Random Utility Functions are Uniquely Determined by User Preferences

Abstract

In decision theory, a traditional way to describe the user’s preferences is to use a utility function. Preferences determine the utility function uniquely { modulo linear transformations (re-scaling). In practice, user’s preferences are often probabilistic: when presented with the choice between the same two alternatives A and A 0 , the user may sometimes select A and sometimes select A 0 . Since deterministic preferences are described by utilities, it is natural to describe probabilistic preferences by random utilities. In this paper, we show that, similar to the deterministic case, random utilities are also uniquely determined by the user preferences. c

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