David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Synthese 172 (1):157 - 176 (2010)
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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Citations of this work BETA
Conor Mayo‐Wilson & Gregory Wheeler (2016). Scoring Imprecise Credences: A Mildly Immodest Proposal. Philosophy and Phenomenological Research 92 (1):55-78.
Arthur Paul Pedersen & Gregory Wheeler (2014). Demystifying Dilation. Erkenntnis 79 (6):1305-1342.
Fabio G. Cozman (2012). Sets of Probability Distributions, Independence, and Convexity. Synthese 186 (2):577-600.
Isaac Levi (2010). Probability Logic, Logical Probability, and Inductive Support. Synthese 172 (1):97 - 118.
Jeffrey Helzner (2013). Rationalizing Two-Tiered Choice Functions Through Conditional Choice. Synthese 190 (6):929-951.
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