Partial Information, Dominance, and Potential Optimality in Multiattribute Utility Theory

Abstract

When a multiattribute utility function is only partially specified by prior preference statements, what can be said about the relative desirability of actual alternatives? This question is addressed for the cases of additively separable cardinal utility with unknown scaling constants; multiplicatively separable cardinal utility with unknown scaling constants; and additively separable ordinal utility. We review previous approaches, and treat issues of consistency (is the prior information consistent?), dominance (does the prior preference information imply that one outcome is preferred to another?) and potential optimality (are there utility functions of the given form, consistent with prior preference information, under which a particular outcome is preference optimal?). In the additive cases, a key relationship between dominance and potential optimality may be derived. The paper concludes by presenting an example application to a well known nuclear siting study.