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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

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.

Suggested Citation

  • Salvador Barbera & Matthew Jackson, 1991. "A Characterization of Strategy-Proof Social Choice Functions for Economies with Pure Public Goods," Discussion Papers 964, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:964
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    References listed on IDEAS

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    1. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    2. Zhou, L., 1989. "Impossibility Of Strategy-Proof Mechanisms For Economies With Pure Public Goods," Papers 343, Princeton, Department of Economics - Econometric Research Program.
    3. 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.
    4. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    5. Lin Zhou, 1991. "Impossibility of Strategy-Proof Mechanisms in Economies with Pure Public Goods," Review of Economic Studies, Oxford University Press, vol. 58(1), pages 107-119.
    6. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    7. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    8. 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).
    9. 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.
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    Cited by:

    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.
    2. Jackson, M.O.Matthew O. & Nicolo, Antonio, 2004. "The strategy-proof provision of public goods under congestion and crowding preferences," Journal of Economic Theory, Elsevier, vol. 115(2), pages 278-308, April.
    3. Perote, Javier & Perote-Pena, Juan, 2004. "Strategy-proof estimators for simple regression," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 153-176, March.
    4. BOSSERT, Walter & WEYMARK, J.A., 2006. "Social Choice: Recent Developments," Cahiers de recherche 01-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    5. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
    6. 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.
    7. Juan Perote Peña, 2003. "Solidarity in Terms of Reciprocity," Economic Working Papers at Centro de Estudios Andaluces E2003/16, Centro de Estudios Andaluces.
    8. Saijo, Tatsuyoshi & Sjostrom, Tomas & Yamato, Takehiko, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
    9. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    10. Walter Bossert & Hans Peters, 2009. "Single-peaked choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(2), pages 213-230, November.
    11. Moreno, Diego & Moscoso, María José, 2001. "A gibbad-satterthwaite theorem for public good economies," UC3M Working papers. Economics we014912, Universidad Carlos III de Madrid. Departamento de Economía.
    12. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
    13. Gordon, Sidartha, 2007. "Public decisions: Solidarity and the status quo," Games and Economic Behavior, Elsevier, vol. 61(2), pages 225-241, November.
    14. Juan Perote-Peña & Javier Perote, 2003. "The impossibility of strategy-proof clustering," Economics Bulletin, AccessEcon, vol. 4(23), pages 1-9.
    15. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.

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