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.
Similar content being viewed by others
References
Billingsley, P. (1979).Probability and Measure. New York: John Wiley and Sons.
Puppe, C. (1990). “The Irrelevance Axiom, Relative Utility and Choice Under Risk,” Department of Statistics and Mathematical Economics, University of Karlsruhe, Karlsruhe, Germany.
Quiggin, J. (1982). “A Theory of Anticipated Utility,”Journal of Economic Behavior and Organization 3, 323–343.
Royden, H.L. (1963). Real Analysis.New York:MacMillan.
Segal, U. (1984). “Nonlinear Decision Weights with the Independence Axiom,” UCLA Working Paper #353.
Segal, U. (1989). “Anticipated Utility: A Measure Representation Approach,”Annals of Operation Research 19, 359–373.
Segal, U. (1990). “Two-Stage Lotteries Without the Reduction Axiom,”Econometrica 58, 349–377.
Tversky, A. and D. Kahneman. (1991). “Cumulative Prospect Theory: An Analysis of Decision Under Uncertainty,” mimeo.
Wakker, P. (1991). “Counterexamples to Segal's Measure Representation Theorem,”Journal of Risk and Uncertainty 6, 91–98.
Yaari, M.E. (1987). “The Dual Theory of Choice Under Risk,”Econometrica 55, 95–115.
Author information
Authors and Affiliations
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.
Rights and permissions
About this article
Cite this article
Segal, U. The measure representation: A correction. J Risk Uncertainty 6, 99–107 (1993). https://doi.org/10.1007/BF01065353
Issue Date:
DOI: https://doi.org/10.1007/BF01065353