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A Note on the Separability Principle in Economies with Single-Peaked

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Abstract

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and continuity (with respect to the social endowment). We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of continuity. Furthermore, we prove that Pareto optimality, equal division lower bound, and separability imply no-envy. Using this result, we strengthen one of Chun's (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, equal division lower bound, separability, and either continuity or duplication-invariance.

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Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 601.04.

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Length: 10
Date of creation: 14 Jan 2004
Date of revision: 14 Nov 2005
Handle: RePEc:aub:autbar:601.04

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Keywords: fair division with single-peaked preferences; separability; duplication-invariance; uniform rule.;

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  1. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, vol. 28(4), pages 511-520.
  2. Moulin, Herve, 1987. "The Pure Compensation Problem: Egalitarianism versus Laissez-Fairism," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 769-83, November.
  3. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
  4. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  5. Thomson, W., 1991. "Population-Monotonic Solutions to the Problem of Fair Division when Preferences are Single-Peaked," RCER Working Papers 302, University of Rochester - Center for Economic Research (RCER).
  6. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
  7. Ching, Stephen, 1992. "A simple characterization of the uniform rule," Economics Letters, Elsevier, vol. 40(1), pages 57-60, September.
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