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.
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- Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
- 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.
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"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).
- 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.
- Maurice Salles, 2000.
"Amartya Sen. Droits et choix social,"
Presses de Sciences-Po, vol. 0(3), pages 445-457.
- Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
- Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
- Batteau, Pierre & Blin, Jean-Marie & Monjardet, Bernard, 1981. "Stability of Aggregation Procedures, Ultrafilters, and Simple Games," Econometrica, Econometric Society, vol. 49(2), pages 527-34, 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 413-17, June.
- 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.
- 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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