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A Graphical Analysis of Some Basic Results in Social Choice

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  • Estelle Cantillon

    (Cowles Foundation, Yale University)

  • Antonio Rangel

    (Stanford, NBER, Instituto de Analisis Economico)

Abstract

We use a simple graphical approach to represent Social Welfare Functions that satisfy Independence of Irrelevant Alternatives and Anonymity. This approach allows us to provide simple and illustrative proofs of May's Theorem, of variants of classic impossibility results, and of a recent result on the robustness of Majority Rule due to Maskin (1995). In each case, geometry provides new insights on the working and interplay of the axioms, and suggests new results including a new characterization of the entire class of Majority Rule SWFs, a strengthening of May's Theorem, and a new version of Maskin's Theorem.

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File URL: http://cowles.econ.yale.edu/P/cd/d12b/d1285.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1285.

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Length: 23 pages
Date of creation: Nov 2000
Date of revision:
Publication status: Published in Social Choice and Welfare (2002), 19: 587-611
Handle: RePEc:cwl:cwldpp:1285

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Graphical analysis; cube; impossibility theorem; majority rule; anonymity; IIA;

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References

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  1. Blackorby, C. & Donaldson, D. & Weymark, J.A., 1990. "A Welfarist Proof Of Arrow'S Theorem," G.R.E.Q.A.M. 90a12, Universite Aix-Marseille III.
  2. Saari, Donald G., 1991. "Calculus and extensions of Arrow's theorem," Journal of Mathematical Economics, Elsevier, vol. 20(3), pages 271-306.
  3. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
  4. Yves Balasko & Hervé Crès, 1995. "The Probability of Condorcet Cycles and Super Majority Rules," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 95.01, Institut d'Economie et Econométrie, Université de Genève.
  5. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, 09.
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Cited by:
  1. Núñez Matias & Valleta Giacomo, 2012. "The informational simplicity of scoring rules," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Martinet, Vincent, 2011. "A characterization of sustainability with indicators," Journal of Environmental Economics and Management, Elsevier, vol. 61(2), pages 183-197, March.
  3. McMorris, F.R. & Powers, R.C., 2013. "Majority decision on median semilattices," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 48-51.

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