Strategy-proof social choice

Research, Preprint English OPEN
Barberà, Salvador, 1946- (2010)
  • Related identifiers: handle: 10261/35321
  • Subject: Social Choice | Domain Restrictions | Elecció social -- Models matemàtics | strategy-proofness, Social Choice, Dominant Strategies, Domain Restrictions, voting | Voting | Strategy-proofness | Dominant Strategies
    • jel: jel:H41 | jel:D51 | jel:D7 | jel:C7

This paper surveys the literature on strategy-proofness from a historical perspective. While I discuss the connections with other works on incentives in mechanism design, the main emphasis is on social choice models. This article has been prepared for the Handbook of Social Choice and Welfare, Volume 2, Edited by K. Arrow, A. Sen and K. Suzumura
  • References (169)
    169 references, page 1 of 17

    3 Strategy-proof social choice functions for unrestricted domains: the Gibbard-Satterthwaite theorem 8 3.1 Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 The impact of the Gibbard-Satterthwaite theorem . . . . . . . 11 3.3 Proofs of the theorem . . . . . . . . . . . . . . . . . . . . . . . 14 3.3.1 Proofs based on the connection with Arrowian social welfare functions. . . . . . . . . . . . . . . . . . . . . . 14 3.3.2 Proofs by inspection and further induction . . . . . . . 15 3.3.3 Proofs based on the necessity of strong monotonicity . 16 3.3.4 Proofs that emphasize the role of pivots . . . . . . . . 16 3.3.5 Proofs that build on the structure of strategy-proof rules and option sets . . . . . . . . . . . . . . . . . . . 17 3.3.6 The Gibbard-Satterthwaite theorem as a corollary . . . 19

    9 Strategy-proofness in personalized domains 76 9.1 Strategy-proof rationing . . . . . . . . . . . . . . . . . . . . . 76 9.2 Strategy-proof exchange . . . . . . . . . . . . . . . . . . . . . 81 9.2.1 Two agent, two goods exchange economies . . . . . . . 85 9.2.2 Two agents, l goods . . . . . . . . . . . . . . . . . . . 89 9.2.3 Three or more agents . . . . . . . . . . . . . . . . . . . 91 9.3 Strategy-proof matching and assignment . . . . . . . . . . . . 92 9.4 Strategy-proof cost sharing . . . . . . . . . . . . . . . . . . . . 97

    10 Further comments on preference domains 101 10.1 Some special domains . . . . . . . . . . . . . . . . . . . . . . . 101 10.2 Maximal domains . . . . . . . . . . . . . . . . . . . . . . . . . 103

    [58] Bogomolnaia, A. and H. Moulin (2001): “A New Solution to the Random Assignment Problem”, Journal of Economic Theory 100, 295-328.

    [59] Borda, J. C. (1784): “Mémoire sur les Élections au Scrutin”. Histoire de l’Académie Royale des Sciences; Paris 1781; translated by Alfred de Grazia as “Mathematical Derivation of an Election System”; Isis; Vol. 44, Parts 1 & 2; June, 1953; 42-51. Also in I. McLean and A. B. Urken (Eds.), Classics of Social Choice, Ann Arbor, University of Michigan Press, 1995.

    [60] Border, K. and J. S. Jordan (1981): “Straightforward Elections, Unanimity and Phantom Voters”, Social Science WP#376, California Institute of Technology.

    [61] Border, K. and J. S. Jordan (1983): “Straightforward Elections, Unanimity and Phantom Voters”, Review of Economic Studies 50, 153-170.

    [62] Bordes, G.; G. La¤ond and M. LeBreton (1990): “Strategy Proofness Issues in Economic and Political Domains”, mimeo.

    [63] Brams, S. J. and P. C. Fishburn (1978): “Approval Voting”, American Political Science Review 72(3), 831-847.

    [64] Brams, S. J. and P. C. Fishburn (1993): “Yes-No Voting”, Social Choice and Welfare 10, 35-50.

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