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A Unified Approach to Strategy-Proofness for Single-Peaked Preferences

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  • John A. Weymark

    () (Department of Economics, Vanderbilt University)

Abstract

This article establishes versions of Moulin's [On strategy-proofness and single peakedness, Public Choice 35 (1980), 31--38] characterizations of various classes of strategy-proof social choice functions when the domain consists of all profiles of single-peaked preferences on an arbitrary subset of the real line. Two results are established that show that the median of 2n+1 numbers can be expressed using a combination of minimization and maximization operations applied to subsets of these numbers when either these subsets or the numbers themselves are restricted in a particular way. These results are used to show how Moulin's characterizations of generalized median social choice functions can be obtained as corollaries of his characterization of min-max social choice functions.

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File URL: http://www.accessecon.com/pubs/VUECON/vu11-w01.pdf
File Function: First version, January 2011
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Bibliographic Info

Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 1101.

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Date of creation: Jan 2011
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Handle: RePEc:van:wpaper:1101

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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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Keywords: Generalized median social choice functions; Moulin; min-max rules; single-peaked preferences; strategy-proofness;

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  1. Jordi Massó & Inés Moreno de Barreda, 2010. "On Strategy-proofness and Symmetric Single-peakedness," UFAE and IAE Working Papers 809.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Barbera, S & Masso, J & Serizawa, S, 1996. "Strategy-Proof Voting on Compact Ranges," UFAE and IAE Working Papers 358.96, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  3. John A. Weymark, 2004. "Strategy-Proofness and the Tops-Only Property," Vanderbilt University Department of Economics Working Papers 0409, Vanderbilt University Department of Economics, revised Sep 2006.
  4. Dolors Berga & Bernardo Moreno, 2007. "Strategic Requirements with Indifference: Single-Peaked versus Single-Plateaued Preferences," Working Papers 325, Barcelona Graduate School of Economics.
  5. Le Breton, Michel & Zaporozhets, Vera, 2006. "On the Equivalence of Coalitional and Individual Strategy-Proofness Properties," IDEI Working Papers 408, Institut d'Économie Industrielle (IDEI), Toulouse.
  6. Le Breton, M. & Weymark, J.A., 1993. "Strategy-Prrof Social Choice with Continuous Saparable Preferences," UBC Departmental Archives 93-29, UBC Department of Economics.
  7. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
  8. Yves Sprumont, 1995. "Strategyproof Collective Choice in Economic and Political Environments," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 68-107, February.
  9. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
  10. Zhou, Lin, 1991. "Impossibility of Strategy-Proof Mechanisms in Economies with Pure Public Goods," Review of Economic Studies, Wiley Blackwell, vol. 58(1), pages 107-19, January.
  11. Barbera, S. & Peleg, B., 1988. "Strategy-Proof Voting Schemes With Continuous Preferences," UFAE and IAE Working Papers 91.88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  12. Border, Kim C & Jordan, J S, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 153-70, January.
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