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A Graphical Analysis of Some Basic Results in Social Choice

Author

Listed:
  • 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.

Suggested Citation

  • Estelle Cantillon & Antonio Rangel, 2000. "A Graphical Analysis of Some Basic Results in Social Choice," Cowles Foundation Discussion Papers 1285, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1285
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d12/d1285.pdf
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    References listed on IDEAS

    as
    1. Saari, Donald G., 1991. "Calculus and extensions of Arrow's theorem," Journal of Mathematical Economics, Elsevier, vol. 20(3), pages 271-306.
    2. 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.
    3. 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, September.
    4. Yves Balasko & Hervé Crès, 1997. "The Probability of Condorcet Cycles and Super-Majority Rules," Post-Print hal-03458336, HAL.
    5. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    6. repec:hal:spmain:info:hdl:2441/10273 is not listed on IDEAS
    7. Balasko, Yves & Cres, Herve, 1997. "The Probability of Condorcet Cycles and Super Majority Rules," Journal of Economic Theory, Elsevier, vol. 75(2), pages 237-270, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Segal-Halevi, Erel & Nitzan, Shmuel & Hassidim, Avinatan & Aumann, Yonatan, 2017. "Fair and square: Cake-cutting in two dimensions," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 1-28.
    2. Matías Núñez & Giacomo Valletta, 2015. "The informational basis of scoring rules," Review of Economic Design, Springer;Society for Economic Design, vol. 19(4), pages 279-297, December.
    3. Yariv, Leeat & Bartholdi, Laurent & Hann-Caruthers, Wade & Josyula, Maya & Tamuz, Omer, 2018. "Equitable Voting Rules," CEPR Discussion Papers 13316, C.E.P.R. Discussion Papers.
      • Laurent Bartholdi & Wade Hann-Caruthers & Maya Josyula & Omer Tamuz & Leeat Yariv, 2018. "Equitable voting rules," Papers 1811.01227, arXiv.org, revised Aug 2020.
    4. Martinet, Vincent, 2011. "A characterization of sustainability with indicators," Journal of Environmental Economics and Management, Elsevier, vol. 61(2), pages 183-197, March.
    5. Laurent Bartholdi & Wade Hann‐Caruthers & Maya Josyula & Omer Tamuz & Leeat Yariv, 2021. "Equitable Voting Rules," Econometrica, Econometric Society, vol. 89(2), pages 563-589, March.
    6. F. McMorris & R. Powers, 2008. "The majority decision function for trees with 3 leaves," Annals of Operations Research, Springer, vol. 163(1), pages 169-175, October.
    7. McMorris, F.R. & Powers, R.C., 2013. "Majority decision on median semilattices," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 48-51.
    8. Nuñez, M. & Valletta, G., 2012. "The information simplicity of scoring rules," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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    More about this item

    Keywords

    Graphical analysis; cube; impossibility theorem; majority rule; anonymity; IIA;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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