Generic impossibility of Arrow’s impossibility theorem
Our major objective is to show that if there are infinitely many alternatives and society can be decomposed into the sum of two non-negligible coalitions, the set of all Arrovian collective choice rules that satisfy the ultrafilter property (its set of decisive coalitions form an ultrafilter), is nowhere dense in the set of all Arrovian collective choice rules. This result entails that (1) almost all Arrovian collective choice rules are non-dictatorial and (2) in any neighborhood of a dictatorial Arrovian collective choice rule, a nondictatorial Arrovian collective choice rule can be found, i.e., the property of admitting a dictator is not a locally stable property for Arrovian collective choice rules in the sense that the property does not withstand a small perturbation.
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- John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer, vol. 26(1), pages 211-215, 07.
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- Campbell, Donald E & Kelly, Jerry S, 1996. "Arrovian Social Choice Correspondences," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 803-23, November.
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- Blair, Douglas H. & Bordes, Georges & Kelly, Jerry S. & Suzumura, Kotaro, 1976. "Impossibility theorems without collective rationality," Journal of Economic Theory, Elsevier, vol. 13(3), pages 361-379, December.
- Armstrong, Thomas E., 1985. "Precisely dictatorial social welfare functions : Erratum and Addendum to `arrows theorem with restricted coalition algebras'," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 57-59, February.
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