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A unifying framework for the problem of adjudicating conflicting claims

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  • Jens Leth Hougaard

    ()
    (Department of Food and Resource Economics, University of Copenhagen)

  • Juan D. Moreno-Ternero

    (Department of Economics, Universidad de Malaga and Pablo de Olavide)

  • Lars Peter Østerdal

    (Department of Economics, University of Copenhagen)

Abstract

In a recent paper, Thomson and Yeh [Operators for the adjudication of conflicting claims, Journal of Economic Theory 143 (2008) 177-198] introduced the concept of operators on the space of rules for the problem of adjudicating conflicting claims. They focussed on three operators in order to uncover the structure of such a space. In this paper, we generalize their analysis upon presenting and studying a general family of operators inspired by three apparently unrelated approaches to the problem of adjudicating conflicting claims. We study the structural properties of this family and show, in particular, that most of Thomson and Yeh’s results are specific cases of our study.

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Bibliographic Info

Paper provided by University of Copenhagen, Department of Food and Resource Economics in its series MSAP Working Paper Series with number 01_2011.

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Length: 23 pages
Date of creation: Jan 2011
Date of revision:
Handle: RePEc:foi:msapwp:01_2011

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Web page: http://www.msap.life.ku.dk/
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Keywords: rationing; operators; baselines; composition; claims;

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References

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  1. 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.
  2. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," MSAP Working Paper Series 05_2010, University of Copenhagen, Department of Food and Resource Economics.
  3. MORENO-TERNERO, Juan D. & VILLAR, Antonio, . "The TAL-family or rules for bankruptcy problems," CORE Discussion Papers RP -1897, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  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. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521887427, Fall.
  7. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
  8. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
  9. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  10. Diego Dominguez & William Thomson, 2004. "A New Solution to the Problem of Adjudicating Conflicting Claims," RCER Working Papers 511, University of Rochester - Center for Economic Research (RCER).
  11. MORENO-TERNERO, Juan D. & ROEMER, John E., 2005. "Impartiality, priority, and solidarity in the theory of justice," CORE Discussion Papers 2005077, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. 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.
  13. Duranton, Gilles & Martin, Philippe & Mayer, Thierry & Mayneris, Florian, 2010. "The Economics of Clusters: Lessons from the French Experience," OUP Catalogue, Oxford University Press, number 9780199592203, Octomber.
  14. HOUGAARD, Jean Leth & MORENO-TERNERO, Juan D. & OSTERDAL, Lars Peter, . "Rationing in the presence of baselines," CORE Discussion Papers RP -2470, 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. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, Fall.
  17. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
  18. Diego Dominguez, 2007. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Working Papers 0705, Centro de Investigacion Economica, ITAM.
  19. William Thomson & Chun-Hsien Yeh, 2006. "Operators for the adjudication of conflicting claims," RCER Working Papers 531, University of Rochester - Center for Economic Research (RCER).
  20. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," 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 2, chapter 21, pages 393-506 Elsevier.
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Citations

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Cited by:
  1. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2012. "Rationing with Baselines: The Composition Extension Operator," MSAP Working Paper Series 08_2012, University of Copenhagen, Department of Food and Resource Economics.
  2. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing in the presence of baselines," Social Choice and Welfare, Springer, vol. 40(4), pages 1047-1066, April.
  3. Pere Timoner & Josep Maria Izquierdo, 2014. "Rationing problems with payoff thresholds," UB Economics Working Papers 2014/311, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.
  4. 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).
  5. Moreno-Ternero, Juan D., 2013. "A new analysis of a simple model of fair allocation," Economics Letters, Elsevier, vol. 118(2), pages 393-395.
  6. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," MSAP Working Paper Series 05_2010, University of Copenhagen, Department of Food and Resource Economics.

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