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Uniform, Equal Division, and Other Envy-free Rules between the Two

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Author Info
Toyotaka Sakai
Takuma Wakayama
Abstract

This paper studies the problem of fairly allocating an amount of a divisible resource when preferences are single-peaked. We characterize the class of envy-free and peak-only rules and show that the class forms a complete lattice with respect to a dominance relation. We also pin down the subclass of strategy-proof rules and show that the subclass also forms a complete lattice. In both cases, the upper bound is the uniform rule, the lower bound is the equal division rule, and any other rule is between the two.

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File URL: http://www.iser.osaka-u.ac.jp/library/dp/2008/DP0723.pdf
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Paper provided by Institute of Social and Economic Research, Osaka University in its series ISER Discussion Paper with number 0723.

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Date of creation: Nov 2008
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Handle: RePEc:dpr:wpaper:0723

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  1. Kesten, Onur, 2006. "More on the uniform rule: Characterizations without Pareto optimality," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 192-200, March. [Downloadable!] (restricted)
  2. Schummer, James & Thomson, William, 1997. "Two derivations of the uniform rule and an application to bankruptcy," Economics Letters, Elsevier, vol. 55(3), pages 333-337, September. [Downloadable!] (restricted)
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  3. Chun, Youngsub, 2000. "Distributional properties of the uniform rule in economies with single-peaked preferences," Economics Letters, Elsevier, vol. 67(1), pages 23-27, April. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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