Chapter 31 Social choice

This chapter discusses social choice and aggregation of individual preferences into a social-welfare ordering. The axiom of independence of irrelevant alternatives (IIA) and Arrow's impossibility result are presented in the chapter. Two ways of overcoming the impossibility is proposed. One is to restrict the preferences to be single-peaked in which case majority voting yields a satisfactory aggregation, and the other is to require that the social-welfare relation be only acyclic: Nakamura's theorem sets narrow limits to the decisiveness of society's preferences. The chapter describes the GibbardSatterthwaite impossibility result and its relation to Arrow's and presents the connection between the IIA axiom and strategyproofness on any restricted domain. The chapter focuses on voting in strong and Nash equilibrium along with the voting by veto example where the strong equilibrium outcomes are consistent with the sophisticated ones. Implementation of arbitrary choice correspondences by strong and Nash equilibrium is discussed in the chapter. Implementability in Nash equilibrium is almost always characterized by the strong monotonicity property. Implementability in strong equilibrium, on the other hand, relies on the concept of effectivity functions.