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Two characterizations of the uniform rule for division problems with single-peaked preferences (*)

Author

Listed:
  • Hans Peters

    (Department of Econometrics, CentER for Economic Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, THE NETHERLANDS)

  • Gert-Jan Otten

    (Department of Econometrics, CentER for Economic Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, THE NETHERLANDS)

  • Oscar Volij

    (CentER for Economic Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, THE NETHERLANDS)

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

  • Hans Peters & Gert-Jan Otten & Oscar Volij, 1996. "Two characterizations of the uniform rule for division problems with single-peaked preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 291-306.
    • Handle: RePEc:spr:joecth:v:7:y:1996:i:2:p:291-306
    Note: Received: June 20, 1994
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    References listed on IDEAS

    as
    1. Dagan, Nir & Volij, Oscar, 1993. "The bankruptcy problem: a cooperative bargaining approach," Mathematical Social Sciences, Elsevier, vol. 26(3), pages 287-297, November.
    2. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
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    Cited by:

    1. 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.
    2. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
    3. 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.
    4. 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.
    5. Gong, Doudou & Dietzenbacher, Bas, 2024. "Equal treatment of unsatisfied agents," Research Memorandum 010, Maastricht University, Graduate School of Business and Economics (GSBE).
    6. 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.
    7. Roy, Souvik & Sadhukhan, Soumyarup, 2020. "On the structure of division rules," MPRA Paper 104402, University Library of Munich, Germany.

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