Subjective expected utility theory

Decision Making under Risk

Decisions are normally choices between alternatives with different probabilities. Even if one chooses an alternative with a sure outcome, one risks rejecting an alternative with some chance of a better outcome. An important understanding is that whether a given decision is viewed as good or bad is not dependent on the outcome but rather on the process. In the world of risk and probability, unfortunately, there is no guarantee of an optimal outcome. Decision makers must make the best decision they can based on the information available to them at the time the decision is made.

Decision theory was derived from economic models, historically constituting gambles. Gambles [Page 1084]provide a paradigm for decision making, in which each alternative has a different value as well as a different probability. Structuring decisions as gambles allows for mathematical analysis of the decision so that a rational or best outcome can be prescribed. The first models were based on expected value (or average value), usually shortened to EV.

Value as a Decision Concept

Mathematical calculation of an optimal decision is easiest when the outcome is defined in terms of money. In that case, both alternatives have the same metric and the metric is quantified. It is taken as a primitive that more money is better than less. However, the amount that a decision maker might be willing to risk is not in a 1:1 relationship to the amount of the alternatives. Prospect theory has demonstrated that there is a decrease in the psychological value of a gain with the increase in overall value of both options. For instance, the subjective difference in the value of a gain of $10 is less when one is betting $2,010 against $2,000 than when one is betting $20 against $10. The opposite is true of loss, although the effect appears to accelerate more rapidly. However, calculation of an optimal choice becomes more problematic when the gamble involves an outcome that is nonmonetary, such as health or a specific physical function.

Probability in Decision Models

Rationality in economic theories of decision making assumes that there are multiple opportunities to make a decision, as is typical in most gambling situations. Over infinite replications of the decision, the best outcome is achieved through choosing the gamble with the largest arithmetic product of value and probability. The assumption underlying this EV model is that people seek to maximize the amount they will gain. Using a gambling paradigm, if one is offered a gamble of .5 probability (a coin flip) of $5 vs. 1.0 probability (a sure thing) of $1, the rational choice would be to take the former gamble because its EV is greater, that is, 5 × $5 = $2.50, versus 1.0 × $1 = $1.00 on average. Sometimes the $5 bet will win $5, and sometimes it will win $0, but over a very large number of gambles, on average, it will gain $5 half the time. On the other hand, the $1 gamble will always win $1, so its expected value = $1.00. This works with money, as long as one is able to bet a very large number of times.

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