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Classification Theorem for Smooth Social Choice

Schofield, Norman (1984) Classification Theorem for Smooth Social Choice. Social Science Working Paper, 514. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20170920-141017060

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Abstract

A classification theorem for voting rules on a smooth choice space W of dimension w is presented. It is shown that, for any non-collegial voting rule, σ, there exist integers v*(σ), w*(σ) (with v*(σ)<w*(σ)) such that (i) structurally stable σ-voting cycles may always be constructed when w ⪴ v*(σ) + 1 (ii) a structurally stable σ-core (or voting equilibrium) may be constructed when w ⪴ v*(σ) - 1 As a corollary, it is shown that a σ-voting cycle may always be constructed if W is finite and of cardinality at leas v*(σ) + 2. Finally, it is shown that for an anonymous q-rule, a structurally stable core exists in dimension (n-2)/(n-q), where n is the cardinality of the society.


Item Type:Report or Paper (Working Paper)
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http://resolver.caltech.edu/CaltechAUTHORS:20171002-111518401Related ItemPublished Version
Alternate Title:Classification Theorem for Smooth Social Choice on a Manifold
Additional Information:This material is based upon work initially supported by a Nuffield Foundation Grant. The final version was prepared while the author was a Sherman Fairchild Distinguished Scholar at the California Institute of Technology. It is a pleasure to thank the colleagues at Caltech for their hospitality. Particular thanks are due to Kim Border, Gary Cox, David Grether, Gerald Kramer, Dick McKelvey and Jeff Strnad for helpful discussion, and for making available their unpublished work. Prepared for presentation at the panel on the Spatial Theory of Voting and Agenda Setting, the Public Choice Meeting, Phoenix, Arizona, March 1984. Published as Schofield, Norman. "Classification theorem for smooth social choice on a manifold." Social Choice and Welfare 1.3 (1984): 187-210.
Group:Social Science Working Papers
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Funding AgencyGrant Number
Nuffield FoundationUNSPECIFIED
Series Name:Social Science Working Paper
Issue or Number:514
Record Number:CaltechAUTHORS:20170920-141017060
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170920-141017060
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81630
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:20 Sep 2017 21:36
Last Modified:03 Oct 2019 18:45

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