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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- Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993.
"Generalized Median Voter Schemes and Committees,"
Journal of Economic Theory,
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- 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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- 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).
- Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
- Maurice Salles, 2000. "Amartya Sen. Droits et choix social," Revue Économique, Programme National Persée, vol. 51(3), pages 445-457.
- Eliaz, K., 2001. "Arrow`s Theorem and the Gibbard-Satterthwaite Theorem as Special Cases of a Single Theorem," Papers 2001-11, Tel Aviv.
- Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
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