The emergence of robustness as an important consideration in Bayesian statistical models has led to a renewed interest in normative models of incomplete preferences represented by imprecise (set-valued) probabilities and utilities. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of state-dependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the state-independence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs.
Keywords. imprecise probabilities and utilities, state-dependent utility
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Authors addresses:
Fuqua School of Business
Duke University
Durham, NC 27708-0120
USA
E-mail addresses:
| Robert Nau | robert.nau@duke.edu |
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