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A simple proof of Sen's possibility theorem on majority decisions

Elsholtz, Christian and List, Christian (2005) A simple proof of Sen's possibility theorem on majority decisions. Elemente Der Mathematik, 60 (2). pp. 45-56. ISSN 1420-8962

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Abstract

Condorcet’s voting paradox shows that pairwise majority voting may lead to cyclical majority preferences. In a famous paper, Sen (1966) identified a general condition on a profile of individual preference orderings, called triplewise value-restriction, which is sufficient for the avoidance of such cycles. This note aims to make Sen’s result easily accessible. We provide an elementary proof of Sen's possibility theorem and a simple reformulation of Sen’s condition. We discuss how Sen’s condition is logically related to a number of precursors. Finally, we state a necessary and sufficient condition for the avoidance of cycles, and suggest that, although there is still some logical space between that condition and Sen’s sufficient condition, Sen’s condition cannot be further generalized in an appealing way.

Item Type: Article
Official URL: http://www.ems-ph.org/journals/journal.php?jrn=em
Additional Information: © 2005 European Mathematical Society
Library of Congress subject classification: B Philosophy. Psychology. Religion > BC Logic
Q Science > QA Mathematics
Sets: Departments > Government
Research centres and groups > Centre for Philosophy of Natural and Social Science (CPNSS)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 17 Jul 2008 14:33
URL: http://eprints.lse.ac.uk/19610/

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