Individual rationality and the concept of social welfare

Abstract

This paper, written in October 1974, deals with some game aspects of the social choice problem. The question asked is whether there exists a social decision rule satisfying the conditions imposed by Arrow over all the preference profiles that may logically arise under it (in the sense of being compatible with individual rationality). This question is answered in the affirmative. The meaning of this result is that if Arrow's condition of unrestricted domain is modified so as to exclude any profile which contradicts individual rationality, then an Arrovian social welfare function can be shown to exist (subject to the assumption that whenever the social outcome is in doubt, individuals use the maximin criterion in order to choose their voting strategy).