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State Dependent Expected Utility for Savage's State Space


  • Peter P. Wakker

    (CentER, Tilburg University, P.O. Box 90153, Tilburg, 5000 LE, The Netherlands)

  • Horst Zank

    (Department of Economics, Maastricht University, P.O. Box 616, Maastricht, 6200 MD, The Netherlands)


This paper generalizes the Debreu/Gorman characterization of additively decomposable functionals and separable preferences to infinite dimensions. The first novelty concerns the very definition of additively decomposable functionals for infinite dimensions. For decision under uncertainty, our result provides a state-dependent extension of Savage's expected utility. A characterization in terms of preference conditions identifies the empirical content of the model; it amounts to Savage's axiom system with P4 (likelihood ordering) dropped. Our approach does not require that a (probability) measure on the state space be given a priori, or can be derived from extraneous conditions outside the realm of decision theory. Bayesian updating of new information is still possible, even though no prior probabilities are given. The finding suggests that the sure-thing principle, rather than prior probability, is at the heart of Bayesian updating.

Suggested Citation

  • Peter P. Wakker & Horst Zank, 1999. "State Dependent Expected Utility for Savage's State Space," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 8-34, February.
  • Handle: RePEc:inm:ormoor:v:24:y:1999:i:1:p:8-34
    DOI: 10.1287/moor.24.1.8

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    References listed on IDEAS

    1. Streufert, P. A., 1995. "A general theory of separability for preferences defined on a countably infinite product space," Journal of Mathematical Economics, Elsevier, vol. 24(5), pages 407-434.
    2. John M. Miyamoto & Peter Wakker, 1996. "Multiattribute Utility Theory Without Expected Utility Foundations," Operations Research, INFORMS, vol. 44(2), pages 313-326, April.
    3. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309-309.
    4. Karl Vind & Birgit Grodal, 1990. "Additive Utility Functions and Other Special Functions in Economic Theory," Discussion Papers 90-21, University of Copenhagen. Department of Economics.
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    Cited by:

    1. Yves Sprumont, 2019. "Relative utilitarianism under uncertainty," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 621-639, December.
    2. Marco Maggis & Andrea Maran, 2018. "Stochastic Dynamic Utilities and Inter-Temporal Preferences," Papers 1803.05244,, revised Feb 2020.
    3. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    4. Pivato, Marcus & Vergopoulos, Vassili, 2018. "Subjective expected utility with topological constraints," MPRA Paper 85749, University Library of Munich, Germany.
    5. Stanca, Lorenzo, 2020. "A simplified approach to subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 151-160.


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