A Representation of Partially Ordered Preferences
Teddy Seidenfeld (*)
Depts of Philosophy and Statistics, CMU
Abstract
This essay considers decision-theoretic foundations for robust
Bayesian statistics. We modify the approach of Ramsey (1930)
deFinetti (1931), Savage (1954), & Anscombe-Aumann (1963) 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.
(*) joint work with Mark Schervish, and Joseph B.Kadane