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The Measure Representation: A Correction

Segal, Uzi (1991) The Measure Representation: A Correction. Social Science Working Paper, 781. California Institute of Technology , Pasadena, CA. (Unpublished)

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Wakker [9] and Puppe [2] point out a mistake in Theorem 1 in Segal [6]. 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 paper 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 [6, 7]), implying that the measure is a product measure (and hence anticipated utility), also guarantee that the measure is bounded.

Item Type:Report or Paper (Working Paper)
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Additional Information:I am grateful to Peter Wakker and to C. Puppe for pointing out to me the mistake in my original paper and to Larry Epstein and Peter Wakker for helpful discussions. Published as Segal, Uzi. "The measure representation: A correction." Journal of Risk and Uncertainty 6, no. 1 (1993): 99-107.
Group:Social Science Working Papers
Subject Keywords:anticipated utility, rank-dependent probabilities, measure representation
Series Name:Social Science Working Paper
Issue or Number:781
Record Number:CaltechAUTHORS:20170830-135419858
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80974
Deposited By: Jacquelyn Bussone
Deposited On:30 Aug 2017 21:06
Last Modified:03 Oct 2019 18:37

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