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Lorenz rankings of rules for the adjudication of conflicting claims

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Abstract

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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Bibliographic Info

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

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Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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Keywords: claims problems; constrained equal awards rule; constrained equal losses rule; Talmud rule; minimal overlap rule; Piniles’ rule; constrained egalitarian rule; ICI rules; CIC rules; consistent rules; Lorenz domination; operators.;

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  1. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, Elsevier, vol. 45(3), pages 249-297, July.
  2. Toru Hokari & William Thomson, 2007. "On properties of division rules lifted by bilateral consistency," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 536, University of Rochester - Center for Economic Research (RCER).
  3. José Alcalde & José Angel Silva & María del Carmen Marco, 2002. "Bankruptcy Games And The Ibn Ezra'S Proposal," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2002-28, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 195-213, August.
  5. Youngsub Chun & William Thomson, 2004. "Convergence under Replication of Rules to Adjudicate Conflicting Claims," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 512, University of Rochester - Center for Economic Research (RCER).
  6. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer, Springer, vol. 31(4), pages 667-692, December.
  7. Antonio Villar Notario & Carmen Herrero Blanco, 2000. "The Three Musketeers: Four Classical Solutions To Bankruptcy Problems," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2000-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  8. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer, Springer, vol. 46(2), pages 283-295, February.
  9. Thierry Marchant, 2008. "Scale invariance and similar invariance conditions for bankruptcy problems," Social Choice and Welfare, Springer, Springer, vol. 31(4), pages 709-710, December.
  10. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198292975, October.
  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. José Alcalde & María Marco & José Silva, 2008. "The minimal overlap rule revisited," Social Choice and Welfare, Springer, Springer, vol. 31(1), pages 109-128, June.
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Cited by:
  1. José M. Jiménez Gómez, 2010. "Why people reach intermediate agreements? Axiomatic and strategic justifications," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2010-29, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  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. Kristof Bosmans & Erik Schokkaert, 2009. "Equality preference in the claims problem: a questionnaire study of cuts in earnings and pensions," Social Choice and Welfare, Springer, Springer, vol. 33(4), pages 533-557, November.
  4. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer, Springer, vol. 46(2), pages 283-295, February.
  5. Nir Dagan, 2008. "An axiomatization of the leveling tax-transfer policy," Economic theory and game theory, Nir Dagan 020, Nir Dagan.

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