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On the Talmud division : equity and robustness

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  • De MESNARD, Louis

    ()
    (LEG - CNRS UMR 5118 - Université de Bourgogne)

Abstract

The Talmud Division is a very old method of sharing developed by the rabbis in the Talmud and brought to the fore in the modern area some authors, among them are Aumann and Maschler. One compares the Talmud Division to other methods, mainly here the most popular, Aristotle’s Proportional Division, but also to the equal division. The Talmud Division is more egalitarian than the Proportional Division for small levels of estate and conversely and it protects the weakest –those who cannot place a non-zero claim–. This suggests that claimants may choose among the claiming methods depending on their interest, what implies a metagame. Unlike other methods as the Proportional Division, the Talmud Division is not robust because the solution depends on the order in which groups of claimants are formed, while it could be impossible to form coalitions without following the increasing order of claimants or to find a general agreement about what precise coalition must be chosen. For a larger number of claimants, fulfilling the order-preserving condition may oblige to backtrack for a very large number of steps what implies an unreasonable volume of computations. The paper discusses also of three generalizations of the Contested Garment method to three or more claimants.

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Bibliographic Info

Paper provided by LEG, Laboratoire d'Economie et de Gestion, CNRS, Université de Bourgogne in its series LEG - Document de travail - Economie with number 2008-07.

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Length: 26 pages
Date of creation: Oct 2008
Date of revision:
Handle: RePEc:lat:legeco:2008-07

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Keywords: Division; Talmud; Aristotle; Contested Garment; Three Wives.;

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References

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  1. Benoit, Jean-Pierre, 1997. "The Nucleolus Is Contested-Garment-Consistent: A Direct Proof," Journal of Economic Theory, Elsevier, vol. 77(1), pages 192-196, November.
  2. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  3. Abraham Diskin & Dan Felsenthal, 2007. "Individual rationality and bargaining," Public Choice, Springer, vol. 133(1), pages 25-29, October.
  4. Dagan, N. & Serrano, R. & Volij, O., 1994. "A Non-Cooperative View of Consistent Bankruptcy Rules," Discussion Paper 1994-11, Tilburg University, Center for Economic Research.
  5. 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).
  6. Diego Dominguez & William Thomson, 2004. "A New Solution to the Problem of Adjudicating Conflicting Claims," RCER Working Papers 511, University of Rochester - Center for Economic Research (RCER).
  7. 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.
  8. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116.
  9. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
  10. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, vol. 21(2), pages 241-261, 03.
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