Social Choice and Welfare

, Volume 31, Issue 3, pp 393–413

Sen’s theorem: geometric proof, new interpretations

Original Paper

DOI: 10.1007/s00355-007-0288-2

Cite this article as:
(Ivy) Li, L. & Saari, D.G. Soc Choice Welfare (2008) 31: 393. doi:10.1007/s00355-007-0288-2


Sen’s classic social choice result supposedly demonstrates a conflict between Pareto and minimal forms of liberalism. By providing the first direct mathematical proof of this seminal result, we underscore a significantly different interpretation: rather than conflicts among rights, Sen’s result occurs because the liberalism assumption negates the requirement that voters have transitive preferences. This explanation enriches interpretations of Sen’s conclusion by introducing radically new kinds of societal conflicts, by suggesting ways to sidestep these difficulties, and by providing insight into other approaches that have been used to avoid the difficulties.

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.CoB, EconomicsUniversity of LouisvilleLouisvilleUSA
  2. 2.Institute for Mathematical Behavioral SciencesUniversity of CaliforniaIrvineUSA

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