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Alternatives vs. Outcomes: A Note on the Gibbard-Satterthwaite Theorem

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  • Weber, Tjark

Abstract

The Gibbard-Satterthwaite theorem is a well-known theorem from the field of social choice theory. It states that every voting scheme with at least 3 possible outcomes is dictatorial or manipulable. Later work on the Gibbard-Satterthwaite theorem frequently does not distinguish between alternatives and outcomes, thereby leading to a less general statement that requires the voting scheme to be onto. We show how the Gibbard-Satterthwaite theorem can be derived from the seemingly less general formulation.

Suggested Citation

  • Weber, Tjark, 2009. "Alternatives vs. Outcomes: A Note on the Gibbard-Satterthwaite Theorem," MPRA Paper 17836, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:17836
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    References listed on IDEAS

    as
    1. John Duggan & Thomas Schwartz, 2000. "Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(1), pages 85-93.
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    3. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    4. Peter Gärdenfors, 1977. "A concise proof of theorem on manipulation of social choice functions," Public Choice, Springer, vol. 32(1), pages 137-142, December.
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    6. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    7. Barbera, Salvador, 1983. "Strategy-Proofness and Pivotal Voters: A Direct Proof of the Gibbard-Satterthwaite Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 413-417, June.
    8. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
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    More about this item

    Keywords

    Gibbard-Satterthwaite theorem; infeasible alternatives;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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    1. Gibbard–Satterthwaite theorem in Wikipedia English
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