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Probabilistic Strategy-Proof Rules over Single-Peaked Domains

  • Storcken A.J.A.
  • Peters H.J.M.
  • Roy S.
  • Sen A.

    (GSBE)

It is proved that every strategy-proof, peaks-only or unanimous, probabilistic rule defined over a minimally rich domain of single-peaked preferences is a probability mixture of strategy-proof, peaks-only or unanimous, deterministic rules over the same domain. The proof employs Farkas Lemma and the max-flow min-cut theorem for capacitated networks.

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File URL: http://pub.maastrichtuniversity.nl/31777bb9-e48b-482a-a6ab-6e8b99c31fd5
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Paper provided by Maastricht University, Graduate School of Business and Economics (GSBE) in its series Research Memorandum with number 040.

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Date of creation: 2013
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Handle: RePEc:unm:umagsb:2013040
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  1. Barbera, S. & Gul, F. & Stacchetti, E., 1992. "Generalized Median Voter Schemes and Committees," UFAE and IAE Working Papers 184.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2002. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 105(2), pages 408-434, August.
  3. Duggan, John, 1996. "A Geometric Proof of Gibbard's Random Dictatorship Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 365-69, February.
  4. John Weymark, 2011. "A unified approach to strategy-proofness for single-peaked preferences," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 529-550, December.
  5. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 153-170.
  6. Chatterji, Shurojit & Roy, Souvik & Sen, Arunava, 2012. "The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 353-366.
  7. Picot, Jérémy & Sen, Arunava, 2012. "An extreme point characterization of random strategy-proof social choice functions: The two alternative case," Economics Letters, Elsevier, vol. 115(1), pages 49-52.
  8. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-81, April.
  9. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
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