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Lorenz rankings of rules for the adjudication of conflicting claims

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  • William Thomson

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Abstract

For the adjudication of conflicting claims, we develop three general approaches to obtain Lorenz rankings of rules. Our first approach concerns a parameterized family that contains several important rules (Thomson in Soc Choice Welf 31:667–692, 2008 ). We give a condition that the parameters defining two members of the family should satisfy for one of them to Lorenz dominate the other. Our second approach exploits the concept of “consistency” (Young in Math Oper Res 12:398–414, 1987 ). We derive a criterion to deduce Lorenz domination for arbitrarily many claimants from Lorenz domination in the two-claimant case. Our third approach is based on the notion of an “operator” on the space of rules (Thomson and Yeh in J Econ Theory 143:177–198, 2008 ). We develop conditions under which operators preserve the Lorenz order, or reverse it. As corollaries of our general theorems, we obtain rankings of most of the rules that have been discussed in the literature. Copyright Springer-Verlag 2012

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 50 (2012)
Issue (Month): 3 (August)
Pages: 547-569

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Handle: RePEc:spr:joecth:v:50:y:2012:i:3:p:547-569

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Related research

Keywords: Claims problems; Lorenz domination; Consistent rules; Operators; C79; D63; D74;

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  1. 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.
  2. 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.
  3. 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.
  4. Hokari, Toru & Thomson, William, 2008. "On properties of division rules lifted by bilateral consistency," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1057-1071, December.
  5. José Alcalde & María Marco & José Silva, 2008. "The minimal overlap rule revisited," Social Choice and Welfare, Springer, vol. 31(1), pages 109-128, June.
  6. 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.
  7. José Alcalde & María Marco & José Silva, 2005. "Bankruptcy games and the Ibn Ezra’s proposal," Economic Theory, Springer, vol. 26(1), pages 103-114, 07.
  8. Youngsub Chun & William Thomson, 2004. "Convergence under Replication of Rules to Adjudicate Conflicting Claims," RCER Working Papers 512, University of Rochester - Center for Economic Research (RCER).
  9. Thierry Marchant, 2008. "Scale invariance and similar invariance conditions for bankruptcy problems," Social Choice and Welfare, Springer, vol. 31(4), pages 709-710, December.
  10. Kasajima, Yoichi & Velez, Rodrigo A., 2010. "Non-proportional inequality preservation in gains and losses," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1079-1092, November.
  11. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer, vol. 46(2), pages 283-295, February.
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Cited by:
  1. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer, vol. 46(2), pages 283-295, February.
  2. Nir Dagan, 2008. "An axiomatization of the leveling tax-transfer policy," Economic theory and game theory 020, Nir Dagan.
  3. BOSMANS, Kristof & SCHOKKAERT, Erik, 2007. "Equality preference in the claims problem: A questionnaire study of cuts in earnings and pensions," CORE Discussion Papers 2007030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. José M. Jiménez Gómez, 2010. "Why people reach intermediate agreements? Axiomatic and strategic justifications," Working Papers. Serie AD 2010-29, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Kasajima, Yoichi & Velez, Rodrigo A., 2010. "Non-proportional inequality preservation in gains and losses," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1079-1092, November.

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