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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 17836.

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Date of creation: 12 Oct 2009
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Handle: RePEc:pra:mprapa:17836

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Keywords: Gibbard-Satterthwaite theorem; infeasible alternatives;

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  1. Benoit, Jean-Pierre, 2000. "The Gibbard-Satterthwaite theorem: a simple proof," Economics Letters, Elsevier, Elsevier, vol. 69(3), pages 319-322, December.
  2. 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, Elsevier, vol. 10(2), pages 187-217, April.
  3. Svensson, Lars-Gunnar, 1999. "The Proof of the Gibbard-Satterthwaite Theorem Revisited," Working Papers, Lund University, Department of Economics 1999:1, Lund University, Department of Economics.
  4. Peter Gärdenfors, 1977. "A concise proof of theorem on manipulation of social choice functions," Public Choice, Springer, Springer, vol. 32(1), pages 137-142, December.
  5. John Duggan & Thomas Schwartz, 2000. "Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized," Social Choice and Welfare, Springer, Springer, vol. 17(1), pages 85-93.
  6. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 413-17, June.
  7. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, Elsevier, vol. 70(1), pages 99-105, January.
  8. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 58, pages 328.
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