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December 1995 A representation of partially ordered preferences
Teddy Seidenfeld, Mark J. Schervish, Joseph B. Kadane
Ann. Statist. 23(6): 2168-2217 (December 1995). DOI: 10.1214/aos/1034713653


This essay considers decision-theoretic foundations for robust Bayesian statistics. We modify the approach of Ramsey, de Finetti, Savage and Anscombe and Aumann in giving axioms for a theory of robust preferences. We establish that preferences which satisfy axioms for robust preferences can be represented by a set of expected utilities. In the presence of two axioms relating to state-independent utility, robust preferences are represented by a set of probability/utility pairs, where the utilities are almost state-independent (in a sense which we make precise). Our goal is to focus on preference alone and to extract whatever probability and/or utility information is contained in the preference relation when that is merely a partial order. This is in contrast with the usual approach to Bayesian robustness that begins with a class of "priors" or "likelihoods," and a single loss function, in order to derive preferences from these probability/utility assumptions.


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Teddy Seidenfeld. Mark J. Schervish. Joseph B. Kadane. "A representation of partially ordered preferences." Ann. Statist. 23 (6) 2168 - 2217, December 1995.


Published: December 1995
First available in Project Euclid: 15 October 2002

zbMATH: 0871.62008
MathSciNet: MR1389871
Digital Object Identifier: 10.1214/aos/1034713653

Primary: 62C05
Secondary: 62A15

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 6 • December 1995
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