David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
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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Leonard J. Savage (1954). The Foundations of Statistics. Wiley Publications in Statistics.
Isaac Levi (1986). Hard Choices: Decision Making Under Unresolved Conflict. Cambridge University Press.
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Citations of this work BETA
Fabio G. Cozman (2012). Sets of Probability Distributions, Independence, and Convexity. Synthese 186 (2):577-600.
Arthur Paul Pedersen & Gregory Wheeler (2014). Demystifying Dilation. Erkenntnis 79 (6):1305-1342.
Jeffrey Helzner (2013). Rationalizing Two-Tiered Choice Functions Through Conditional Choice. Synthese 190 (6):929-951.
Isaac Levi (2010). Probability Logic, Logical Probability, and Inductive Support. Synthese 172 (1):97 - 118.
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