An Axiomatization of Utility Based on the Notion of Utility Differences

In the literature of economics the notion of utility differences has been much discussed in connection with the theory of measurement of utility. However, to the best of our knowledge, no adequate axiomatization for this difference notion has yet been given at a level of generality and precision comparable to the von Neumann and Morgenstern construction of a probabilistic scheme for measuring utility. (The early study of Wiener is not axiomatically oriented.) The purpose of this paper is to present an axiomatization of this notion and to establish the expected representation theorem guaranteeing measurement unique up to a linear transformation.