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Desirability relations in Savage’s model of decision making

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  • Dov Samet

    (Tel Aviv University)

  • David Schmeidler

    (Tel Aviv University)

Abstract

We propose a model of an agent’s probability and utility that is a compromise between Savage (The foundations of statistics, Wiley, 1954) and Jeffrey (The Logic of Decision, McGraw Hill, 1965). In Savage’s model the probability–utility pair is associated with preferences over acts which are assignments of consequences to states. The probability is defined on the state space, and the utility function on consequences. Jeffrey’s model has no consequences, and both probability and utility are defined on the same set of propositions. The probability–utility pair is associated with a desirability relation on propositions. Like Savage we assume a set of consequences and a state space. However, we assume that states are comprehensive, that is, each state describes a consequence, as in Aumann (Econometrica 55:1–18, 1987). Like Jeffrey, we assume that the agent has a preference relation, which we call desirability, over events, which by definition involves uncertainty about consequences. For a given probability and utility of consequences, the desirability relation is presented by conditional expected utility, given an event. We axiomatically characterize desirability relations that are represented by a probability–utility pair . We characterize the family of all the probability–utility pairs that represent a given desirability relation.

Suggested Citation

  • Dov Samet & David Schmeidler, 2023. "Desirability relations in Savage’s model of decision making," Theory and Decision, Springer, vol. 94(1), pages 1-33, January.
    • Handle: RePEc:kap:theord:v:94:y:2023:i:1:d:10.1007_s11238-022-09883-y
    DOI: 10.1007/s11238-022-09883-y
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    References listed on IDEAS

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    1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    2. Kenneth I. Carlaw & Richard G. Lipsey & Ryan Webb, 2007. "Has the ICT Revolution Run its Course?," Discussion Papers dp07-18, Department of Economics, Simon Fraser University.
    3. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    4. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    5. David S. Ahn, 2008. "Ambiguity Without a State Space," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(1), pages 3-28.
    6. Luce, R Duncan & Krantz, David H, 1971. "Conditional Expected Utility," Econometrica, Econometric Society, vol. 39(2), pages 253-271, March.
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