15.7 Summary
Prospect Theory (PT) and Cumulative Prospect Theory (CPT) challenge EU theory. The experimental studies which support PT and CPT are obtained by employing the certainty equivalent (CE) approach which suffers from the “certainty effect.” Moreover, these studies are confined to bets with only two outcomes, which must be either positive or negative, but not mixed.
In this chapter we suggest SD rules to test CPT, a paradigm which does not suffer from the above drawbacks of the CE approach. Prospect Stochastic Dominance (PSD) and Markowitz’s Stochastic Dominance (MSD) corresponding to S-shape function and reverse S-shape function are presented. These decision rules are generally employed with cumulative distributions, F and G, derived from objective probabilities. However, they can be employed also with subjective cumulative distributions in some specific cases. Using these rules, CPT is rejected as 62%–66% of the subjects select, say, prospect G despite the fact that another prospect, say prospect F dominates it by PSD.
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References
The proof, as the proofs of the SD criteria, holds also for the unbounded case (see Hanoch and Levy, Review of Economic Studies, 36, 1969, pp. 335–346).
See footnote 8 in Chapter 14.
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Notice that for mixed prospects the decision weights do not generally add up to 1 (Tversky & Kahneman, 1992, p. 301). In Task II, the decision weights add up to.875 for F and to.866 for G. We assign the probability which is “missing” to the outcome 0, which of course does not affect the results by CPT V(0) = 0. If all outcomes are either positive or negative we obtain by CPT that εw(p) = 1. In such cases, experimental findings strongly reject CPT. For more details, see Levy, H., “Cumulative Prospect Theory: New Evidence,” 2005, working paper, Hebrew University of Jerusalem.
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(2006). Stochastic Dominance and Prospect Theory. In: Stochastic Dominance. Studies in Risk and Uncertainty, vol 12. Springer, Boston, MA . https://doi.org/10.1007/0-387-29311-6_15
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