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A Genuine Rank‐Dependent Generalization of the Von Neumann‐Morgenstern Expected Utility Theorem
Author(s) -
Abdellaoui Mohammed
Publication year - 2002
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00301
Subject(s) - von neumann–morgenstern utility theorem , expected utility hypothesis , axiom , mathematical economics , mathematics , stochastic dominance , subjective expected utility , isoelastic utility , von neumann architecture , axiom independence , generalization , probability distribution , probabilistic logic , rank (graph theory) , weighting , mathematical optimization , combinatorics , statistics , pure mathematics , mathematical analysis , medicine , geometry , radiology
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.