 
Summary: Extensions of Expected Utility Theory and
Some Limitations of Pairwise Comparisons
M. J. SCHERVISH
Carnegie Mellon University, USA
T. SEIDENFELD
Carnegie Mellon University, USA
J. B. KADANE
Carnegie Mellon University, USA
I. LEVI
Columbia University, USA
Abstract
We contrast three decision rules that extend Expected Utility to contexts
where a convex set of probabilities is used to depict uncertainty: Maximin,
Maximality, and Eadmissibility. The rules extend Expected Utility theory
as they require that an option is inadmissible if there is another that carries
greater expected utility for each probability in a (closed) convex set. If the
convex set is a singleton, then each rule agrees with maximizing expected
utility. We show that, even when the option set is convex, this pairwise com
parison between acts may fail to identify those acts which are Bayes for some
