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Maximal Domains for Strategy-proof or Maskin Monotonic Choice Rules

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  • Olivier Bochet
  • Ton Storcken

Abstract

Domains of individual preferences for which the well-known impossibility Theorems of Gibbard-Satterthwaite and Muller-Satterthwaite do not hold are studied. First, we introduce necessary and sufficient conditions for a domain to admit non-dictatorial, Pareto efficient and either strategy-proof or Maskin monotonic social choice rules. Next, to comprehend the limitations the two Theorems imply for social choice rules, we search for the largest domains that are possible. Put differently, we look for the minimal restrictions that have to be imposed on the unrestricted domain to recover possibility results. It turns out that, for such domains, the conditions of inseparable pair and of inseparable set yield the only maximal domains on which there exist non-dictatorial, Pareto efficient and strategy-proof social choice rules. Next, we characterize the maximal domains which allow for Maskin monotonic, non-dictatorial and Pareto-optimal social choice rules.

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Bibliographic Info

Paper provided by Universitaet Bern, Departement Volkswirtschaft in its series Diskussionsschriften with number dp0901.

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Date of creation: Aug 2008
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Handle: RePEc:ube:dpvwib:dp0901

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Keywords: Strategy-proofness; Maskin monotonicity; Restricted domains; Maximal domains;

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References

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  1. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
  2. Bettina Klaus & Olivier Bochet, 2013. "The relation between monotonicity and strategy-proofness," Social Choice and Welfare, Springer, vol. 40(1), pages 41-63, January.
  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. Alejandro Neme & Jordi MassÔ & Salvador BarberÁ, 1999. "Maximal domains of preferences preserving strategy-proofness for generalized median voter schemes," Social Choice and Welfare, Springer, vol. 16(2), pages 321-336.
  5. 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.
  6. 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.
  7. Ehud Kalai & Eitan Muller, 1977. "Characterization of Domains Admitting Nondictatorial Social Welfare Functions and Nonmanipulable Voting Procedures," Discussion Papers 234, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Gibbard, Allan, 1978. "Straightforwardness of Game Forms with Lotteries as Outcomes," Econometrica, Econometric Society, vol. 46(3), pages 595-614, May.
  9. Ehud Kalai & Zvi Ritz, 1978. "Characterization of the Private Alternative Domains Admitting Arrow Social Welfare Functions," Discussion Papers 341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Ching, Stephen & Serizawa, Shigehiro, 1998. "A Maximal Domain for the Existence of Strategy-Proof Rules," Journal of Economic Theory, Elsevier, vol. 78(1), pages 157-166, January.
  11. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  12. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
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Cited by:
  1. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona Graduate School of Economics.
  2. Toyotaka Sakai & Takuma Wakayama, 2012. "Strategy-proofness, tops-only, and the uniform rule," Theory and Decision, Springer, vol. 72(3), pages 287-301, March.

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