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This chapter begins with a description of a model of individual choice under uncertainty, namely, the expected utility model of preferences for lotteries. A number of problems are examined from the perspective of linearity in the probabilities: the ‘Allais’ paradox or fanning out of indifference curves, the common-ratio effect for negative pay-offs, the effect of risk aversion, preference reversal, and framing effects (i.e., where systematic differences occur in choice due to alternative means of representing probalistically equivalent choice problems). The final section of the chapter discusses how private-sector decision analysts, government agencies, and environmental policy makers should adjust their prescriptive (normative) decision practices in the light of these findings.

This chapter explains the meaning of the payoffs that are used to quantify the outcomes of games. The theory of revealed preference assumes only that players are consistent. With appropriate consistency assumptions, it is shown that players act as though maximizing a utility function. The game of Russian Roulette is introduced to show that the players need to reveal preferences over lotteries so that risky situations can be accommodated. Von Neumann and Morgenstern's consistency postulates are shown to imply that an agent acts as though maximizing the expected value of a utility function in risky situations. Risk aversion is identified with having a concave Von Neumann and Morgenstern utility function. The properties of such functions are then explored. Russian Roulette is then analyzed to show that the outcome depends on the level of risk aversion of the players. Finally, Allais' paradox and Zeckhauser's paradox are used to comment on the difference between rational behavior in the presence of risk and actual behavior.

Standard presentations of decision theory adopt some version of the invariance principle (that it is irrational to assign different utilities to propositions known to be equivalent). This normative principle raises problems for the idea that decision theory can serve as a theory of motivation. Frederic Schick has responded to this tension by proposing an intensional version of decision theory that allows a single outcome to be understood in different ways (and utilities to be assigned accordingly). This raises problems (such as the failure of the expected utility theorem) that can be dealt with by a more fine-grained way of individuating outcomes (as in Broome's theory of individuation by justifiers). Again, though, none of these strategies serves all three of the explanatory projects under consideration.

Chapter 16 shows how the validity of expected utility theory (EUT) was increasingly called into question between the mid-1960s and the mid-1970s and discusses how a series of experiments performed from 1974 to 1985 undermined the earlier confidence that EUT makes it possible to measure utility. Beginning in the mid-1960s, in a series of experiments seminal to the field later called behavioral economics, Sarah Lichtenstein, Paul Slovic, Amos Tversky, and others showed that decision patterns violating EUT are systematic. The new experimenters who engaged with the EUT-based measurement of utility from the mid-1970s, namely Uday Karmarkar, Richard de Neufville, Paul Schoemaker, and coauthors, showed that different elicitation methods to measure utility, which according to EUT should produce the same outcome, generate different measures. These findings contributed to destabilizing EUT, undermined the confidence in EUT-based utility measurement, and helped foster a blossoming of novel behavioral models of decision-making under risk.

The orthodox belief that economic systems fundamentally differ from other social systems by virtue of the self-regulating properties of competition and the countervailing forces it automatically unleashes in moments of crisis has been shown to be false on both theoretical and empirical grounds. Perhaps no single episode is more revelatory of the discomfort economists feel in the presence of inconvenient facts than the 1952 encounter between Savage and Allais, where Savage was led to reject his own choice criterion for decision-making under uncertainty. Yet no attempt has been made since to come to terms with the implications of Allais's paradox: still today the maximization of expected utility remains the basic economic model for describing rational behavior in the face of risk. Nothing will change unless economists look beyond instrumental rationality and think of value not as an inherent property of objects, but as a social institution.

The Allais and Ellsberg paradoxes are presented. Various generalizations of expected utility motivated by these and other paradoxes are discussed, including betweenness preferences, rank‐dependent preferences, multiple prior max‐min preferences, and prospect theory. For betweenness preferences, which include weighted utility and disappointment aversion, an investor’s marginal utility is proportional to a stochastic discount factor. Disappointment averse utility and rank‐dependent utility have first‐order risk aversion. Multiple prior max‐min utility is one way to accomodate the Ellsberg paradox (ambiguity aversion or Knightian uncertainty). The dynamic consistency of updating multiple priors is discussed.

This chapter begins by introducing the notions of mathematical expectation and utility. Then we explain how expected utility theory connects preference rankings to credence and utilities. We develop Savage’s decision theory, Jeffrey’s evidential decision theory, and causal decision theory. Along the way, such problems as risk aversion, Allais’ paradox, and Newcomb’s problem are considered.

The literature on expected utility formulates in two ways the principle to maximize expected utility. One version of the principle requires choices that literally maximize expected utility. The other version requires choices that are “as if” maximizing expected utility. The first principle is substantive and applies to a single choice. The second principle is representational and applies to a set of choices; it requires only a type of consistency among choices and is weaker than the first, substantive principle. The justification of the substantive version of the principle is that following it amounts to following preferences among the options in a decision problem. The justification takes an option’s risk as a consequence of the option’s realization. Making this move yields a simple decision principle, using evaluations of options that do not add weights to the probabilities or the utilities of an option’s possible outcomes.

Formal theories of instrumental rationality, such as orthodox decision theory, often provide a powerful account of the rationality of choice under risk. Can the extended theory of instrumental rationality (ETR) be similarly extended to contexts of risk and uncertainty? Chapter 9 argues that ETR can provide a satisfactory account of rationality in these contexts and that it can actually co-opt the resources of decision theory exactly in the cases in which the theory seems most plausible; namely, the pursuit of what I call “general means” (such as the pursuit of health or wealth). Moreover ETR plausibly renders coherent certain ubiquitous choice dispositions (such as the ones manifested in the Allais paradox) that seem incompatible with orthodox decision theory.

Combining acts combines their risks. Their risks are not additive, either using their sizes or their intrinsic utilities. This creates the possibility of hedging, that is, adopting a risk to lower overall risk. Evaluation of combinations of acts that produce risks depends on whether the acts are simultaneous or in a sequence. Rationality evaluates a set of simultaneous acts as one act, given an ideal agent’s awareness of performing all together and at will. It evaluates a sequence of acts by evaluating its components one by one; their rationality suffices for the sequence’s rationality. This method of evaluation contrasts with evaluation of a sequence by comparing its utility to the utilities of rival sequences. Rationality does not evaluate sequences using utility maximization, even when the sequences bring neither unanticipated information nor changes in goals, because sequences are not options in the sense of being performable at will.

This chapter traces the history of decision-making and rationality in Western culture. Despite the fact that the concept of rationality has been tackled by philosophers since early Greek antiquity, it only really emerged in popular culture after the Middle Ages. The science of rationality culminated in the twentieth century with the axiomatization of preferences and theories of decision-making development by economists. Ultimately, psychologists and economists agree that the concept of rationality is relative. To summarize: when a subject decides, they do not usually optimize choice. For behaviourists, explanation is to be found in exploratory behaviour: evolutionary pressure has selected behaviours that anticipate possible changes in environmental conditions. The subject (animal or human) exchanges some immediate efficacy against information which may serve him later. For economists, the answer is more complex. It is a combination of the inability to understand all of the options relating to the problem (bounded rationality) associated with biases that cloud judgement.