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

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Author Info
William Thomson () (University of Rochester)

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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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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_529.pdf
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Publisher Info
Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 529.

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Length: 11 pages
Date of creation: Apr 2006
Date of revision:
Handle: RePEc:roc:rocher:529

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Postal: UNIVERSITY OF ROCHESTER, CENTER FOR ECONOMIC RESEARCH, DEPARTMENT OF ECONOMICS, HARKNESS 231 ROCHESTER NEW YORK 14627 U.S.A.

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Related research
Keywords: Conflicting claims; Division rules; Consistency; Consistent extension; Claims-truncated proportional rule.;

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Find related papers by 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

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, vol. 21(2), pages 241-261, 03. [Downloadable!] (restricted)
  2. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
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  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, vol. 26(1), pages 11-25.
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  5. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  6. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer, vol. 31(4), pages 667-692, December. [Downloadable!] (restricted)
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