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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

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Bibliographic Info

Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 781.

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Date of creation: Oct 1991
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Publication status: Published:
Handle: RePEc:clt:sswopa:781

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Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
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Cited by:
  1. Ulrich Schmidt, 2001. "Lottery Dependent Utility: a Reexamination," Theory and Decision, Springer, vol. 50(1), pages 35-58, February.
  2. GRANT, Simon & KAJII, Atsushi, 1994. "Ausi Expected Utility : An Anticipated Utility Theory of Relative Disappointment Aversion," CORE Discussion Papers 1994045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. LiCalzi, Marco, 1998. "Variations on the measure representation approach," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 255-269, April.
  4. 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.
  5. Nathalie Etchart-Vincent, 2009. "Probability weighting and the 'level' and 'spacing' of outcomes: An experimental study over losses," Post-Print hal-00395876, HAL.
  6. repec:hal:journl:halshs-00211906 is not listed on IDEAS
  7. Erio Castagnoli & Marco LiCalzi, 2005. "Benchmarking real-valued acts," Microeconomics 0502001, EconWPA.
  8. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.
  9. repec:hal:journl:halshs-00348822 is not listed on IDEAS
  10. 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.
  11. Alexander Zimper, 2007. "Strategic games with security and potential level players," Theory and Decision, Springer, vol. 63(1), pages 53-78, August.

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