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A Note on Thomson's Characterizations of the Uniform Rule

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Abstract

Thomson (Consistent solutions to the problem of fair division when preferences are single-peaked, J. Econ. Theory 63 (1994), 219-245) proved that the uniform rule of fair division problem, where preferences are single-peaked, is the unique rule which is bilaterally consistent, continuous, Pareto optimal, and envy-free, in a setting of an infinite number of potential agents. We show that the uniqueness of the uniform rule is achieved without assuming continuity, even in a setting of a finite number of potential agents. A similar result is obtained by replacing envy-freeness with individual rationality from equal division.

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Bibliographic Info

Paper provided by Nir Dagan in its series Economic theory and game theory with number 003.

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Length: 7 pages
Date of creation: 1996
Date of revision:
Publication status: Published in Journal of Economic Theory 69:255-261 (1996)
Handle: RePEc:nid:ndagan:003

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Postal: Nir Dagan, Dept. of Economics and Management, Tel-Hai Academic College, Upper Galilee, Israel.
Web page: http://www.nirdagan.com/research/

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Cited by:
  1. Carmen Herrero & Ricardo Martínez, 2011. "Allocation problems with indivisibilities when preferences are single-peaked," SERIEs, Spanish Economic Association, vol. 2(4), pages 453-467, December.
  2. Lahiri, Somdeb, 2001. "Axiomatic characterizations of the CEA solution for rationing problems," European Journal of Operational Research, Elsevier, vol. 131(1), pages 162-170, May.
  3. Nir Dagan, 1995. "Consistent solutions in exchange economies: A characterization of the price mechanism," Economics Working Papers 141, Department of Economics and Business, Universitat Pompeu Fabra.
  4. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with maximal capacity constraints," SERIEs, Spanish Economic Association, vol. 3(1), pages 29-57, March.
  5. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with voluntary participation," Social Choice and Welfare, Springer, vol. 38(3), pages 371-406, March.
  6. Thomson, W., 1998. "Consistency and its Converse: an Introduction," RCER Working Papers 448, University of Rochester - Center for Economic Research (RCER).
  7. Pablo Amorós, 2002. "Single-peaked preferences with several commodities," Social Choice and Welfare, Springer, vol. 19(1), pages 57-67.
  8. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2013. "The Division Problem under Constraints," UFAE and IAE Working Papers 942.13, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
  10. Toyotaka Sakai & Takuma Wakayama, 2012. "Strategy-proofness, tops-only, and the uniform rule," Theory and Decision, Springer, vol. 72(3), pages 287-301, March.
  11. Kesten, Onur, 2006. "More on the uniform rule: Characterizations without Pareto optimality," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 192-200, March.

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