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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

Suggested Citation

  • William Thomson, 2012. "Lorenz rankings of rules for the adjudication of conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 547-569, August.
  • Handle: RePEc:spr:joecth:v:50:y:2012:i:3:p:547-569
    DOI: 10.1007/s00199-010-0575-5
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    References listed on IDEAS

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    1. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 283-295, February.
    2. 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.
    3. Thierry Marchant, 2008. "Scale invariance and similar invariance conditions for bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 709-710, December.
    4. José Alcalde & María Marco & José Silva, 2008. "The minimal overlap rule revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 109-128, June.
    5. 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.
    6. José Alcalde & María Marco & José Silva, 2005. "Bankruptcy games and the Ibn Ezra’s proposal," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 103-114, July.
    7. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 667-692, December.
    8. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 791-807, November.
    9. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    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. 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.
    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. 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.
    14. Hougaard, Jens Leth & Osterdal, Lars Peter, 2005. "Inequality preserving rationing," Economics Letters, Elsevier, vol. 87(3), pages 355-360, June.
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    Cited by:

    1. Javier Arin & Juan Miguel Benito, 2012. "Lorenz and lexicographic maximal allocations for bankruptcy problems," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 1202, Departamento de Economía - Universidad Pública de Navarra.
    2. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    3. Patrick Harless, 2017. "Endowment additivity and the weighted proportional rules for adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 755-781, March.
    4. 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.
    5. Giménez-Gómez, José Manuel, 2011. "A way to play bankruptcy problems," Working Papers 2072/169781, Universitat Rovira i Virgili, Department of Economics.
    6. 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;The Society for Social Choice and Welfare, vol. 33(4), pages 533-557, November.
    7. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 283-295, February.
    8. 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).
    9. José-Manuel Giménez-Gómez & Josep Peris, 2014. "Mediation in claims problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 5(4), pages 357-375, November.
    10. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    11. Nir Dagan, 2008. "An axiomatization of the leveling tax-transfer policy," Economic theory and game theory 020, Nir Dagan.
    12. repec:eee:gamebe:v:105:y:2017:i:c:p:316-328 is not listed on IDEAS

    More about this item

    Keywords

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

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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