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Non-proportional inequality preservation in gains and losses

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  • Kasajima, Yoichi
  • Velez, Rodrigo A.

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Claims problems Minimal award functions Proportional rule Lorenz domination Inequality preservation;

References

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  1. Biung-Ghi Ju & Juan D. Moreno-Ternero, 2007. "On the equivalence between progressive taxation and inequality reduction," Discussion Paper Series 0718, Institute of Economic Research, Korea University.
  2. Lars Peter Østerdal & Jens Leth Hougaard, 2004. "Inequality Preserving Rationing," Discussion Papers 04-23, University of Copenhagen. Department of Economics.
  3. Moulin Herve, 1984. "Egalitarianisme and utilitarianism in quasi-linear bargaining," CEPREMAP Working Papers (Couverture Orange) 8417, CEPREMAP.
  4. William Thomson, 2012. "Lorenz rankings of rules for the adjudication of conflicting claims," Economic Theory, Springer, vol. 50(3), pages 547-569, August.
  5. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
  6. 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.
  7. 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.
  8. 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.
  9. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
  10. Juan D. Moreno-Ternero & Antonio Villar, 2006. "On the Relative Equitability of a Family of Taxation Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(2), pages 283-291, 05.
  11. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer, vol. 46(2), pages 283-295, February.
  12. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, vol. 4(3), pages 255-272.
  13. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  14. 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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Cited by:
  1. William Thomson, 2012. "Lorenz rankings of rules for the adjudication of conflicting claims," Economic Theory, Springer, vol. 50(3), pages 547-569, August.
  2. Yoichi Kasajima & Rodrigo Velez, 2011. "Reflecting inequality of claims in gains and losses," Economic Theory, Springer, vol. 46(2), pages 283-295, February.
  3. William Thomson, 2013. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update," RCER Working Papers 578, University of Rochester - Center for Economic Research (RCER).

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