Abstract
Voting problems with a continuum of voters and finitely many alternatives are considered. Since the Gibbard–Satterthwaite theorem persists in this model, we relax the non-manipulability requirement as follows: are there social choice functions (SCFs) such that for every profile of preferences there exists a strong Nash equilibrium resulting in the alternative assigned by the SCF? Such SCFs are called exactly and strongly consistent. The paper extends the work of Peleg (Econometrica 46:153–161, 1978a) and others. Specifically, a class of anonymous SCFs with the required property is characterized through blocking coefficients of alternatives and through associated effectivity functions.
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References
Abdou J, Keiding H (1991) Effectivity functions in social choice. Kluwer, Dordrecht
Dutta B, Pattanaik PK (1978) On nicely consistent voting systems. Econometrica 46:163–170
Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–601
Halmos PR, Vaughan HE (1950) The marriage problem. Am J Math 72:214–215
Hart S, Kohlberg E (1974) Equally distributed correspondences. J Math Econ 1:167–174
Holzman R (1986a) On strong representations of games by social choice functions. J Math Econ 15:39–57
Holzman R (1986b) The capacity of a committee. Math Soc Sci 12:139–157
Ishikawa S, Nakamura K (1980) Representations of characteristic function games by social choice functions. Int J Game Theory 9:191–199
Kim KH, Roush FW (1981) Properties of consistent voting systems. Int J Game Theory 10:45–52
Kirman A, Sondermann D (1972) Arrow’s theorem, many agents, and invisible dictators. J Econ Theory 3:267–277
Moulin H, Peleg B (1982) Cores of effectivity functions and implementation theory. J Math Econ 10:115–145
Oren I (1981) The structure of exactly strongly consistent social choice functions. J Math Econ 8:207–220
Peleg B (1978a) Consistent voting systems. Econometrica 46:153–161
Peleg B (1978b) Representations of simple games by social choice functions. Int J Game Theory 7:81–94
Peleg B (1984) Game theoretic analysis of voting in committees. Cambrdige University Press, Cambridge, UK
Peleg B (1991) A solution to the problem of mass elections. In: Arrow KJ (eds). Issues in contemporary economics, Markets and Welfare, vol 1. Macmillan, London, pp. 287–294
Peleg B Peters H (2003) Consistent voting systems with a continuum of voters. Discussion Paper # 308, Center for the Study of Rationality, The Hebrew University of Jerusalem (www.ratio.huji.ac.il)
Polishchuck I (1978) Monotonicity and uniqueness of consistent voting systems. Center for Research in Mathematical Economics and Game Theory, Hebrew University of Jerusalem
Satterthwaite MA (1975) Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10:187–217
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An erratum to this article can be found at http://dx.doi.org/10.1007/s00355-006-0174-3
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Pezaleleleg, B., Peters, H. Consistent Voting Systems with a Continuum of Voters. Soc Choice Welfare 27, 477–492 (2006). https://doi.org/10.1007/s00355-006-0140-0
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DOI: https://doi.org/10.1007/s00355-006-0140-0