Original and cumulative prospect theory: A discussion of empirical differences

This paper discusses dierences between prospect theory and cumulative prospect theory. It shows that cumulative prospect theory is not merely a formal correction of some theoretical problems in prospect theory, but it also gives dierent predictions. Some experiments by Lola Lopes are re-analyzed, and are demon-strated to favor cumulative prospect theory over prospect theory. It turns out that the mathematical form of cumulative prospect theory is well suited for modeling the psychological phenomenon of diminishing sensitivity.*c 1997 by John Wiley & Sons, Ltd. KEY WORDS prospect theory; diminishing sensitivity; rank-dependence; decision weights; risk aversion Prospect Theory (PT) has been one of the most important theories of decision making under risk in the past decade, and has been applied in a wide variety of contexts. By including distortions of probabil-ities, diminishing sensitivity, and the status quo as a reference point, PT can explain the major deviations from expected utility such as the Allais paradox, the certainty eect, and framing eects (Kahneman and Tversky, 1979). However, there are some theoretical problems in PT. The main problem is that the functional form of PT violates ‘stochastic dominance ’ (Kahneman and Tversky, 1979, pp. 283–284). Stochastic dominance requires that a shift of probability mass from bad outcomes to better outcomes leads to an improved prospect. The theoretical problems have recently been solved in a new version of PT, called cumulative prospect theory (CPT), that was introduced by Tversky and Kahneman (1992); in particular, CPT satisfies stochastic dominance. Similar forms were introduced by Starmer and Sugden (1989) and Luce and Fishburn (1991). Cumulative prospect theory adopts the rank-dependent method for trans