Coherent Choice Functions under Uncertainty

<p>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<br>decision problems under uncertainty – where only the probability component of S is indeterminate. Coherent choice distinguishes between each pair of sets of<br>probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence<br>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.</p>