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Two Characterizations of the Uniform Rule for Division Problems with Single-Peaked Preferences

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  • Volij, Oscar
  • Otten, Gert-Jan
  • Peters, Hans

Abstract

The uniform rule is considered to be the most important rule for the problem of allocating an amount of a perfectly divisible good between agents who have single-peaked preferences. The uniform rule was studied extensively in the literature and several characterizations were provided. The aim of this paper is to provide two different formulations and corresponding axiomatizations of the uniform rule. These formulations resemble the Nash and the lexicographic egalitarian bargaining solutions; the corresponding axiomatizations are based on axioms of independence of irrelevant alternatives and restricted monotonicity.

Suggested Citation

  • Volij, Oscar & Otten, Gert-Jan & Peters, Hans, 1996. "Two Characterizations of the Uniform Rule for Division Problems with Single-Peaked Preferences," Staff General Research Papers Archive 5108, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genres:5108
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    Cited by:

    1. Gong, Doudou & Dietzenbacher, Bas, 2025. "Equal treatment of unsatisfied agents," Mathematical Social Sciences, Elsevier, vol. 137(C).
    2. Kim, Sunyoung & Bergantiños, Gustavo & Chun, Youngsub, 2015. "The separability principle in single-peaked economies with participation constraints," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 69-75.
    3. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
    4. Shuhei Morimoto & Shigehiro Serizawa & Stephen Ching, 2013. "A characterization of the uniform rule with several commodities and agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 871-911, March.
    5. Roy, Souvik & Sadhukhan, Soumyarup, 2020. "On the structure of division rules," MPRA Paper 104402, University Library of Munich, Germany.
    6. 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.
    7. Souvik Roy & Soumyarup Sadhukhan, 2024. "Domains where the uniform rule is well behaved," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 1033-1071, September.
    8. Youngsub Chun, 2006. "The Separability Principle in Economies with Single-Peaked Preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 239-253, April.

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