# A Representation of Partially Ordered Preferences

#### Abstract or Description

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.

*This paper has been withdrawn.*