The Formal Analysis of Rights

Abstract

Amartya Sen has made many important contributions to the development of the theory of rational choice.1 One of those contributions was his introduction, in the early seventies, of individual rights into the formal analysis of processes of collective decision making.2 Sen formulated individual rights in terms of properties of specific decision procedures and showed that it is impossible to define decision procedures which satisfy both a very mild assumption about the rights of individuals and the Pareto condition — the condition which states that an alternative may not be chosen whenever there is another alternative unanimously preferred to it. The assumption about the rights of individuals was defended as a necessary requirement of any theory of liberalism. The impossibility theorem became therefore known as the ‘impossibility of the Paretian liberal’ or simply as ‘Sen’s liberal paradox’.3 Alan Gibbard extended Sen’s framework in an interesting way. In (Gibbard 1974) he defined conditions of liberalism which are logically stronger than Sen’s but which, Gibbard argued, are perfectly in line with Sen’s notion of individual rights. He showed that these conditions cannot be satisfied by any decision procedure, not even when the Pareto condition is dropped. This result became known as ‘Gibbard’s paradox’. In this chapter we describe the theoretical background of our study. Since the two liberal paradoxes are important parts of that background, we present Sen’s liberal paradox in section 1 and Gibbard’s paradox in section 2.KeywordsSocial StateSocial ChoiceGame FormDeontic LogicAdmissible StrategyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.