Chapter 31 Social choice

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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 Gibbard–Satterthwaite 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.

References (84)

  • MullerE. et al.

    The equivalence of strong positive association and strategyproofness

    Journal of Economic Theory

    (1977)
  • WilsonR.

    Social choice without the Pareto principle

    Journal of Economic Theory

    (1972)
  • AbdouJ. et al.

    Effectivity functions in social choice

    (1991)
  • AbreuD. et al.

    Virtual implementation in iteratively undominated strategies: complete information

    (1989)
  • AbreuD. et al.

    Virtual implementation in Nash equilibrium

    Econometrica

    (1991)
  • ArrowK.

    Social choice and individual values

    (1963)
  • BarberaS.

    Majority and positional voting in a probabilistic framework

    Review of Economic s Studies

    (1979)
  • BarberaS.

    Strategy-proofness and pivotal voters:a direct proof of the Gibbard-Satterthwaite theorem

    International Economic Review

    (1983)
  • BarberaS. et al.

    A characterization of strategy-proof social choice functions for economies pure public goods

    Social Choice and Welfare

    (1992)
  • BarberaS. et al.

    Voting under constraints

    (1993)
  • BarberaS. et al.

    Strategy-proof voting schemes with continuous preferences

    Social Choice and Welfare

    (1990)
  • BarberaS. et al.

    Voting by committees

    Econometrica

    (1991)
  • BlackD.

    The theory of committees and elections

    (1958)
  • BlairD. et al.

    Acyclic collective choice rules

    Econometrica

    (1982)
  • BlauJ. et al.

    Social decision functions and the veto

    Econometrica

    (1977)
  • BordaJ.C.

    Mémoire sur les élections au scrutin

    Histoire de l'Académie Royale des Sciences, Paris

    (1781)
  • BorderK. et al.

    Straightforward elections, unanimiy and phantom agents

    Review of Economic Studies

    (1983)
  • ChichilniskyG. et al.

    Incentive Compatibility and Local Simplicity

    (1981)
  • ChichilniskyG.

    Social Choice and Game Theory: recent results with a topological approach

  • CondorcetMarquis de

    Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix, Paris

    (1985)
  • DanilovV.

    Implementation via Nash equilibrium

    Econometrica

    (1992)
  • DanilovV.

    On strongly implementable social choice correspondences

  • DuttaB. et al.

    Implementation under strong equilibrium: a complete characterization

    Journal of Mathematical Economics

    (1991)
  • DuttaB. et al.

    A necessary and sufficient condition for two-person Nash implementation

    Review of Economic Studies

    (1991)
  • FarqharsonR.

    Theory of voting

    (1969)
  • GibbardA.

    Manipulation of voting schemes: a general result

    Econometrica

    (1973)
  • GibbardA.

    Straightforwardness of game forms with lotteries as outcomes

    Econometrica

    (1978)
  • GolbergA. et al.

    Secret and extensive dominance solvable veto voting schemes

    (1986)
  • GretleinR.

    Dominance elimination procedures on finite alternative games

    International Journal of Game Theory

    (1983)
  • HurwiczL.

    The design of mechanisms for resource allocation

    American Economic Review

    (1973)
  • HyllandA.

    Strategyproofness of voting procedures with lotteries as outcomes and infinite sets of strategies

    (1980)
  • IchiishiT.

    The effectivity function approach to the core

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      Both rely on “vertical” information, in the sense of making the decision to rank alternative x above or below alternative y in the social preference depend on the way the individuals rank x above or below y. Specifically, the weak Pareto principle asserts that if all individuals agree to rank x above y then the social preference must rank x above y, whereas the IIA condition states that if the relative ranking between x and y is the same in every individual preference in two preference matrices then the relative ranking between x and y must be the same in the social preferences associated with those matrices. This “vertical” approach has been retained in subsequent attempts to escape from, or generalize, Arrow’s theorem; see, for instance, Sen (1986) and Moulin (1994). This note departs from this approach by considering preference aggregation (still in the strict preference case) from a “horizontal” perspective (Powers (2004) also incorporates positional information but as a constraint on IIA).

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    The comments of an anonymous referee are gratefully acknowledged.

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