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The Reverse Talmud Rule for Bankruptcy Problems

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Author Info

  • Rene van den Brink

    ()
    (VU University Amsterdam)

  • Yukihiko Funaki

    ()
    (Waseda University Tokyo)

  • Gerard van der Laan

    ()
    (VU University Amsterdam)

Abstract

We introduce a new solution for bankruptcy problems that satisfies weaker versions of the Exemption en Exclusion properties from the literature. Although the principles of Exclusion and Exemption are appealing, the specific conditions under which an agent receives its claim, respectively nothing, seem arbitrary and are inconsistent in the sense that there is no bankruptcy rule that satisfies both. However, weakening these conditions (by putting lower boundaries on what is considered to be a ‘small claim’), there do exist rules satisfying both principles. In this paper we consider a Weak Exemption and a Weak Exclusion property such that there is a unique bankruptcy rule that satisfies these two properties together with Consistency and Weak Proportionality (i.e. a change in the estate effects the payoffs of agents with bigger claims more than the payoffs of agents with smaller claims). This rule turns out to be some kind of reverse of the famous Talmud rule. Moreover, we show that Weak Exemption and Weak Exclusion are each others dual, and that the Reverse Talmud rule also can be characterized as the unique Self-Dual solution that satisfies Weak Proportionality and either Weak Exemption or Weak Exclusion. Finally, we generalize the Reverse Talmud rule to a class of bankruptcy rules that all satisfy some Weak Exemption and some Weak Exclusion property (that are not necessarily each others dual), which contains the famous Constrained Equal Awards and Constrained Equal Losses rules as extreme cases.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-026/1.

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Date of creation: 07 Mar 2008
Date of revision: 27 Mar 2008
Handle: RePEc:dgr:uvatin:20080026

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Web page: http://www.tinbergen.nl

Related research

Keywords: Bankruptcy problem; Exemption; Exclusion; Self-Duality; Talmud rule; Reverse Talmud Rule;

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References

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  1. Antonio Villar Notario & Juan D. Moreno Ternero, 2001. "The Tal-Family Of Rules For Bankruptcy Problems," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2001-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Herrero, Carmen & Maschler, Michael & Villar, Antonio, 1999. "Individual rights and collective responsibility: the rights-egalitarian solution," Mathematical Social Sciences, Elsevier, Elsevier, vol. 37(1), pages 59-77, January.
  3. Dagan, Nir & Volij, Oscar, 1993. "The bankruptcy problem: a cooperative bargaining approach," Mathematical Social Sciences, Elsevier, Elsevier, vol. 26(3), pages 287-297, November.
  4. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, Elsevier, vol. 15(3), pages 231-246, June.
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  6. William Thomson, 2007. "Two families of rules for the adjudication of conflicting claims," RCER Working Papers 535, University of Rochester - Center for Economic Research (RCER).
  7. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, Elsevier, vol. 44(2), pages 321-335, April.
  8. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, Elsevier, vol. 42(3), pages 307-328, November.
  9. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, Elsevier, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357 Elsevier.
  10. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer, Springer, vol. 28(4), pages 511-520.
  11. Nir Dagan, 1996. "New Characterizations of Old Bankruptcy Rules," Economic theory and game theory, Nir Dagan 002, Nir Dagan.
  12. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series, Institute of Economic Research, Seoul National University no1, Institute of Economic Research, Seoul National University.
  13. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, Econometric Society, vol. 68(3), pages 643-684, May.
  14. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer, Springer, vol. 18(2), pages 327-386.
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Cited by:
  1. HOUGAARD, Jean Leth & MORENO-TERNERO, Juan D. & OSTERDAL, Lars Peter, . "Rationing in the presence of baselines," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -2470, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," Discussion Papers 10-16, University of Copenhagen. Department of Economics.

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