BASIC TOOLS FOR APPLIED DECISION THEORY
Decision analysis, or applied decision theory, was developed about 35 years ago to bring together two technical fields that had developed separately. One field was the theoretical development of how to help a person make simple decisions in the face of uncertainty. This field was begun in the 18th century with the work of Bernoulli, then Bayes, and finally Laplace. It was improved and refined to a high state of development in the years following World War II.
At that time the control and systems engineering development during World War II was available to make practical the application of fundamental ideas about decision making under uncertainty to the actual problems faced by decision makers. The new field of decision analysis provided both a formal, systematic way to analyze decisions and an important communication medium for achieving mutual understanding between decision makers and those who advise them.
Many important creative activities—from engineering design through medical treatment to business strategy—have unique features in their technological basis and their possible consequences, among many other elements; however, they all share the characteristic of being fundamental decisions. They differ in their alternatives, forms of uncertainty, and preferences for consequences, but they share the features of all decisions: the need to distinguish the quality of the decision from the desirability of the consequence, the need to incorporate uncertainty and to value experiments, tests, surveys, and other forms of information gathering that might reduce uncertainty at a cost, and the need to establish preferences for outcomes, including outcomes achieved with different probabilities. This is true whether we are designing a planetary probe or managing a portfolio of chemical entities for a pharmaceutical company. Recognizing the similarities of all decision processes allows us to use important general insights in applying them; this is particularly true for engineering design.
The purpose of decision analysis is to provide decision makers with clarity of action in an uncertain decision situation. The metaphor for decision analysis can be conceptualized as a high-quality conversation about a decision. Sometimes the conversation can be very brief and carried on by oneself. More difficult and puzzling decision problems may require the assistance of several analysts and extensive computer modeling. This spectrum is the domain of decision analysis.
Perhaps the single most important distinction of decision analysis is that between making a good decision and achieving a good outcome. The quality of the decision can be evaluated only in light of the situation when the decision was made and not with any reference to its results.
A good decision is one that is best for me given the alternatives I have, the information I possess, and the preferences I assess. For example, if someone offers to sell me for $10 one of 100 lottery tickets for a prize of $10,000, I would readily buy the ticket. Of course, if I am sure of the validity of the offer, as I am assuming, I would like to buy all 100 tickets, but he offers me only one. I know the good outcome is winning the $10,000 and the bad outcome would be losing the $10. However, I am making a good decision to buy the ticket, even though there is a 99 percent chance of the bad outcome. I always want to choose the alternative that gives me the best combination of probabilities and outcomes for my given risk preferences. The fact that I am not likely to enjoy a good outcome, as in this case, is no indication I have made an improper decision.
There is a common but fallacious belief that experiencing a bad outcome implies a bad decision was made. Such opinions are commonly voiced in sports. The football team tried to make a two-point conversion and failed: The coach made a bad decision. That the operation was a success but the patient died may simply be an example of a bad outcome following a good decision. One necessary test of a good decision is whether you would make the same decision again in the same situation if you had not yet learned its consequences.
THE DECISION BASIS
What is a good decision? A good decision is one that is systematically correct given a decision situation properly framed by a committed decision maker. The specific description of this situation is the decision basis. The three elements of the decision basis can be thought of as the legs of a three-legged stool, as shown in Figure 3–1. The quality of a decision rests on having framed the decision correctly, that is, answering the right question, understanding the issues (knowledge), what can be done (options), and what you want (desired outcomes). Tools for applying logic help the decision-making group or individual to reach a conclusion and direct action.
One element is what the decision maker can do in the face of the alternatives to be considered, which may call for an immediate decision or allow for postponing it to the future after some of the uncertainties are resolved. These sequential decisions allow us to represent options and to calculate their value.
The second element of the decision basis is information (i.e., what links the alternatives to what will ultimately happen), which can be in the form of models describing the field of concern in the decision. Some decisions, like the launching of a satellite, have the advantage of extensive physical models to guide the decision. Other decisions (say, those related to the spread of wildfires or the progress of a disease) will involve considerably more uncertainty. Still more uncertain will be the behavior of a jury or of consumers responding to advertising.
Regardless of the extent of modeling available, the decision maker will ultimately face some uncertainty in any significant decision problem. The decision maker represents these uncertainties in the form of probabilities or probability distributions. These distributions will be informed by any available experimental data, but in many cases, particularly in applications of new devices or systems, the experienced judgment of experts may be the only available resource.
The third element of the decision basis is preference, or what the decision maker wants. Preference has three identifiable dimensions in most cases. The first is valuation, or the trade-off among different attributes of the consequences of the decisions. This is summarized by a value function specifying how much more valuable one set of attributes is than another. The second dimension of preference is time: how much values in the future will be worth relative to values today. This dimension is essential in purely financial decisions, but it also has application in, for example, medical decisions, where the patient’s quality of life must be balanced against the duration of life, and in any other decisions where the attributes of the future must be balanced against the attributes of the near term. The third dimension of preference is risk preference. Risk preference is the dimension of preference stating which probability distributions over attributes of each outcome are preferable to others. This can be as simple as whether the decision maker prefers to receive a sure million dollars or to toss a coin for a payoff that will be either $3 million or nothing.
When all three elements of the decision basis are formally specified, the best decision can be determined by employing rules (axioms) to extend the exercise of choice to the case where the uncertainties facing a decision maker are explicitly recognized. In fact, all alternatives will be ranked and evaluated by this decision process.
