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The Measure Representation: A Correction

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  • Segal, Uzi

Abstract

Wakker (1991) and Puppe (1990) point out a mistake in theorem 1 in Segal (1989). This theorem deals with representing preference relations over lotteries by the measure of their epigraphs. An error in the theorem is that it gives wrong conditions concerning the continuity of the measure. This article corrects the error. Another problem is that the axioms do not imply that the measure is bounded; therefore, the measure representation applies only to subsets of the space of lotteries, although these subsets can become arbitrarily close to the whole space of lotteries. Some additional axioms (Segal, 1989, 1990) implying that the measure is a product measure (and hence anticipated utility) also guarantee that the measure is bounded. Copyright 1993 by Kluwer Academic Publishers

Suggested Citation

  • Segal, Uzi, 1993. "The Measure Representation: A Correction," Journal of Risk and Uncertainty, Springer, vol. 6(1), pages 99-107, January.
  • Handle: RePEc:kap:jrisku:v:6:y:1993:i:1:p:99-107
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    Cited by:

    1. Castagnoli, Erio & LiCalzi, Marco, 2006. "Benchmarking real-valued acts," Games and Economic Behavior, Elsevier, vol. 57(2), pages 236-253, November.
    2. repec:hal:journl:halshs-00348822 is not listed on IDEAS
    3. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications, Elsevier.
    4. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.
    5. Chateauneuf, Alain, 1999. "Comonotonicity axioms and rank-dependent expected utility theory for arbitrary consequences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 21-45, August.
    6. 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.
    7. Grant, Simon & Kajii, Atsushi, 1998. "AUSI expected utility: An anticipated utility theory of relative disappointment aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 37(3), pages 277-290, November.
    8. LiCalzi, Marco, 1998. "Variations on the measure representation approach," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 255-269, April.
    9. Nathalie Etchart-Vincent, 2009. "Probability weighting and the ‘level’ and ‘spacing’ of outcomes: An experimental study over losses," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 45-63, August.
    10. Zimper, Alexander, 2004. "On the Existence of Strategic Solutions for Games with Security- and Potential Level Players," Sonderforschungsbereich 504 Publications 04-04, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    11. Alexander Zimper, 2007. "Strategic games with security and potential level players," Theory and Decision, Springer, vol. 63(1), pages 53-78, August.
    12. Ariel Rubinstein & Yuval Salant, 2016. ""Isn't everyone like me?": On the presence of self-similarity in strategic interactions," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 11(2), pages 168-173, March.
    13. Ulrich Schmidt, 2001. "Lottery Dependent Utility: a Reexamination," Theory and Decision, Springer, vol. 50(1), pages 35-58, February.

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