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 demonstrated 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 probabilities, 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 satis®es 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 transforming probabilities that was introduced by Quiggin (1982); see also Lopes (1984), Luce (1988), and Allais (1988. For a survey of non-expected utility, see Slovic, Lichtenstein, andFischho (1988) andCamerer (1992).This paper describes the PT and CPT theories and discusses dierences. In particular, we ®nd that CPT does not only avoid some theoretical problems but also gives dierent empirical predictions that, for the experiments considered in this paper, are better than those of the original PT. The key feature of CPT is that it permits a satisfactory modeling of diminishing sensitivity, not only with respect to CCC 0894±3257/97/010053±12
Experimental investigations of non-expected utility have primarily concentrated on decision under risk Uprobability triangles"). The literature suggests, however, that ambiguity is one of the main causes for deviations from expected utility (EUt. This article investigates the descriptive performance of rank-dependent utility (RDU) in the context of choice under ambiguity. We use the axiomatic difference between RDU and EU to critically test RDU against EU. Surprisingly, the RDU model does not provide any descriptive improvement over EU. Our data suggest other "framing" factors that do provide descriptive improvements over EU.In the past decades, students of individual choice have demonstrated that preference behavior deviates from Expected Utility theory (EU). In response, various generalizations and alternatives to EU have been put forward. Axioms that are thought to be descriptively invalid have been weakened to accommodate the observed violations. For most theorists, the independence axiom is the major culprit, exemplified by the Allais and Ellsberg paradoxes. In the early 1980s, several new models have been proposed that weaken the independence axiom, thus generalizing EU. Two major kinds of transitive generalizations have emerged: betweenness models and rank-dependent models.Recently, empirical research is cumulating that tests whether the new proposals are able to explain the experimental facts found thus far (Camerer and Ho, 1994). Most of this research can be summarized using so-called probability triangles. These triangles employ three outcomes that are kept constant. Gambles are constructed by varying the probabilities assigned to these outcomes. Most of the theories considered can be tested by observing preference behavior on selected pairs of gambles from these triangles. The overall picture emerging from this research is that none of the generalized expected utility theories can explain all the systematic violations that have been discovered. The betweenness condition, for example, is found to be systematically violated (Camerer and Ho, 1994). The rank-dependent models (RDU), especially the new version of prospect theory, Cumulative Prospect theory, are at the moment probably the leading contender for best descriptive theory. However, some remarks must be made.
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 demonstrated 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 probabilities, 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 satis®es 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 transforming probabilities that was introduced by Quiggin (1982); see also Lopes (1984), Luce (1988), and Allais (1988. For a survey of non-expected utility, see Slovic, Lichtenstein, andFischho (1988) andCamerer (1992).This paper describes the PT and CPT theories and discusses dierences. In particular, we ®nd that CPT does not only avoid some theoretical problems but also gives dierent empirical predictions that, for the experiments considered in this paper, are better than those of the original PT. The key feature of CPT is that it permits a satisfactory modeling of diminishing sensitivity, not only with respect to CCC 0894±3257/97/010053±12
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