If you look at that Palm Beach ballot, it's easy to understand how 3,000 or so people might have made the mistake of voting for Pat Buchanan when they meant to vote for Al Gore. But why would a much larger number of people--19,120 out of 461,988 who voted--invalidate their ballots by voting for two candidates for president?
One possibility suggested by a lawyer friend of mine: A large proportion of those people thought they were voting separately for the offices of president and vice president. Look at the ballot again. Each pair of candidates appears inside a box. The presidential candidate's name appears on one line, his running mate's name on the next line. Many Democratic voters might have punched the two seemingly adjacent holes, thinking they were voting separately for Al Gore and Joe Lieberman.
This mistake is made even more likely by the confusing ballot instructions on the left side of the ballot. The instructions should say, "Vote for one." Instead, they read, "Electors for President and Vice President (A vote for the candidates will actually be a vote for their electors.) (Vote for Group)." "Electors" and "candidates" are plural terms." Group" is a singular term that sounds like a plural one.
That people thought they were voting separately for the president and vice president would explain two anomalies in the story so far. First, it would explain why only 3,783 made the mistake of voting for two candidates in the Senate race, which appears next on the ballot. Senatorial candidates don't have running mates. Second, it would explain why we've heard so many complaints from people who think they voted for the wrong guy, but few from people who think they spoiled their ballot by voting twice. Most of the people who voted twice don't realize they made a mistake! If they had, many would have done something about it while still at the polling place. If you screw up your ballot by punching the wrong hole, you don't simply punch another hole. You turn in your spoiled ballot and ask for a replacement.
The spoiled ballots themselves should tell the story. A little old lady who thought she was voting for Gore and Lieberman probably would not have punched the second and third holes, in effect voting for Buchanan and Gore. More likely, she would have punched the third and fourth holes, voting for Gore and David McReynolds, the Socialist Party candidate for president. Likewise, if someone tried to vote for Bush and Cheney, he would probably have punched the first and second holes -- for Bush and Buchanan.
And if my friend's theory is correct, it suggests a possible remedy short of a re-vote. A judge could re-validate those ballots where the intention is evident. A vote for Gore and McReynolds was meant as a vote for Gore-Lieberman. A vote for Bush and Buchanan was meant as a vote for Bush-Cheney.