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Theory and Decision

, Volume 29, Issue 2, pp 119–132 | Cite as

Under stochastic dominance Choquet-expected utility and anticipated utility are identical

  • Peter Wakker
Article

Abstract

The aim of this paper is to convince the reader that Choquet-expected utility, as initiated by Schmeidler (1982, 1989) for decision making under uncertainty, when formulated for decision making under risk naturally leads to anticipated utility, as initiated by Quiggin/Yaari. Thus the two generalizations of expected utility in fact are one.

Keywords

Nonadditive probabilities decision making under risk decision making under uncertainty prospect theory Choquet-expected utility anticipated utility rank-dependent utility cumulative utility comonotonicity 

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References

  1. Chew, S. H.: 1989, ‘An Axiomatic Generalization of the Quasilinear Mean and Gini Mean with Application to Decision Theory’, Johns Hopkins University and Tulane University; rewritten version of Chew, S. H. (1985), ‘An Axiomatization of the Rank-Dependent Quasilinear Mean Generalizing the Gini Mean and the Quasilinear Mean’, Economics Working Paper #156, Johns Hopkins University.Google Scholar
  2. Chew, S. H., Karni, E., and Safra, Z.: 1987, ‘Risk Aversion in the Theory of Expected Utility with Rank Dependent Probabilities’, Journal of Economic Theory 42, 370–381.Google Scholar
  3. Choquet, G.: 1953–54, ‘Theory of Capacities’, Annales de l'Institut Fourier (Grenoble), pp131–295.Google Scholar
  4. Edwards, W.: 1954, ‘The Theory of Decision Making’, Psychological Bulletin 51, 380–417.Google Scholar
  5. Feller, W.: 1966, An Introduction to Probability Theory, Vol. II, Wiley, New York.Google Scholar
  6. Fishburn, P. C.: 1986, ‘The Axioms of Subjective Probability’, Statistical Science 1, 335–358.Google Scholar
  7. Fishburn, P. C.: 1988, Nonlinear Preference and Utility Theory, Johns Hopkins University Press, Baltimore.Google Scholar
  8. Gilboa, I.: 1985, ‘Subjective Distortions of Probabilities and Non-Additive Probabilities’, Working paper 18–85, Foerder Institute for Economic Research, Tel-Aviv University, Ramat Aviv, Israel.Google Scholar
  9. Gilboa, I.: 1987, ‘Expected Utility with Purely Subjective Non-Additive Probabilities’, Journal of Mathematical Economics 16, 65–88.Google Scholar
  10. Kahneman, D. and Tversky, A.: 1979, ‘Prospect Theory: An Analysis of Decision under Risk’, Econometrica 47, 263–291.Google Scholar
  11. Knight, F. H.: 1921, Risk, Uncertainty, and Profit, Houghton Mifflin, New York.Google Scholar
  12. Kraft, C. H., Pratt, J. W., and Seidenberg, A.: 1959, ‘Intuitive Probability on Finite Sets’, Annals of Mathematical Statistics 30, 408–419.Google Scholar
  13. Luce, R. D.: 1988, ‘Rank-Dependent, Subjective Expected-Utility Representations’, Journal of Risk and Uncertainty 1, 305–332.Google Scholar
  14. Nakamura, Y.: 1990, ‘Subjective Expected Utility with Non-Additive Probabilities on Finite State Space’, University of Tsukuba, Tsukuba, Ibaraki, Japan.Google Scholar
  15. Quiggin, J.: 1982, ‘A Theory of Anticipated Utility’, Journal of Economic Behaviour and Organization 3, 323–343.Google Scholar
  16. Savage, L. J.: 1954, The Foundations of Statistics, Wiley, New York. (Second edition 1972, Dover, New York).Google Scholar
  17. Schmeidler, D.: 1982, 1989, ‘Subjective Probability and Expected Utility without Additivity’, Econometrica 57 (1989), 571–587; first version 1982.Google Scholar
  18. Wakker, P. P.: 1981, ‘Agreeing Probability Measures for Comparative Probability Structures’, The Annals of Statistics 9, 658–662.Google Scholar
  19. Wakker, P. P.: 1989a, ‘Continuous Subjective Expected Utility with Nonadditive Probabilities’, Journal of Mathematical Economics 18, 1–27.Google Scholar
  20. Wakker, P. P.: 1989b, Additive Representations of Preferences, A New Foundation of Decision Analysis, Kluwer (Academic Publishers), Dordrecht.Google Scholar
  21. Wakker, P. P.: 1989c, ‘Transforming Probabilities without Violating Stochastic Dominance’, in E. E. Ch. I. Roskam (ed.), Mathematical Psychology in Progress, Springer, Berlin, 29–48.Google Scholar
  22. Wakker, P. P.: 1989d, ‘A Behavioral Foundation for Fuzzy Measures’, Fuzzy Sets and Systems, forthcoming.Google Scholar
  23. Wakker, P. P.: 1989e, ‘From Finite-to Infinite-Dimensional Integral Representations; Unbounded Utility for Savage (1954) and Others’, Duke University, Fuqua School of Business, working paper 8928.Google Scholar
  24. Wakker, P. P.: 1990, In preparation.Google Scholar
  25. Yaari, M. E.: 1987, ‘The Dual Theory of Choice under Risk’, Econometrica 55, 95–115.Google Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Peter Wakker
    • 1
  1. 1.University of Nijmegen, Nijmegen Institute for Cognition research and Information technology (NICI)NijmegenThe Netherlands

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