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Axiomatic utility theories with the betweenness property

  • Part IV New Results In Nonlinear Preference Theory
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Abstract

This paper focuses on the betweenness property of expected utility theory. We provide an axiomatization of the class of betweenness-conforming utility theories. Subclasses of betweenness-conforming preferences are axiomatized with ‘substitution’ axioms of intermediate generality. The latter axioms incorporate specifically the effects of replacing a certain outcome with a lottery that is indifferent to it. Our representation is applied to the second-price auction mechanism where we show that its demand-revelation property under expected utility is not robust with respect to the class of betweenness-conforming preferences.

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Authors and Affiliations

  1. Department of Economics, Johns Hopkins University, 21218, Baltimore, Maryland, USA

    S. H. Chew

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  1. S. H. Chew
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Additional information

I would like to thank Larry Epstein, Itzhak Gilboa, Joe Harington, Edi Karni, Mark Machina, Roger Myerson, Zvi Safra, Fernando Saldanha, Itzhak Zilcha and Steve Zucker for their useful comments and helpful discussions. This is a revised version of an earlier working paper (Chew [5]). A simple version of semi-weighted utility was presented in an ‘exchange of views’ session at the Second International Conference on the Foundations of Utility and Risk Theories in Venice, June 1984. Versions of this paper have been presented at the University of California, San Diego (November 1985), the University of Pennsylvania (October 1985), Johns Hopkins University (October 1984), University of Arizona (January 1985) and Tel Aviv University (December 1984 and May 1985). I also wish to acknowledge the partial financial support from the National Science Foundation SES 8213602.

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Chew, S.H. Axiomatic utility theories with the betweenness property. Ann Oper Res 19, 273–298 (1989). https://doi.org/10.1007/BF02283525

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