Cardinal Utility and Decision Making under Uncertainty

Abstract

In the expected utility theory developed by von Neuman and Morgenstern (1947) (See also Marschak, 1950), cardinal utility indices for an individual corresponding to a finite set of prizes {x₁,...,x_i,...,x_n}, are derived from the ordering by the individual of the probability distributions over the set of prizes. It is shown that if the ordering of these probability distributions satisfies certain, so called, rationality conditions or rules,¹ then cardinal utility indices u^v _i, constant up to positive affine transformations, can be assigned to the prizes x_i such that the individual orders the probability distributions as if he or she were maximizing the expected value of the utilities u^v _i. According to some interpretations of the expected utility theory, the cardinal utility function u^v _i(x_i) = u^v _i represents a joint effect of the attitude toward risk’of the individual and his or her “utility” or satisfaction of the prizes. There is no need, therefore, according to these interpretations of the theory, to assume the actual reality of utility as a cardinal magnitude under riskless conditions thus by-passing the controversy of cardinality versus ordinality where the existence in riskless conditions of utility as cardinal magnitude and the need to use it in economic theory are the main issues.