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A characterization of a family of rules for the adjudication of conflicting claims

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  • Thomson, William

Abstract

We consider the problem of adjudicating conflicting claims, and characterize the family of rules satisfying four standard invariance requirements, homogeneity, two composition properties, and consistency. It takes as point of departure the characterization of the family of two-claimant rules satisfying the first three requirements, and describes the restrictions imposed by consistency on this family and the further implications of this requirement for problems with three or more claimants. The proof, which is an alternative to Moulinʼs original proof [Moulin, H., 2000. Priority rules and other asymmetric rationing methods. Econometrica 68, 643–684], is based on a general method of constructing consistent extensions of two-claimant rules [Thomson, W., 2007. On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach. Rev. Econ. Design 11, 225–251], which exploits geometric properties of paths of awards, seen in their entirety.

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  • Thomson, William, 2013. "A characterization of a family of rules for the adjudication of conflicting claims," Games and Economic Behavior, Elsevier, vol. 82(C), pages 157-168.
    • Handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:157-168
    DOI: 10.1016/j.geb.2013.07.002
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    1. H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
    2. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    3. William Thomson, 2007. "On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach," Review of Economic Design, Springer;Society for Economic Design, vol. 11(3), pages 225-251, November.
    4. Oscar Volij & Nir Dagan, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 11-25.
    5. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    6. Diego Dominguez & William Thomson, 2006. "A new solution to the problem of adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 283-307, June.
    7. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    8. Hokari, Toru & Thomson, William, 2008. "On properties of division rules lifted by bilateral consistency," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1057-1071, December.
    9. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 667-692, December.
    10. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
    11. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
    12. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    13. Iain McLean & Fiona Hewitt (ed.), 1994. "Condorcet," Books, Edward Elgar Publishing, number 309.
    14. 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.
    15. William Thomson, 2013. "Game-Theoretic Analysis Of Bankruptcy And Taxation Problems: Recent Advances," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-14.
    16. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 241-261, March.
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    Cited by:

    1. Zhengxing Zou & Rene van den Brink & Yukihiko Funaki, 2020. "Compromising between the proportional and equal division values: axiomatization, consistency and implementation," Tinbergen Institute Discussion Papers 20-054/II, Tinbergen Institute.
    2. Wulf Gaertner & Lars Schwettmann, 2017. "Burden sharing in deficit countries: a questionnaire-experimental investigation," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 8(2), pages 113-144, June.
    3. Wulf Gaertner & Richard Bradley & Yongsheng Xu & Lars Schwettmann, 2019. "Against the proportionality principle: Experimental findings on bargaining over losses," PLOS ONE, Public Library of Science, vol. 14(7), pages 1-18, July.
    4. Flores-Szwagrzak, Karol, 2015. "Priority classes and weighted constrained equal awards rules for the claims problem," Journal of Economic Theory, Elsevier, vol. 160(C), pages 36-55.
    5. Martínez, Ricardo & Moreno-Ternero, Juan D., 2022. "Compensation and sacrifice in the probabilistic rationing of indivisible units," European Journal of Operational Research, Elsevier, vol. 302(2), pages 740-751.
    6. Sylvain Béal & André Casajus & Frank Huettner & Eric Rémila & Philippe Solal, 2016. "Characterizations of weighted and equal division values," Theory and Decision, Springer, vol. 80(4), pages 649-667, April.
    7. Gaertner, Wulf & Xu, Yongsheng, 2020. "Loss sharing: Characterizing a new class of rules," Mathematical Social Sciences, Elsevier, vol. 107(C), pages 37-40.
    8. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    9. Moulin, Herve, 2017. "Consistent bilateral assignment," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 43-55.
    10. Erik Ansink & Hans-Peter Weikard, 2015. "Composition properties in the river claims problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 807-831, April.
    11. Zou, Zhengxing & van den Brink, René & Funaki, Yukihiko, 2021. "Compromising between the proportional and equal division values," Journal of Mathematical Economics, Elsevier, vol. 97(C).

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    More about this item

    Keywords

    Claims problems; Consistent extensions; Proportional rule; CEA rule; CEL rule;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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