TY - UNPB

T1 - The Need for Discontinuous Probability Weighting Functions

T2 - How Cumulative Prospect Theory is Torn Between the Allais Paradox and the St. Petersburg Paradox

AU - Dierkes, Maik

AU - Sejdiu, Vulnet

N1 - Fundin information: We thank Aur ́elien Baillon, Han Bleichrodt, Carsten Erner, Sascha F ̈ullbrunn, Glenn Harrison, Peter Wakker, Stefan Zeisberger, and participants at the International Conference of the French Association of Experimental Economics 2018, the Advances in Decision Analysis 2019, and the Subjective Probability, Utility, and Decision Making 2019 for comments. We are particularly grateful to Johannes Jaspersen and Walther Paravicini. All remaining errors are our own. Financial support by the Dr. Werner Jackst ̈adt Foundation is gratefully acknowledged.

PY - 2019/12/12

Y1 - 2019/12/12

N2 - Cumulative Prospect Theory (CPT) must embrace probability weighting functions with a discontinuity at probability zero to pass the two most prominent litmus tests for descriptive decision theories under risk: the Allais paradox and the St. Petersburg paradox. We prove in a nonparametric framework that, with continuous preference functions, CPT cannot explain both paradoxes simultaneously. Thus, Kahneman and Tversky’s (1979) originally proposed discontinuous probability weighting function has - when applied in a rank-dependent framework, of course - much more predictive power compared to all other popular, but continuous weighting functions, including e.g. Tversky and Kahneman's (1992) proposal. Neo-additive weighting functions constitute another parsimonious, yet promising class of discontinuous weighting functions. In other words, if we rashly restricted CPT to continuous preference functions we might erroneously jump to the conclusion that risk preferences are not stable over similar tasks or even reject CPT.

AB - Cumulative Prospect Theory (CPT) must embrace probability weighting functions with a discontinuity at probability zero to pass the two most prominent litmus tests for descriptive decision theories under risk: the Allais paradox and the St. Petersburg paradox. We prove in a nonparametric framework that, with continuous preference functions, CPT cannot explain both paradoxes simultaneously. Thus, Kahneman and Tversky’s (1979) originally proposed discontinuous probability weighting function has - when applied in a rank-dependent framework, of course - much more predictive power compared to all other popular, but continuous weighting functions, including e.g. Tversky and Kahneman's (1992) proposal. Neo-additive weighting functions constitute another parsimonious, yet promising class of discontinuous weighting functions. In other words, if we rashly restricted CPT to continuous preference functions we might erroneously jump to the conclusion that risk preferences are not stable over similar tasks or even reject CPT.

U2 - 10.2139/ssrn.3465830

DO - 10.2139/ssrn.3465830

M3 - Working paper/Discussion paper

BT - The Need for Discontinuous Probability Weighting Functions

ER -