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On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach
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On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach

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  • William Thomson

Abstract

For the problem of adjudicating conflicting claims, a rule is consistent if the choice it makes for each problem is always in agreement with the choice it makes for each "reduced problem" obtained by imagining that some claimants leave with their awards and reassessing the situation from the viewpoint of the remaining claimants. We develop a general technique to determine whether a given two-claimant rule admits a consistent extension to general populations, and to identify this extension if it exists. We apply the technique to a succession of examples. One application is to a one-parameter family of rules that offer a compromise between the constrained equal awards and constrained equal losses rules. We show that a consistent extension of such a rule exists only if all the weight is placed on the former or all the weight is placed on the latter. Another application is to a family of rules that provide a compromise between the constrained equal awards and proportional rules, and a dual family that provide a compromise between the constrained equal losses and proportional rules. In each case, we identify the restrictions implied by consistency.
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  • 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.
    • Handle: RePEc:spr:reecde:v:11:y:2007:i:3:p:225-251
    DOI: 10.1007/s10058-007-0027-2
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    14. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    15. 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.
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    Cited by:

    1. William Thomson, 2015. "For claims problems, compromising between the proportional and constrained equal awards rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 495-520, November.
    2. Ruben Juarez & Kohei Nitta, 2017. "Profit-Sharing and Implementation of Efficient Outcomes," Working Papers 201702, University of Hawaii at Manoa, Department of Economics.
    3. van den Brink, René & Funaki, Yukihiko & van der Laan, Gerard, 2013. "Characterization of the Reverse Talmud bankruptcy rule by Exemption and Exclusion properties," European Journal of Operational Research, Elsevier, vol. 228(2), pages 413-417.
    4. Ruben Juarez & Rajnish Kumar, 2013. "Implementing efficient graphs in connection networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 359-403, October.
    5. 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.
    6. 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.
    7. 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.
    8. Arin, J. & Benito-Ostolaza, J. & Inarra, E., 2017. "The reverse Talmud family of rules for bankruptcy Problems: A characterization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 43-49.
    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. José-Manuel Giménez-Gómez, 2014. "A Way to Play Claims Problems," Group Decision and Negotiation, Springer, vol. 23(3), pages 617-627, May.
    11. William Thomson, 2014. "Compromising between the proportional and constrained equal awards rules," RCER Working Papers 584, University of Rochester - Center for Economic Research (RCER).
    12. William Thomson, 2015. "For claims problems, another compromise between the proportional and constrained equal awards rules," RCER Working Papers 592, University of Rochester - Center for Economic Research (RCER).
    13. Karl Jandoc & Ruben Juarez, 2017. "Self-enforcing coalitions with power accumulation," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 327-355, May.

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    More about this item

    Keywords

    Claims problems; Consistent extensions; Proportional rule; Constrained equal awards rule; Constrained equal losses rule; C79; D63; D74;
    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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