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Lorenz rankings of rules for the adjudication of conflicting claims

For the problem of adjudicating conflicting claims, we offer simple criteria to compare rules on the basis of the Lorenz order. These criteria pertain to three families of rules. The first family contains the constrained equal awards, constrained equal losses, Talmud, and minimal overlap rules (Thomson, 2007a). The second family, which also contains the constrained equal awards and constrained equal losses rules, is obtained from the first one by exchanging, for each problem, how well agents with relatively larger claims are treated as compared to agents with relatively smaller claims. The third family consists of consistent rules (Young, 1987). We also address the issue whether certain operators on the space of rules preserve the Lorenz order.

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Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 538.

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Length: 33 pages
Date of creation: Dec 2007
Date of revision:
Handle: RePEc:roc:rocher:538
Contact details of provider: Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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  1. Thierry Marchant, 2008. "Scale invariance and similar invariance conditions for bankruptcy problems," Social Choice and Welfare, Springer, vol. 31(4), pages 709-710, December.
  2. 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.
  3. Kristof Bosmans & Luc Lauwers, 2007. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," Center for Economic Studies - Discussion papers ces0705, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  4. 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.
  5. Chun, Youngsub & Thomson, William, 2005. "Convergence under replication of rules to adjudicate conflicting claims," Games and Economic Behavior, Elsevier, vol. 50(2), pages 129-142, February.
  6. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975, March.
  7. Toru Hokari & William Thomson, 2007. "On properties of division rules lifted by bilateral consistency," RCER Working Papers 536, University of Rochester - Center for Economic Research (RCER).
  8. 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.
  9. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer, vol. 46(2), pages 283-295, February.
  10. 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.
  11. 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.
  12. 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.
  13. José Alcalde & María Marco & José Silva, 2008. "The minimal overlap rule revisited," Social Choice and Welfare, Springer, vol. 31(1), pages 109-128, June.
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