Journal of Risk and Uncertainty

, Volume 6, Issue 1, pp 99–107 | Cite as

The measure representation: A correction

  • Uzi Segal


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.

Key words

anticipated utility rank-dependent probabilities measure representation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Billingsley, P. (1979).Probability and Measure. New York: John Wiley and Sons.Google Scholar
  2. Puppe, C. (1990). “The Irrelevance Axiom, Relative Utility and Choice Under Risk,” Department of Statistics and Mathematical Economics, University of Karlsruhe, Karlsruhe, Germany.Google Scholar
  3. Quiggin, J. (1982). “A Theory of Anticipated Utility,”Journal of Economic Behavior and Organization 3, 323–343.Google Scholar
  4. Royden, H.L. (1963). Real Analysis.New York:MacMillan.Google Scholar
  5. Segal, U. (1984). “Nonlinear Decision Weights with the Independence Axiom,” UCLA Working Paper #353.Google Scholar
  6. Segal, U. (1989). “Anticipated Utility: A Measure Representation Approach,”Annals of Operation Research 19, 359–373.Google Scholar
  7. Segal, U. (1990). “Two-Stage Lotteries Without the Reduction Axiom,”Econometrica 58, 349–377.Google Scholar
  8. Tversky, A. and D. Kahneman. (1991). “Cumulative Prospect Theory: An Analysis of Decision Under Uncertainty,” mimeo.Google Scholar
  9. Wakker, P. (1991). “Counterexamples to Segal's Measure Representation Theorem,”Journal of Risk and Uncertainty 6, 91–98.Google Scholar
  10. Yaari, M.E. (1987). “The Dual Theory of Choice Under Risk,”Econometrica 55, 95–115.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Uzi Segal
    • 1
  1. 1.Department of EconomicsUniversity of TorontoTorontoCanada

Personalised recommendations