The Annals of Statistics

A representation of partially ordered preferences

Teddy Seidenfeld, Mark J. Schervish, and Joseph B. Kadane

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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.

Article information

Ann. Statist., Volume 23, Number 6 (1995), 2168-2217.

First available in Project Euclid: 15 October 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62C05: General considerations
Secondary: 62A15

Robust statistics axioms of decision theory state-dependent utility partial order


Seidenfeld, Teddy; Schervish, Mark J.; Kadane, Joseph B. A representation of partially ordered preferences. Ann. Statist. 23 (1995), no. 6, 2168--2217. doi:10.1214/aos/1034713653.

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