A Theorem on Preference Aggregation
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.
|Date of creation:||01 Jul 2003|
|Contact details of provider:|| Postal: 08193, Bellaterra, Barcelona|
Phone: 34 93 592 1203
Fax: +34 93 542-1223
Web page: http://pareto.uab.cat
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
- Eliaz, K., 2001. "Arrow`s Theorem and the Gibbard-Satterthwaite Theorem as Special Cases of a Single Theorem," Papers 2001-11, Tel Aviv.
- Maurice Salles, 2000. "Amartya Sen. Droits et choix social," Revue Économique, Programme National Persée, vol. 51(3), pages 445-457.
- Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
- Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993.
"Generalized Median Voter Schemes and Committees,"
Journal of Economic Theory,
Elsevier, vol. 61(2), pages 262-289, December.
- Barbera, S. & Gul, F. & Stacchetti, E., 1992. "Generalized Median Voter Schemes and Committees," UFAE and IAE Working Papers 184.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
- 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.
- Benoit, Jean-Pierre, 2000. "The Gibbard-Satterthwaite theorem: a simple proof," Economics Letters, Elsevier, vol. 69(3), pages 319-322, December.
- Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
- 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.
- Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
- Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
- 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).
- Barbera, Salvador, 1980. "Pivotal voters : A new proof of arrow's theorem," Economics Letters, Elsevier, vol. 6(1), pages 13-16. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:aub:autbar:601.03. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Xavier Vila)
If references are entirely missing, you can add them using this form.