Rights Revisited, and Limited

Abstract

One of the most justly famous result of social choice theory is Sen’s Theorem on the impossibility of a Paretian liberal. In two recent papers, Salles introduced the notion of limited rights both in an aggregation function framework and in a social choice function framework. He then proved Sen-type impossibility theorems. In the aggregation function framework an individual has a “right” if whenever she prefers an option (social state), say a, to another social state, say b, the social preference ranks a before b. Salles proposed to consider the following weakening. Rather than a being socially ranked before b, he suggests that b should not be ranked before a. The social choice framework is a framework which was introduced later than the aggregation function framework, but is thought to be more or less equivalent it. In this framework, if the individual prefers a to b, then b must not be chosen from any set to which a belongs. Salles’s weakening amounts to say that if it happens that b be chosen, then a must be chosen too. In the present paper, we will describe from an intuitive point of view the technical results obtained by Salles in the light of the distinction between possibility and obligation, and we will present a research program based on the use of tools borrowed from modal logic.