Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2002, Volume 70, Issue 2

A Genuine Rank‐Dependent Generalization of the Von Neumann‐Morgenstern Expected Utility Theorem

https://doi.org/10.1111/1468-0262.00301
p. 717-736

Mohammed Abdellaoui

This paper uses “revealed probability trade‐offs” to provide a natural foundation for probability weighting in the famous von Neumann and Morgenstern axiomatic set‐up for expected utility. In particular, it shows that a rank‐dependent preference functional is obtained in this set‐up when the independence axiom is weakened to stochastic dominance and a probability trade‐off consistency condition. In contrast with the existing axiomatizations of rank‐dependent utility, the resulting axioms allow for complete flexibility regarding the outcome space. Consequently, a parameter‐free test/elicitation of rank‐dependent utility becomes possible. The probability‐oriented approach of this paper also provides theoretical foundations for probabilistic attitudes towards risk. It is shown that the preference conditions that characterize the shape of the probability weighting function can be derived from simple probability trade‐off conditions.


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