The Formal Analysis of Rights
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 State Social Choice Game Form Deontic Logic Admissible Strategy
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- 1.We use the term rational choice theory to refer to formal theories of individual and collective decision making. Rational choice theory encompasses social choice theory,which focuses especially on the procedural aspects of collective decision making, as well as game theory which is concerned with the strategic aspects of decision making. For introductions to and reviews of the theory of social choice, see (Kelly 1978; Sen 1986). (Luce and Raiffa 1957) is the classic introduction to game theory. (Fudenberg and Tirole, 1991) is a more recent introduction. (Pattanaik 1978; Moulin 1983; Peleg 1984) border on the frontiers between game theory and social choice theory.Google Scholar
- 2.In our exposition of Sen’s contribution to the study of the concepts of freedom and liberalism we concentrate on his formal analysis.Google Scholar
- 3.We shall follow the terminology of the original statement of the paradox and speak about ‘liberalism’. However, Sen later preferred the term ‘libertarianism’ (Sen 1976). In (Sen 1983) the theorem is formulated as a tension between liberty and the Pareto condition.Google Scholar
- 4.Sen 1976; Sen 1983; Wriglesworth 1985) contain reviews of the literature.Google Scholar
- 5.For an extensive review of this research see (Wriglesworth 1985).Google Scholar
- 14.As Gaertner et al. (1992, p. 166) argue, the reasoning does not depend on the rule of behaviour which individuals adopt in situations of uncertainty. For any rule it is possible to construct a choice situation in which the free choices made by the individuals lead to an outcome that condition S and G exclude.Google Scholar
- 16.Note, by the way, that an effectivity function cannot be described as a game form since the intersection of the individual strategies need not always yield a one-element set.Google Scholar
- 17.For a detailed and systematic account of the relationship between game forms and effectivity functions in the context of the analysis of rights, see (Deb 1990).Google Scholar
- 18.Stated formally, any cc-effectivity function associated with a game form is always monotonic with respect to the players. See (Peleg 1984, p. 89).Google Scholar
- 20.For an excellent survey, see (Aqvist 1984). (Hintikka 1971) contains a lucid discussion of some of the central topics of deontic logic. For critical accounts of the foundations of deontic logic, see (Weinberger, 1991) and (Von Wright, 1991 ).Google Scholar
- 23.With respect to the application of deontic logic to rational choice theory the work of Sven Ove Hansson deserves attention (Hansson 1988 ). He presents a formal model of collective decision making which incorporates concepts from deontic logic in a subtle way. Using definitions of ‘legal positions’ he offers a new interpretation of the liberal paradoxes.Google Scholar