JOURNAL OF MATHEMATICAL PSYCHOLOGY 28, 1 lo-1 17 (1984) Cardinal Coordinate Independence for Expected Utility

A representation theorem for binary relations on IF? ” is derived. It is interpreted in the context of decision making under uncertainty. There we consider the existence of a subjective expected utility model to represent a preference relation of a person on the set of bets for money on a finite state space. The theorem shows that, for this model to exist, it is not only necessary (as has often been observed), but it also is sufficient, that the appreciation for money of the person has a cardinal character, independent of the state of nature. This condition of cardinal appreciation is simple and thus easily testable in experiments. Also it may be of help in relating the neoclassical economic interpretation of cardinal utility to the von Neumann-Morgenstern interpretation. 1. INTR~OUCTI~N In this paper a characterization of the subjective expected utility (SEU) model is given. To this end in Section 2 a representation theorem for binary relations on IR ” is given. It is based mainly on Debreu (1960), or Chapter 6 of Krantz, Lute, Suppes, and Tversky (1971). The new characterizing property, denoted by CCI, is simple, and yields a handy, empirically testable, criterion. The question what such a propert