The Distorted Theory of Rank-Dependent Expected Utility

30 Pages Posted: 23 Apr 2007 Last revised: 8 Oct 2009

See all articles by Hui Huang

Hui Huang

Department of Economics, University of Waterloo

Shunming Zhang

Xiamen University - School of Economics

Date Written: Feb 9, 2009

Abstract

This paper re-examines the rank-dependent expected utility theory. Firstly, we follow Quiggin's assumption (Quiggin 1982) that the transformation of cumulative distribution functions is a continuous function of the whole probability distribution to deduce the rank-dependent expected utility formula over lotteries and hence extend it to the case of general random variables. Secondly, we employ an axiomatic approach to build a distorted theory of rank-dependent expected utility. The transformation of the cumulative distribution functions is the decision weights function in the rank-dependent expected utility formula which reflects decision-makers' beliefs. We call it the distortion function which `distorts' the decision-maker's probabilities. Utilizing this distortion function, we propose a distorted independence axiom to prove the representation theorem of rank-dependent expected utility. Finally, we make direct use of the distorted independence axiom to explain the Allais paradox and the common ratio effect. We show that the inconsistency in these examples arises when the distortion function takes specific forms under the framework of the distorted independence axiom.

Keywords: Expected utility, Rank Dependent Expected, Distortion function, Distorted independence axiom, The Allais paradox, The common ratio effect.

JEL Classification: D81

Suggested Citation

Huang, Hui and Zhang, Shunming, The Distorted Theory of Rank-Dependent Expected Utility (Feb 9, 2009). Available at SSRN: https://ssrn.com/abstract=981309 or http://dx.doi.org/10.2139/ssrn.981309

Hui Huang (Contact Author)

Department of Economics, University of Waterloo ( email )

Department of Economics
University of Waterloo
Waterloo, Ontario N2L 3G1
Canada

Shunming Zhang

Xiamen University - School of Economics ( email )

Xiamen, Fujian 361005
China

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