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Lorenz rankings of rules for the adjudication of conflicting claims

  • William Thomson

    ()

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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File URL: http://hdl.handle.net/10.1007/s00199-010-0575-5
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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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  1. 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.
  2. 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.
  3. Thierry Marchant, 2008. "Scale invariance and similar invariance conditions for bankruptcy problems," Social Choice and Welfare, Springer, vol. 31(4), pages 709-710, December.
  4. José Alcalde & José Angel Silva & María del Carmen Marco, 2002. "Bankruptcy Games And The Ibn Ezra'S Proposal," Working Papers. Serie AD 2002-28, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. 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.
  6. José Alcalde & María Marco & José Silva, 2008. "The minimal overlap rule revisited," Social Choice and Welfare, Springer, vol. 31(1), pages 109-128, June.
  7. 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).
  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. 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.
  10. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer, vol. 40(4), pages 791-807, 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.
  12. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975, March.
  13. 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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