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A Pedagogical Proof of Arrow's Impossibility Theorem

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  • Dardanoni, Valentino

Abstract

In this note I consider a simple proof of Arrow's Impossibility Theorem (Arrow 1963). I start with the case of three individuals who have preferences on three alternatives. In this special case there are 133=2197 possible combinations of the three individuals' rational preferences. However, by considering the subset of linear preferences, and employing the full strength of the IIA axiom, I reduce the number of cases necessary to completely describe the SWF to a small number, allowing an elementary proof suitable for most undergraduate students.

Suggested Citation

  • Dardanoni, Valentino, 1999. "A Pedagogical Proof of Arrow's Impossibility Theorem," University of California at San Diego, Economics Working Paper Series qt96n108ts, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt96n108ts
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    References listed on IDEAS

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    1. Barbera, Salvador, 1980. "Pivotal voters : A new proof of arrow's theorem," Economics Letters, Elsevier, vol. 6(1), pages 13-16.
    2. Blau, Julian H, 1972. "A Direct Proof of Arrow's Theorem," Econometrica, Econometric Society, vol. 40(1), pages 61-67, January.
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    Cited by:

    1. Susumu Cato, 2013. "Alternative proofs of Arrow’s general possibility theorem," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 131-137, November.
    2. Susumu Cato, 2010. "Brief proofs of Arrovian impossibility theorems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 267-284, July.
    3. Mark Fey, 2014. "A straightforward proof of Arrow's theorem," Economics Bulletin, AccessEcon, vol. 34(3), pages 1792-1797.

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