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A Characterization of Strategy-Proof Social Choice Functions for Economies with Pure Public Goods

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Salvador Barbera
Matthew Jackson

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Abstract

We characterize strategy-proof social choice functions when individual have strictly quasi-concave, continuous and satiated utility functions on convex subsets |R^l, representing preferences for the provision of l pure public goods. When specialized to the case l=1, these assumptions amount to requiring that preferences are single peaked, and for such a domain there exists a wide class of strategy-proof social choice functions. These were studied by Moulin (1980) under additional assumptions. Our first results characterize the complete class, after an appropriate extension of the single-peakedness condition. The new characterization retains the flavor of Moulin's elegant representation theorem. For the general l-dimensional case, previous results have shown that there is no efficient, strategy-proof, nondictatorial social choice function, even within the domain restrictions under consideration [Border and Jordan (1983), Zhou (1991)]. In fact, Zhou's powerful results indicates that nondictatorial strategy-proof s.c.f.'s will have a range of dimension one. This allows us to conclude with a complete characterization of all strategy-proof s.c.f.'s on |R^l, because restrictions of preferences from our admissible class to one dimensional subsets satisfy the slightly generalized notion of single-peakedness that is used in our characterization for the case l=1. We feel that a complete knowledge of the class of strategy-proof mechanisms, in this as well as in other contexts, is an important step in the analysis of the trade-offs between strategy-proofness and other performance criteria, like efficiency.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 964.

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Date of creation: May 1991
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Handle: RePEc:nwu:cmsems:964

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July. [Downloadable!] (restricted)
  2. 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).
  3. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May. [Downloadable!] (restricted)
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  4. Border, Kim C & Jordan, J S, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Blackwell Publishing, vol. 50(1), pages 153-70, January. [Downloadable!] (restricted)
  5. Zhou, L., 1989. "Impossibility Of Strategy-Proof Mechanisms For Economies With Pure Public Goods," Papers 343, Princeton, Department of Economics - Econometric Research Program.
  6. Zhou, Lin, 1991. "Impossibility of Strategy-Proof Mechanisms in Economies with Pure Public Goods," Review of Economic Studies, Blackwell Publishing, vol. 58(1), pages 107-19, January. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Javier Perote Peña & Juan Perote Peña, 2003. "A Social Choice Trade-off Between Alternative Fairness Concepts: Solidarity versus Flexibility," Economic Working Papers at Centro de Estudios Andaluces E2003/10, Centro de Estudios Andaluces. [Downloadable!]
  2. Juan Perote-Peña & Javier Perote, 2003. "The impossibility of strategy-proof clustering," Economics Bulletin, Economics Bulletin, vol. 4(23), pages 1-9. [Downloadable!]
    Other versions:
  3. BOSSERT, Walter & WEYMARK, J.A., 2006. "Social Choice: Recent Developments," Cahiers de recherche 2006-01, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  4. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
    Other versions:
  5. Salvador Barbera, 1995. "Strategy-Proof Allotment Rules," Discussion Papers 1142, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  6. Jackson, Matthew O. & Nicolo, Antonio, 2002. "The Strategy-Proof Provision of Public Goods Under Congestion and Crowding Preferences," Working Papers 1148, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  7. Alejandro Saporiti & Fernando Tohmé, 2003. "Single-Crossing, Strategic Voting and the Median Choice Rule," CEMA Working Papers: Serie Documentos de Trabajo. 237, Universidad del CEMA. [Downloadable!]
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  8. John A. Weymark, 2004. "Strategy-Proofness and the Tops-Only Property," Working Papers 0409, Department of Economics, Vanderbilt University, revised Sep 2006. [Downloadable!]
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  9. Diego Moreno & María José Moscoso, 2001. "A Gibbad-Satterthwaite Theorem for Public Good Economies," Economics Working Papers we014912, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  10. Tatsuyoshi Saijo & Tomas Sjostrom & Takehiko Yamato, 2005. "Secure Implementation," Economics Working Papers 0056, Institute for Advanced Study, School of Social Science. [Downloadable!]
  11. Perea Andrés, 2006. "Epistemic Foundations for Backward Induction: An Overview," Research Memoranda 036, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  12. Alejandro Saporiti & Fernando Tohmé, 2001. "Order-restricted preferences and strategy-proof social choices rules," CEMA Working Papers: Serie Documentos de Trabajo. 191, Universidad del CEMA. [Downloadable!]
  13. Javier Perote Peña & Juan Perote Peña, 2003. "Strategy-Proof Estimators for Simple Regression," Economic Working Papers at Centro de Estudios Andaluces E2003/14, Centro de Estudios Andaluces. [Downloadable!]
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  14. BOSSERT, Walter & PETERS, Hans, 2006. "Single-Peaked Choice," Cahiers de recherche 2006-14, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
    • Bossert Walter & Peters Hans, 2006. "Single-peaked choice," Research Memoranda 037, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  15. GORDON, Sidartha, 2006. "Public Decisions: Solidarity and the Status Quo," Cahiers de recherche 2006-05, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  16. Juan Perote Peña, 2003. "Solidarity in Terms of Reciprocity," Economic Working Papers at Centro de Estudios Andaluces E2003/16, Centro de Estudios Andaluces. [Downloadable!]
  17. Tatsuyoshi Saijo & Tomas Sjöström & Takehiko Yamato, 2004. "Secure Implementation," Levine's Bibliography 122247000000000615, UCLA Department of Economics. [Downloadable!]
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