Readings in Formal Epistemology pp 493-519

# Advances in Prospect Theory: Cumulative Representation of Uncertainty

## Abstract

Expected utility theory reigned for several decades as the dominant normative and descriptive model of decision making under uncertainty, but it has come under serious question in recent years. There is now general agreement that the theory does not provide an adequate description of individual choice: a substantial body of evidence shows that decision makers systematically violate its basic tenets. Many alternative models have been proposed in response to this empirical challenge (for reviews, see Camerer J Risk Uncertain 2:61–104, 1989; Fishburn Nonlinear preference and utility theory. The Johns Hopkins University Press, Baltimore, 1988; Machina Econ Perspect 1(1):121–154, 1987). Some time ago we presented a model of choice, called prospect theory, which explained the major violations of expected utility theory in choices between risky prospects with a small number of outcomes (Kahneman and Tversky Econometrica 47:263–291, 1979; Tversky and Kahneman J Bus 59(4):S251–S278, 1986). The key elements of this theory are (1) a value function that is concave for gains, convex for losses, and steeper for losses than for gains, and (2) a nonlinear transformation of the probability scale, which overweights small probabilities and underweights moderate and high probabilities. In an important later development, several authors (Quiggin J Econ Behav Organ 3, 323–343; Schmeidler Econometrica 57:571–587, 1989; Yaari Econometrica 55:95–115, 1987; Weymark Math Soc Sci 1:409–430, 1981) have advanced a new representation, called the rank-dependent or the cumulative functional, that transforms cumulative rather than individual probabilities. This article presents a new version of prospect theory that incorporates the cumulative functional and extends the theory to uncertain as well to risky prospects with any number of outcomes. The resulting model, called cumulative prospect theory, combines some of the attractive features of both developments (see also Luce and Fishburn J Risk Uncertain 4:29–59, 1991). It gives rise to different evaluations of gains and losses, which are not distinguished in the standard cumulative model, and it provides a unified treatment of both risk and uncertainty.

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