The two-agent claims-truncated proportional rule has no consistent extension: A constructive proof
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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- Volij, Oscar & Dagan, Nir, 1997.
"Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems,"
Staff General Research Papers
5141, Iowa State University, Department of Economics.
- 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.
- Nir Dagan & Oscar Volij, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," Economic theory and game theory 004, Nir Dagan.
- Antonio Villar Notario & Carmen Herrero Blanco, 2000.
"The Three Musketeers: Four Classical Solutions To Bankruptcy Problems,"
Working Papers. Serie AD
2000-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- 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.
- Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
- Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, vol. 21(2), pages 241-261, 03.
- O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
- 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.
- 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.
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