Abstract
Social choice functions are studied with an infinite population framework that includes algebras over the set of individuals. It is shown that continuous social choice functions are either dictatorial or manipulable. Weak anonymity is shown to be incompatible with continuity and neutrality.
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References
Armstrong TE (1980) Arrow’s Theorem with restricted coalition algebras. J Math Econ 7:55–75
Armstrong TE (1985) Precisely dictatorial social welfare functions. Erratum and addendum to Arrow’s Theorem with restricted coalition algebras. J Math Econ 14:57–59
Arrow KJ (1963) Social choice and individual values, 2nd edn. Yale University Press, New Haven
Fey M (2004) May’s Theorem with an infinite population. Soc Choice Welfare 23:275–293
Fishburn PC (1970) Arrow’s impossibility Theorem: concise proof and infinite voters. J Econ Theory 2:103–106
Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–601
Gomberg A, Martinelli C, Torres R (2005) Anonymity in large societies. Soc Choice Welfare 25:187–205
Hansson B (1976) The existence of group preferences. Public Choice 28:89–98 (Working Paper 1972, Mattias Fremling Society No. 3.)
Kirman AP, Sondermann D (1972) Arrow’s Theorem, many agents, and invisible dictators. J Econ Theory 5:267–277
Koshevoy G (1997) Homotopy properties of Pareto aggregation rules. Soc Choice Welfare 14:295–302
Lauwers L (2000) Topological social choice. Math Soc Sci 40:1–39
Lauwers L (2004) Topological manipulators form an ultrafilter. Soc Choice Welfare 22:437–445
Mihara HR (1997) Anonymity and neutrality in Arrow’s Theorem with restricted coalition algebras. Soc Choice Welfare 14:503–512
Mihara HR (2000) Coalitionally strategyproof functions depend only on the most-preferred alternatives. Soc Choice Welfare 17:393–402
Mihara HR (2001) Existence of a coalitionally strategyproof social choice function: a constructive proof. Soc Choice Welfare 18:543–553
Mihara HR (2004) Nonanonymity and sensitivity of computable simple games. Math Soc Sci 48:329–341
Pazner EA, Wesley E (1977) Stability of social choices in infinitely large societies. J Econ Theory 14:252–262
Salonen H, Saukkonen K (2005) On Continuity of Arrovian social welfare functions. Soc Choice Welfare 25:85–93
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
Taylor AD (2005) Social choice and the mathematics of manipulation. Cambridge University Press, Cambridge
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An earlier version of this paper was presented at the Logic, Game Theory and Social Choice 4, Caen 2005, and at the First Spain Italy Netherlands Meeting on Game Theory, Maastricht 2005.
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Saukkonen, K. Continuity of social choice functions with restricted coalition algebras. Soc Choice Welfare 28, 637–647 (2007). https://doi.org/10.1007/s00355-006-0181-4
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DOI: https://doi.org/10.1007/s00355-006-0181-4