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Geometry and impossibility


  • Juan Perote-Peña

    () (School of Management and Economics, Queen's University, Belfast BT7 1NN, U.K.)

  • Ashley Piggins

    () (School of Management and Economics, Queen's University, Belfast BT7 1NN, U.K.)


This note presents a simple proof of Arrow's impossibility theorem using Saari's [3, 4] "geometry of voting".

Suggested Citation

  • Juan Perote-Peña & Ashley Piggins, 2002. "Geometry and impossibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 831-836.
  • Handle: RePEc:spr:joecth:v:20:y:2002:i:4:p:831-836 Note: Received: March 5, 2001; revised version: August 16, 2001

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    References listed on IDEAS

    1. Aumann, Robert J, 1975. "Values of Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 43(4), pages 611-646, July.
    2. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    3. Shapley, Lloyd S & Shubik, Martin, 1969. "Pure Competition, Coalitional Power, and Fair Division," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(3), pages 337-362, October.
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    Cited by:

    1. Conal Duddy & Ashley Piggins, 2012. "The proximity condition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 353-369, July.

    More about this item


    Arrow's theorem; Voting geometry; Representation triangle.;

    JEL classification:

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


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