that given only small variations in people’s preferences – of the kind that under FPTP determine general election results in the sense of whether the government is Tory or Labour – AV would mean all elections resulted in hung parliaments. Given how the Liberal Democrat brand is promoted as being between the other two brands (and also how the Tory and Labour brands are promoted as being diametrically opposed), this would mean the LDs were permanently be in the government. The LDs would also always get to choose who the big party in the government would be – either in post-election haggling or before the election, in circumstances where they brought down the previous government and therefore would have to team up with the other show afterwards. Of course it would be possible to argue that this would be a good thing. But that would beg the question, “If so, then why bother holding elections?”

Con/Lab/LD/Oth 37/28/25/10, 28/37/25/10, 42/28/20/10, 28/42/20/10 – they would all have the same result: a coalition government containing the LDs.

The arrangement of the brands in the order Con…LD…Lab is unlikely to change as a result of any change in the voting system and is highly relevant to the issue of FPTP or AV. Considering mathematics alone fails to recognise this.

I didn’t follow (still less, support!) the referendum campaigns of either side, but as far as I know, neither of them made a big thing about this point, if they recognised it at all.

But given that the support for AV was roughly similar to the support for the LDs, and one presumes most LDs voted for AV, it seems possible that many people in the electorate did recognise it.

• David North Says:

@yes@yes.com, I assure you that the claim that AV would always/nearly always/usually result in a coalition government was frequently made by supporters of the No campaign. However, while AV would be likely to increase the number of LDs, and possibly others, elected, which would be likely to increase the chance of a hung parliament, I am far from convinced that it would make it anywhere near inevitable, or even probable. It is even more of a stretch to claim that it would always give the LDs a choice of coalition partner, as did not happen in 2010 despite the hung parliament (unless you believe that a Lab-LD minority coalition government or a rainbow coalition with a tiny majority were realistic options). If the Scottish Parliamentary election system can produce an overall majority (and a minority administration before that, rather than a coalition) in a four-party system, then I’m confident that AV could, and frequently would, do so in a three-party system.

263. Cloud Computing Says:

Cloud Computing…

[...]Is AV better than FPTP? « Gowers's Weblog[...]…

264. louis Says:

The last word?
The truth is that all parties are coalitions.
Those in favour of FPTP want our coalitions formed before the election not afterwards.
This is the political truth. No maths involved!

265. medical forums Says:

medical forums…

[...]Is AV better than FPTP? « Gowers's Weblog[...]…

266. Why I will be supporting AV on the 5th of May | The Alethiophile Says:

[...] Independent The Guardian New Scientist Mathematics Professor from Cambridge University Economics Professor from Warwick [...]