A Note on Savage's Theorem with a Finite Number of States

Thorsten Hens

Journal of Risk and Uncertainty, 1992, vol. 5, issue 1, 63-71

Abstract: This article gives a preference-based characterization of subjective expected utility for the general equilibrium model with a finite number of states. The characterization follows L. Savage (1954) as closely as possible but has to abandon his axiom (P6), atomlessness of events, since this requires an infinite state space. To introduce continuity the author replaces (P6) with a continuity assumption on the set of consequences and assumes the preferences are smooth. Then he applies Savage's sure-thing principle and his state-independence axiom to get an additively separable utility representation. Finally, to separate subjective probabilities from basic tastes, the author applies a new axiom, which states that for each pair of states the marginal rate of substitution is constant along the certainty line. Copyright 1992 by Kluwer Academic Publishers

Date: 1992
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