We discuss several features of coherent choice functions – where the admissible options in a decision problem are exactly those which 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. Coherent choice distinguishes between each pair of 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, Gamma-Maximin, Maximality, uncertainty, state-independent utility.
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Authors addresses:
Teddy Seidenfeld
135J Baker Hall
Carnegie Mellon University
Pgh. PA 15213
Mark Schervish
Department of Statistics
Carnegie Mellon University
Pittsburgh, PA 15213-3890
USA
Joseph Kadane
Department of Statistics
Carnegie Mellon University
Pittsburgh, PA 15213
E-mail addresses:
| Teddy Seidenfeld | teddy@stat.cmu.edu |
| Mark Schervish | mark@stat.cmu.edu |
| Joseph Kadane | kadane@stat.cmu.edu |