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Non-proportional inequality preservation in gains and losses

  • 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.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 6 (November)
Pages: 1079-1092

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Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1079-1092
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. JU, Biung-Ghi & MORENO-TERNERO, Juan D., 2007. "On the equivalence between progressive taxation and inequality reduction," CORE Discussion Papers 2007002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  3. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357 Elsevier.
  4. William Thomson, 2007. "Lorenz rankings of rules for the adjudication of conflicting claims," RCER Working Papers 538, University of Rochester - Center for Economic Research (RCER).
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  8. Moulin Herve, 1984. "Egalitarianisme and utilitarianism in quasi-linear bargaining," CEPREMAP Working Papers (Couverture Orange) 8417, CEPREMAP.
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  10. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
  11. 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.
  12. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
  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. MORENO-TERNERO, Juan D. & VILLAR, Antonio, . "On the relative equitability of a family of taxation rules," CORE Discussion Papers RP -1899, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. 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.
  16. Chambers, Christopher P. & Thomson, William, 2002. "Group order preservation and the proportional rule for the adjudication of conflicting claims," Mathematical Social Sciences, Elsevier, vol. 44(3), pages 235-252, December.
  17. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
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