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A Theorem on Preference Aggregation

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  • Salvador Barberà

Abstract

I present a general theorem on preference aggregation. This theorem implies, as corollaries, Arrow's Impossibility Theorem, Wilson's extension of Arrow's to non-Paretian aggregation rules, the Gibbard-Satterthwaite Theorem and Sen's result on the Impossibility of a Paretian Liberal. The theorem shows that these classical results are not only similar, but actually share a common root. The theorem expresses a simple but deep fact that transcends each of its particular applications: it expresses the tension between decentralizing the choice of aggregate into partial choices based on preferences over pairs of alternatives, and the need for some coordination in these decisions, so as to avoid contradictory recommendations.

Suggested Citation

  • Salvador Barberà, 2003. "A Theorem on Preference Aggregation," Working Papers 166, Barcelona School of Economics.
  • Handle: RePEc:bge:wpaper:166
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    References listed on IDEAS

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    1. Maurice Salles, 2000. "Amartya Sen. Droits et choix social," Revue Économique, Programme National Persée, vol. 51(3), pages 445-457.
    2. Batteau, Pierre & Blin, Jean-Marie & Monjardet, Bernard, 1981. "Stability of Aggregation Procedures, Ultrafilters, and Simple Games," Econometrica, Econometric Society, vol. 49(2), pages 527-534, March.
    3. Barbera, Salvador, 1983. "Strategy-Proofness and Pivotal Voters: A Direct Proof of the Gibbard-Satterthwaite Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 413-417, June.
    4. Barbera, Salvador, 1980. "Pivotal voters : A new proof of arrow's theorem," Economics Letters, Elsevier, vol. 6(1), pages 13-16.
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    9. Barbera, S. & Peleg, B., 1988. "Strategy-Proof Voting Schemes With Continuous Preferences," UFAE and IAE Working Papers 91.88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
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    12. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
    13. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-157, Jan.-Feb..
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    Cited by:

    1. Ceyhun Coban & M. Sanver, 2014. "Social choice without the Pareto principle under weak independence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 953-961, December.

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