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The Two-Agent Claims-Truncated Proportional Rule Has No Consistent Extension: A Constructive Proof

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Abstract

We consider the problem of adjudicating conflicting claims. A rule to solve such problems 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 a that point. It says that each remaining claimant should receive what he received initially. We consider the version of the proportional rule that selects for each problem, the awards vector that is proportional to the vector of claims truncated at the amount to divide. We illustrate a geometric technique developed by Thomson (2001) by showing that the two-claimant truncated proportional rule has no consistent extension to general populations (Dagan and Volij, 1997).

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  • William Thomson, 2006. "The Two-Agent Claims-Truncated Proportional Rule Has No Consistent Extension: A Constructive Proof," RCER Working Papers 529, University of Rochester - Center for Economic Research (RCER).
  • Handle: RePEc:roc:rocher:529
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    References listed on IDEAS

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    1. 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.
    2. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    3. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    4. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
    5. 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.
    6. 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.
    7. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
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    Cited by:

    1. 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.
    2. 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.
    3. Maurice Koster, 2012. "Consistent cost sharing," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(1), pages 1-28, February.
    4. repec:spr:compst:v:75:y:2012:i:1:p:1-28 is not listed on IDEAS
    5. Koster, M., 2009. "Contracts, cost sharing and consistency," CeNDEF Working Papers 09-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

    More about this item

    Keywords

    Conflicting claims; Division rules; Consistency; Consistent extension; Claims-truncated proportional rule.;

    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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