A NOTE ON THE THEORY OF SOCIAL CHOICE

Abstract

Professor Arrow brings to his treatment of the theory of social welfare (I) a fine unity of mathematical rigour and insight into fundamental issues of social philosophy. The problem is the old one of the relationship of individual values to the general well-being of the group. Arrow eschews any concept of a utility measure which could be validly employed in inter-personal comparison of aggregation. The justification for doing so lies, of course, in the fact that if such a measure is not operationally undefinable, a t least it has never been operationally defined. In common with other theorists of the new welfare economics, Arrow must be content t o fall back on the purely ordinal properties of personal preferences. These ordinal properties are defined by two simple axioms: I. Given any two alternatives, each individual can state that a particular one of them is at least as good as the other. (If one of the alternatives is judged to be better than the other, it is, perforce, at least as good as the other. If the two alternatives are judged to be indifferent, each is a t least as good as the other.) II. Given any three alternatives, if the first is a t least as good as the second, and the second a t least as good as the third, the individual will judge the first a t least as good as the third. The force of these two axioms together is simply that, given any number of alternatives, each individual is able to arrange them in an array such that each alternative is a t least as good as any that follows it and no better than any that preceeds it. (When the individual is indifferent among several alternatives, their position in the array vis-d-vis one another has, of course, no significance since any arrangement of them will satisfy the conditions above.) Arrow defines a social welfare function as a function defined on the system of all sets of individual arrays carrying each set of indi-