The Routledge Companion to Ethics by Skorupski John

Author:Skorupski, John
Language: eng
Format: epub
Tags: Humanities
Publisher: Taylor & Francis (CAM)
Published: 2010-06-30T04:00:00+00:00

Decision and game theory

Decision theory is the study of individual rational decision-making. Its core tenet is that a rational agent maximizes her expected utility. Each option in a particular situation of choice is supposed to have a finite set of possible outcomes, exactly one of which will be actual if the option is chosen. For each option, the agent assigns, in a consistent way, a probability to each of its possible outcomes, on the condition that the option is chosen. Further, the agent is assumed to have a complete and transitive preference ordering over the set of possible outcomes. Given that these and certain other axioms hold, it can be shown that there is a “utility function,” assigning numerical values to the outcomes in such a way that the agent prefers option a to option b if and only if a has greater expected utility than b. (This was first proved by von Neumann and Morgenstern 1947.) It should be stressed that, in decision theory, “utility” just refers to a representation of a rational person’s preferences, and not to some independent value that he seeks to maximize. The expected utility of an option is calculated by multiplying, for each of its possible outcomes, the utility of the outcome with its probability, and then summing these products. Thus, suppose that option a has two possible outcomes, x and y, with utilities 9 and 5, and probabilities 0.3 and 0.7, respectively. The expected utility of a is then (9 × 0.3) + (5 × 0.7) = 6.2.

Importantly, a utility function contains information not merely about which options are preferred to which, but also about the strengths of the agent’s preferences. If the difference between the utilities of outcomes x and y is twice the difference between the utilities of z and w, we can infer that she prefers x to y twice as strongly as she prefers z to w. This amounts to measurement on an interval scale.

Not everybody accepts maximization of expected utility as a criterion of rationality. There are situations where it is far from obviously irrational to violate one or more of the axioms of standard decision theory. Completeness and transitivity of preferences are debatable as universal requirements, and much discussed cases like “Allais’ paradox” and the “St Petersburg paradox” cast doubt on other axioms.

Decision theory has had considerable influence on normative ethics, especially on consequentialist theories. Thus, some recently proposed forms of consequentialism maintain that an action is right just in case it maximizes expected value (Jackson 1991). According to such a theory, the value to be maximized is intrinsic or final value, rather than the agent’s utility. Nevertheless, the structural part of the theory emulates decision theory. Some utilitarian versions of consequentialism resemble decision theory even more closely, by understanding intrinsic value in terms of the aggregated utilities of everyone affected by the action. Others have proposed the maximization of expected value, not as a criterion of rightness, but rather as a moral decision-making procedure.

Game theory is an extension of decision theory.

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