The importance of models in engineering design leads us to discuss them in more detail by means of the problem space in Figure 3–2. This diagram illustrates the three dimensions of difficulty a problem may have: uncertainty, complexity, and dynamic or time effects. The corners with fewer
degrees of difficulty tend to be those explored early in human history and are studied early in the engineering curriculum. As we move from problems with few of these factors to more of them, our ability to model decreases, until at the corner numbered 8 we have very few mathematical representations, if any, where all three dimensions can be treated in a general way. This means there will be a need for judgment in deciding which factors must be carefully considered and which can be treated approximately. As stated in the Executive Summary, design is not an endeavor that can be totally automated.
Returning to the stool, the seat is the logic acting on the decision basis to produce a course of action. The person seated on the stool is the decision maker who has stated the decision to be made. The ground on which the stool is placed is the frame developed for the decision situation.
Framing concerns how we choose the decision problem to which we will apply this structure. For example, suppose a manufacturer of buggy whips in the early 1900s noted profits were falling and decided to call in a consultant to see how manufacturing could be done more efficiently. The decision would be framed as one of improving the buggy whip manufacturing process. Observing the growing automobile revolution, however, the framing would more appropriately address how to change the product line to serve the new demands of automobile owners while phasing out buggy whip production. Framing is the most critical part of the process of decision making, because making the right decision in the wrong decision frame can be a serious error.
Proper framing is the key to working on the right problem. Improving the efficiency of buggy whip production would be the correct solution to the wrong problem. In principle the methods of decision analysis could be used in selecting a frame, this use would be a meta-application. The choice of a frame can usually be accomplished by a guided conversation. An aid in framing is the decision hierarchy shown in Figure 3–3. The frame selected for the decision separates it from other decisions made previously or taken as given, shown above, and those to be made later, shown below.
Because all aspects of the problem are explicitly considered, a sensitivity analysis can be performed on every input. Sensitivity to changes in alternatives, changes in information, and changes in preference can be determined. Because the formal decision model links every input to the ultimate value measure, sensitivity analysis is a simple computational task. Judgment is required to choose the extent of multi-variable sensitivity analysis.
Of particular importance, and unique to decision analysis, is the ability to place a value on the resolution of any uncertainty, provided a value measure is one of the attributes of the decision problem. The decision maker can thus determine what it would be worth to resolve any or all of the uncertainty. If opportunities for information-gathering exist such as surveys, experiments, pilot plants, prototypes, or market trials, the decision maker must determine whether their value exceeds their cost. The same logic guides design of the most beneficial experiments and the application of their results to present and future decisions.
Most important is the notion of framing to ensure that the problem being addressed is the fundamental problem facing the decision maker. Often the successful practice of decision analysis requires a complete reframing of the originally contemplated decision. Professional decision analysts also ensure that the decision maker is actively involved in the decision-making process, to gain their commitment both to the process and to any resulting decisions.
The practice of decision analysis is based not only on the pioneering contributions from probability, decision theory, and systems engineering, but also on the insights provided in the last few decades by cognitive psychologists. These professionals have sensitized us to the types of mistakes people make in thinking about decisions, which can be as subtle as making decisions based on percentages rather than absolute amounts. The cognitive biases to which we are all subjected must be recognized both in providing the inputs to a decision analysis and in appreciating the necessity for formal analysis in complex decision situations.
The analysis of the decision can be carried out using any of several tools, such as those shown in Figure 3–4. Examples are shown later in the report Only a few are illustrated here. The decision analysis cycle depicts the overall iterative nature of the formulating, analyzing, and learning process.
Figure 3–5 shows a simple influence or decision diagram for a simple decision. A rectangular box represents a decision node, an action under the control of the decision maker. Ovals represent uncertainties or, in some cases, calculations. Finally, hexagons represent the value node, with inputs showing what the decision maker values. Arrows into any node show what its value depends on, either functionally or in the sense of conditioned probability. Arrows into decision nodes show what is known when the decision is made.
In the sample decision diagram in Figure 3–6, note that the manufacturing cost will be known only when the price decision has been made. Such diagrams have important properties. First, at the level of relation, they reveal the logical structure of the problem in a way that allows nontechnical people to understand and contribute. Every relevant thought should have a representation in the diagram. However, decision diagrams are more than useful graphics. When each decision in the diagram is properly specified, the decisions can be processed directly by a computer to yield the best overall decision. This method can calculate the value of information regarding any uncertainty and can also illustrate many of the sensitivities for a preferred course of action. Decision diagrams also serve as an important communication link among those involved in the decision.
Another valuable idea is a form of sensitivity analysis known as the tornado diagram because of its shape. Figure 3–7 illustrates for a particular strategy how the net present value of the final decision implementation changes as each uncertainty ranges from a low to a high value. A low value is defined as one with a very high probability of being exceeded, a high value as one with very low probability of being exceeded. The effect on net present value for each factor is ordered in decreasing range of
impact to produce the tornado shape. This diagram quickly demonstrates the effect of each uncertainty for a given alternative. A series of tornado diagrams would show engineers at all levels of the design process the economic implications of their decisions.
A useful guide in assessing decision quality is the spider diagram shown in Figure 3–8. Here the state of quality in each of the six elements can be plotted as a percentage and then connected to form a web. In this diagram “100 percent” does not represent perfection but rather a situation in which further improvement would not be economical. The result of such an assessment is knowledge of where, if anywhere, to direct additional analysis effort.