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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. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
    3. 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.
    4. Alain Chateauneuf & Michèle Cohen, 2008. "Cardinal extensions of EU model based on the Choquet integral," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00348822, HAL.
    5. 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.
    6. Edi Karni, 2024. "Ambiguity aversion, risk aversion, and the weight of evidence," Theory and Decision, Springer, vol. 97(4), pages 595-611, December.
    7. 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.
    8. Zimper, Alexander, 2004. "On the existence of strategic solutions for games with security- and potential level players," Papers 04-04, Sonderforschungsbreich 504.
    9. repec:cup:judgdm:v:11:y:2016:i:2:p:168-173 is not listed on IDEAS
    10. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    11. Ruinstein, Ariel & Salant, Yuval, 2015. "\Isn't everyone like me?": On the presence of self-similarity in strategic interactions," Foerder Institute for Economic Research Working Papers 275834, Tel-Aviv University > Foerder Institute for Economic Research.
    12. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.
    13. 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.
    14. LiCalzi, Marco, 1998. "Variations on the measure representation approach," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 255-269, April.
    15. Alexander Zimper, 2007. "Strategic games with security and potential level players," Theory and Decision, Springer, vol. 63(1), pages 53-78, August.
    16. Ulrich Schmidt, 2001. "Lottery Dependent Utility: a Reexamination," Theory and Decision, Springer, vol. 50(1), pages 35-58, February.
    17. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    18. 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.
    19. Lasso de la Vega, Casilda & Volij, Oscar, 2018. "Ranking scholars: A measure representation," Journal of Informetrics, Elsevier, vol. 12(2), pages 510-517.
    20. Wei-zhi Qin & Hendrik Rommeswinkel, 2024. "Quasi-separable preferences," Theory and Decision, Springer, vol. 96(4), pages 555-595, June.

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