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Rank-Dependent, Subjective Expected-Utility Representations

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  • Luce, R Duncan

Abstract

Gambles are recursively generated from pure payoffs, events, and other gambles, and a preference order over them is assumed. Weighted average utility representations are studied that are strictly increasing in each payoff and for which the weights depend both on the events underlying the gamble and the preference ranking over the several component payoffs. Basically two results are derive: a characterization of monotonicity in terms of the weights, and an axiomatization of the representation. The latter rests on two important conditions: a decomposition of gambles into binary ones and a necessary commutativity condition on events in a particular class of binary gambles. A number of unsolved problems are cited. Copyright 1988 by Kluwer Academic Publishers

Suggested Citation

  • Luce, R Duncan, 1988. "Rank-Dependent, Subjective Expected-Utility Representations," Journal of Risk and Uncertainty, Springer, vol. 1(3), pages 305-332, September.
  • Handle: RePEc:kap:jrisku:v:1:y:1988:i:3:p:305-32
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    Cited by:

    1. Border, K.C. & Segal, U., 1997. "Coherent Odds and Subjective Probability," UWO Department of Economics Working Papers 9717, University of Western Ontario, Department of Economics.
    2. Camerer, Colin & Weber, Martin, 1992. "Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-370, October.
    3. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.
    4. Wakker, Peter, 1996. "The sure-thing principle and the comonotonic sure-thing principle: An axiomatic analysis," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 213-227.
    5. Marc Willinger, 1990. "La rénovation des fondements de l'utilité et du risque," Revue Économique, Programme National Persée, vol. 41(1), pages 5-48.
    6. Nakamura Y., 1996. "Rank dependent utility for arbitrary consequnce spaces," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 54-54, February.
    7. Wakker, Peter P. & Zank, Horst, 1999. "A unified derivation of classical subjective expected utility models through cardinal utility," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 1-19, August.

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