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Abstract
Cumulative prospect theory was introduced by Tversky and Kahneman so as to combine the empirical realism of their original prospect theory with the theoretical advantages of Quiggin's rank-dependent utility. Preference axiomatizations were provided in several papers. All those axiomatizations, however, only consider decision under uncertainty. No axiomatization has been provided as yet for decision under risk, i.e., the case in which given probabilities are transformed. Providing the latter is the purpose of this note. The resulting axiomatization is considerably simpler than that for uncertainty.
Key words: prospect theory, rank-dependent utility, rank-dependence, sign-dependence, comonotonicity, tradeoff consistency
JEL Classification: D81
- . Prospect theory Kahneman and Tversky, 1979 was one of the first models for decision under risk that permitted descriptive deviations from rationality and achieved theoretical tractability at the same time. However, a difficulty in its method for transforming probabilities is that violations of stochastic dominance are - . implied Fishburn, 1978; Kahneman and Tversky, 1979, pp. 283r284 . The problem - . has been solved by Quiggin's 1981 rank-dependent utility. Tversky and Kahneman - . 1992 invoke Quiggin's idea and thus combine the descriptive advantages of original prospect theory with the theoretical advantages of rank-dependent utility. Their theory provides one of the most promising nonexpected utility models presently available.
An additional advantage of cumulative prospect theory as compared to original prospect theory is that it can also be applied to uncertainty, i.e., the case in which probabilities of events are not given. Preference axioms have been provided by - . - . Tversky and Kahneman 1992 , Wakker and Tversky 1993 , and, in a somewhat - . different setup, by Luce and Fishburn 1991 . The functional of cumulative prospect - . theory already appeared in Starmer and Sugden 1989, Appendix , but they did not provide a preference axiomatization.
Although the theory is meant to apply to both uncertainty and risk, preference axiomatizations have hitherto been provided only for decision under uncertainty. There is no preference axiomatization of cumulative prospect theory available for risk yet, i.e., the case where probabilities are given and are to be transformed. Filling that gap is the purpose of this note. The result for risk turns out to be considerably simpler than that for uncertainty. We...