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From Condorcet’s paradox to Arrow: yet another simple proof of the impossibility theorem

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  • Massimo D’Antoni

    (Università di Siena)

Abstract

Condorcet exposed a limitation of majority-based pairwise comparison by showing that, for specific preference profiles over three alternatives, it leads to a contradiction. Arrow’s theorem is often introduced as a generalization of this finding. A novel formulation of the proof is presented that strictly adheres to this logic, establishing that for any non-dictatorial social choice rule, a contradiction-generating preference profile always exists and can be identified using a straightforward procedure.

Suggested Citation

  • Massimo D’Antoni, 2025. "From Condorcet’s paradox to Arrow: yet another simple proof of the impossibility theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 64(4), pages 961-970, June.
    • Handle: RePEc:spr:sochwe:v:64:y:2025:i:4:d:10.1007_s00355-024-01557-8
    DOI: 10.1007/s00355-024-01557-8
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    References listed on IDEAS

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    1. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    2. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    3. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
    4. Suzumura, Kotaro, 1988. "Reduction of Social Choice Problems : A Simple Proof of Arrow’s General Possibility Theorem," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 29(2), pages 219-221, December.
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