The shape of incomplete preferences


Journal Article

Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of state-dependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the state-independence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs. © Institute of Mathematical Statistics, 2006.

Full Text

Duke Authors

Cited Authors

  • Nau, R

Published Date

  • October 1, 2006

Published In

Volume / Issue

  • 34 / 5

Start / End Page

  • 2430 - 2448

International Standard Serial Number (ISSN)

  • 0090-5364

Digital Object Identifier (DOI)

  • 10.1214/009053606000000740

Citation Source

  • Scopus