Coherent choice functions under uncertainty

Synthese 172 (1):157 - 176 (2010)
Abstract
We discuss several features of coherent choice functions —where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility.
Keywords Choice functions  Coherence  Γ-Maximin   Maximality  Uncertainty  State-independent utility
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References found in this work BETA
Isaac Levi (1974). On Indeterminate Probabilities. Journal of Philosophy 71 (13):391-418.
Citations of this work BETA
Gregory Wheeler (2012). Introduction. Synthese 186 (2):443-446.
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