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ISIPTA'07 -
FIFTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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Charles University, Faculty of Mathematicsand Physics

Prague, Czech Republic

16-19 July 2007

## ELECTRONIC PROCEEDINGS

## Teddy Seidenfeld, Mark Schervish, Joseph Kadane

# Coherent Choice Functions under Uncertainty

### Abstract

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.

** Paper Download **

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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: **

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