###
3rd International Symposium
on

Imprecise
Probabilities and Their Applications

ISIPTA '03

#####
University of Lugano

Lugano, Switzerland

14-17 July 2003

####
ELECTRONIC PROCEEDINGS

## Mark Schervish, Teddy Seidenfeld, Joseph Kadane, Isaac Levi

# Extensions of Expected Utility Theory and some Limitations of Pairwise Comparisons

### Abstract

We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: Gamma-Maximin, Maximality, and E-admissibility. 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 comparison between acts may fail to identify those acts which are Bayes for some probability in a convex set that is not closed. This limitation affects two of the decision rules but not E-admissibility, which is not a pairwise decision rule. E-admissibility can be used to distinguish between two convex sets of probabilities that intersect all the same supporting hyperplanes.

** Keywords. ** Bayes admissible, E-admissible, Gamma-Maximin, Maximality, convex set

**Paper Download **

The paper is availabe in the following formats:

** Authors addresses: **

Mark Schervish

Department of Statistics

Carnegie Mellon University

Pittsburgh, PA 15213

Teddy Seidenfeld

135J Baker Hall

Carnegie Mellon University

Pgh. PA 15213

Joseph Kadane

Department of Statistics

Carnegie Mellon University

Pittsburgh, PA 15213

Isaac Levi

718 Philosophy Hall

Columbia University

New York

USA

** E-mail addresses: **

[ back
to the Proceedings of ISIPTA '03 home page ]

Send any remarks to the following address:
smc@decsai.ugr.es