Domains, ranges and strategy-proofness: the case of single-dipped preferences
We characterize the set of all individual and group strategy-proof rules on the domain of all single-dipped preferences on a line. For rules defined on this domain, and on several of its subdomains, we explore the implications of these strategy-proofness requirements on the maximum size of the rules' range. We show that when all single-dipped preferences are admissible, the range must contain two alternatives at most. But this bound changes as we consider different subclasses of single-dipped preferences: we provide examples of subdomains admitting strategy-proof rules with larger ranges. We establish exact bounds on the maximal size of strategy-proof functions on each of these domains, and prove that the relationship between the sizes of the subdomains and those of the ranges of strategy-proof functions on them need not be monotonic. Our results exhibit a sharp contrast between the structure of strategy-proof rules defined on subdomains of single-dipped preferences and those defined on subsets of single-peaked ones.
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Volume (Year): 39 (2012)
Issue (Month): 2 (July)
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- H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
- 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).
- Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012.
"Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 41(4), pages 791-808, November.
- Salvador Barberà & Dolors Berga & Bernardo Moreno, 2010. "Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results," UFAE and IAE Working Papers 853.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Salvador Barberà & Dolors Berga & Bernardo Moreno, 2010. "Group Strategy-Proof Social Choice Functions with Binary Ranges and Arbitrary Domains: Characterization Results," Working Papers 448, Barcelona Graduate School of Economics.
- Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August.
- Salvador Barberà & Dolors Berga & Bernardo Moreno, 2009.
"Individual versus group strategy-proofness: when do they coincide?,"
UFAE and IAE Working Papers
761.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
- Salvador Barberà & Dolors Berga & Bernardo Moreno, 2009. "Individual versus group strategy proofedness: when do they coincide?," Working Papers 372, Barcelona Graduate School of Economics.
- Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990.
"Voting by Committees,"
Cowles Foundation Discussion Papers
941, Cowles Foundation for Research in Economics, Yale University.
- Manjunath, Vikram, 2012. "Group strategy-proofness and voting between two alternatives," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 239-242.
- Saari, Donald G. & Valognes, Fabrice, 1999. "The geometry of Black's single peakedness and related conditions," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 429-456, December.
- Larsson, Bo & Svensson, Lars-Gunnar, 2006. "Strategy-proof voting on the full preference domain," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 272-287, December.
- Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, September.
- Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
- 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.
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