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Strategy-Proof Allocation of Multiple Public Goods

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  • Svensson, Lars-Gunnar

    ()
    (Department of Economics, Lund University)

  • Torstensson, Pär

    (Department of Economics, Lund University)

Abstract

We characterize the set of strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. The set of feasible alternatives is a subset of a product set with a finite number of elements. We do not require the SCFs to be ‘onto’, but instead impose the weaker requirement that every element in each category of public goods is attained at some preference profile. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. We find that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial in each component of the range. If the range cannot be decomposed at all, the SCF is dictatorial in spite of the separability assumption on preferences, and a form of the Gibbard-Satterthwaite theorem with a restricted preference domain is obtained.

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Bibliographic Info

Paper provided by Lund University, Department of Economics in its series Working Papers with number 2005:3.

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Length: 16 pages
Date of creation: 19 Jan 2005
Date of revision: 02 Feb 2007
Publication status: Published as Svensson, Lars-Gunnar and Pär Torstensson, 'Strategy-Proof Allocation of Multiple Public Goods' in Social Choice and Welfare, 2008, pages 181-196.
Handle: RePEc:hhs:lunewp:2005_003

Note: The paper is forthcoming in "Social Choice and Welfare".
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Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund,Sweden
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Fax: +46 +46 2224613
Web page: http://www.nek.lu.se/en
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Keywords: Strategy-proof; multiple public goods; decomposability; weakly onto; component-wise dictatorial.;

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References

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  1. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October.
  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. ASWAL, Navin & CHATTERJI, Shurojit & SEN, Arunava, 1999. "Dictatorial domains," CORE Discussion Papers 1999040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  5. 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.
  6. Le Breton, Michel & Weymark, John A., 1999. "Strategy-proof social choice with continuous separable preferences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 47-85, August.
  7. 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).
  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. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
  10. Barbera, S. & Sonnenschein, H., 1988. "Voting By Quota And Committee," UFAE and IAE Working Papers 95-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  11. Le Breton, M. & Sen, A., 1995. "Strategyproofness and decomposability : Weak Orderings," G.R.E.Q.A.M. 95a38, Universite Aix-Marseille III.
  12. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
  13. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-57, Jan.-Feb..
  14. G. Chichilnisky & G. M. Heal, 1997. "The geometry of implementation: a necessary and sufficient condition for straightforward games (*)," Social Choice and Welfare, Springer, vol. 14(2), pages 259-294.
  15. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers 941, Cowles Foundation for Research in Economics, Yale University.
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Citations

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Cited by:
  1. Alexander Reffgen, 2011. "Generalizing the Gibbard–Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness," Social Choice and Welfare, Springer, vol. 37(1), pages 39-59, June.
  2. Shurojit Chatterji & Arunava Sen, 2009. "Tops-Only Domains," Working Papers 06-2009, Singapore Management University, School of Economics.
  3. Gustavo Bergantiños & Leticia Lorenzo & Silvia Lorenzo-Freire, 2011. "New characterizations of the constrained equal awards rule in multi-issue allocation situations," Computational Statistics, Springer, vol. 74(3), pages 311-325, December.
  4. Reffgen, Alexander & Svensson, Lars-Gunnar, 2012. "Strategy-proof voting for multiple public goods," Theoretical Economics, Econometric Society, vol. 7(3), September.
  5. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona Graduate School of Economics.
  6. Mishra, Debasis & Roy, Souvik, 2012. "Strategy-proof partitioning," Games and Economic Behavior, Elsevier, vol. 76(1), pages 285-300.
  7. 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.

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