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Threshold strategy-proofness: on manipulability in large voting problems

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  • Ehlers, Lars
  • Peters, Hans
  • Storcken, Ton

Abstract

In voting problems where agents have well behaved (Lipschitz continuous) utility functions on a multidimensional space of alternatives, a voting rule is threshold strategy-proof if any agent can only obtain a limited utility gain by not voting for a most preferred alternative,given that the number of agents is large enough. For anonymous voting rules it is shown that this condition is not only implied by but in fact equivalent to the influence of any single agent reducing to zero as the number of agents grows. If there are at least five agents, the mean rule (taking the average vote) is shown to be the unique anonymous and unanimous voting rule that meets a lower bound with respect to the number of agents needed to obtain threshold strategy-proofness.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 49 (2004)
Issue (Month): 1 (October)
Pages: 103-116

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Handle: RePEc:eee:gamebe:v:49:y:2004:i:1:p:103-116

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
  2. 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.
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  5. Jose M. Cordoba & Peter J. Hammond, 1998. "Asymptotically Strategy-Proof Walrasian Exchange," Working Papers 98005, Stanford University, Department of Economics.
  6. James Schummer, 1999. "Almost-dominant Strategy Implementation," Discussion Papers 1278, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Gul, Faruk & Postlewaite, Andrew, 1992. "Asymptotic Efficiency in Large Exchange Economies with Asymmetric Information," Econometrica, Econometric Society, vol. 60(6), pages 1273-92, November.
  8. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  9. 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.
  10. Roberts, Donald John & Postlewaite, Andrew, 1976. "The Incentives for Price-Taking Behavior in Large Exchange Economies," Econometrica, Econometric Society, vol. 44(1), pages 115-27, January.
  11. R. J. Gary-Bobo & T. Jaaidane, 1996. "Polling mechanisms and the demand revelation problem," THEMA Working Papers 96-31, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  12. Pazner, Elisha A & Wesley, Eugene, 1978. "Cheatproofness Properties of the Plurality Rule in Large Societies," Review of Economic Studies, Wiley Blackwell, vol. 45(1), pages 85-91, February.
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Cited by:
  1. Marchese, Carla & Montefiori, Marcello, 2005. "Mean voting rule and strategical behavior: an experiment," POLIS Working Papers 49, Institute of Public Policy and Public Choice - POLIS.
  2. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona Graduate School of Economics.
  3. Donald Campbell & Jerry Kelly, 2009. "Gains from manipulating social choice rules," Economic Theory, Springer, vol. 40(3), pages 349-371, September.
  4. Marchese, Carla & Montefiori, Marcello, 2011. "Strategy versus sincerity in mean voting," Journal of Economic Psychology, Elsevier, vol. 32(1), pages 93-102, February.
  5. Carla Marchese & Marcello Montefiori, 2008. "Voting the public expenditure: an experiment," Labsi Experimental Economics Laboratory University of Siena 020, University of Siena.
  6. Régis Renault & Alain Trannoy, 2011. "Assessing the extent of strategic manipulation: the average vote example," SERIEs, Spanish Economic Association, vol. 2(4), pages 497-513, December.

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