Coherent choice functions under uncertainty |
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Authors: | Teddy Seidenfeld Mark J Schervish Joseph B Kadane |
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Institution: | 1.Department of Philosophy,Carnegie Mellon University,Pittsburgh,USA |
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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. |
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