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October 2006 The shape of incomplete preferences
Robert Nau
Ann. Statist. 34(5): 2430-2448 (October 2006). DOI: 10.1214/009053606000000740


Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. 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.


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Robert Nau. "The shape of incomplete preferences." Ann. Statist. 34 (5) 2430 - 2448, October 2006.


Published: October 2006
First available in Project Euclid: 23 January 2007

zbMATH: 1106.62001
MathSciNet: MR2291506
Digital Object Identifier: 10.1214/009053606000000740

Primary: 62C05
Secondary: 62A01

Keywords: axioms of decision theory , Bayesian robustness , Coherence , imprecise probabilities and utilities , partial order , state-dependent utility

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 5 • October 2006
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