Cardinal coordinate independence for expected utility

A representation theorem for binary relations on $\text{R}$ⁿ 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 neo-classical economic interpretation of cardinal utility to the von Neumann-Morgenstern interpretation.