A Note on the Relationships between Utility and Value Functions

Abstract

In order to dissipate the confusion created by the notion of “measurability”, many authors have argued that, in general, a von Neumann-Morgenstern utility function does not measure preference differences between outcomes since it is only based on simple lottery comparisons. Nevertheless the relationships between a von Neumann-Morgenstern utility function and a function measuring preference differences have rarely been studied from a theoretical point of view. The aim of this paper is to provide a simple necessary and sufficient condition, relating even chance lotteries and preference differences, for the two functions to coincide. The discussion of the acceptability and reasonableness of this easily interpretable condition could shed a new light on this question through avoiding the problem, encountered in most empirical studies, of the dependence of the shape of the functions on the assessment method used.