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Non-proportional inequality preservation in gains and losses

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  • Kasajima, Yoichi
  • Velez, Rodrigo A.

Abstract

We characterize the family of claims-inequality and claims-order preserving continuous rules in the three-agent case for the problem of adjudicating conflicting claims. We show that there are infinitely many of such rules and provide a simple geometric construction that spans the whole family. Additionally, we prove that this family endowed with the partial order of Lorenz domination is a lattice that has maximal and minimal elements.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1079-1092
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    References listed on IDEAS

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    7. 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.
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    11. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Miguel Ángel Mirás Calvo & Iago Núñez Lugilde & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2023. "Deviation from proportionality and Lorenz-domination for claims problems," Review of Economic Design, Springer;Society for Economic Design, vol. 27(2), pages 439-467, June.
    5. José-Manuel Giménez-Gómez & M. Carmen Marco-Gil & Juan-Francisco Sánchez-García, 2022. "New empirical insights into conflicting claims problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 13(4), pages 709-738, December.

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