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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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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_529.pdf
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Bibliographic 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
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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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Keywords: Conflicting claims; Division rules; Consistency; Consistent extension; Claims-truncated proportional rule.;

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References

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  1. Antonio Villar Notario & Carmen Herrero Blanco, 2000. "The Three Musketeers: Four Classical Solutions To Bankruptcy Problems," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2000-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Nir Dagan & Oscar Volij, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," Economic theory and game theory, Nir Dagan 004, Nir Dagan.
  3. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 195-213, August.
  4. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, Econometric Society, vol. 68(3), pages 643-684, May.
  5. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, Elsevier, vol. 45(3), pages 249-297, July.
  6. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, Springer, vol. 21(2), pages 241-261, 03.
  7. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, Elsevier, vol. 2(4), pages 345-371, June.
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Cited by:
  1. Maurice Koster, 2012. "Consistent cost sharing," Computational Statistics, Springer, Springer, vol. 75(1), pages 1-28, February.
  2. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer, Springer, vol. 31(4), pages 667-692, December.

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