Consistent voting systems with a continuum of voters
Voting problems with a continuum of voters and finitely many alternatives are considered. The classical Arrow and Gibbard-Satterthwaite theorems are shown to persist in this model, not for single voters but for coalitions of positive size. The emphasis of the study is on strategic considerations, relaxing the nonmanipulability requirement: are there social choice functions such that for every profile of preferences there exists a strong Nash equilibrium resulting in the alternative assigned by the social choice function? Such social choice functions are called exactly and strongly consistent. The study offers an extension of the work of Peleg (1978a) and others. Specifically, a class of anonymous social choice functions with the required property is characterized through blocking coefficients of alternatives, and associated effectivity functions are studied. Finally, representation of effectivity functions by game forms having a strong Nash Equilibrium is studied.
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Volume (Year): 27 (2006)
Issue (Month): 3 (December)
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References listed on IDEAS
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- Hart, Sergiu & Kohlberg, Elon, 1974.
"Equally distributed correspondences,"
Journal of Mathematical Economics,
Elsevier, vol. 1(2), pages 167-174, August.
- Hart, Sergiu & Kohlberg, Elon, 2017. "Equally distributed correspondences," Center for Mathematical Economics Working Papers 11, Center for Mathematical Economics, Bielefeld University.
- Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
- Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, number 9780521074650, November.
- Peleg, Bezalel, 2002. "Game-theoretic analysis of voting in committees," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 8, pages 395-423 Elsevier.
- repec:dau:papers:123456789/13220 is not listed on IDEAS
- Peleg, Bezalel, 1978. "Consistent Voting Systems," Econometrica, Econometric Society, vol. 46(1), pages 153-161, January.
- Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July. Full references (including those not matched with items on IDEAS)
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