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A unifying framework for the problem of adjudicating conflicting claims

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  • Hougaard, Jens Leth
  • Moreno-Ternero, Juan D.
  • Østerdal, Lars Peter

Abstract

In a recent paper, Thomson and Yeh [Thomson, W., Yeh, C.-H., 2008. Operators for the adjudication of conflicting claims. Journal of Economic Theory 143, 177–198] introduced the concept of operators on the space of rules for the problem of adjudicating conflicting claims. They focused 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

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

Volume (Year): 48 (2012)
Issue (Month): 2 ()
Pages: 107-114

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Handle: RePEc:eee:mateco:v:48:y:2012:i:2:p:107-114

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

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Keywords: Rationing; Operators; Baselines; Composition; Claims;

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References

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  1. Diego Dominguez, 2007. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Working Papers, Centro de Investigacion Economica, ITAM 0705, Centro de Investigacion Economica, ITAM.
  2. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, Elsevier, vol. 47(2), pages 245-257, March.
  3. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing in the presence of baselines," Social Choice and Welfare, Springer, Springer, vol. 40(4), pages 1047-1066, April.
  4. MORENO-TERNERO, Juan D. & ROEMER, John E., 2005. "Impartiality, priority, and solidarity in the theory of justice," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2005077, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Thomson, William & Yeh, Chun-Hsien, 2008. "Operators for the adjudication of conflicting claims," Journal of Economic Theory, Elsevier, Elsevier, vol. 143(1), pages 177-198, November.
  6. Diego Dominguez & William Thomson, 2004. "A New Solution to the Problem of Adjudicating Conflicting Claims," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 511, University of Rochester - Center for Economic Research (RCER).
  7. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," Discussion Papers, University of Copenhagen. Department of Economics 10-16, University of Copenhagen. Department of Economics.
  8. Duranton, Gilles & Martin, Philippe & Mayer, Thierry & Mayneris, Florian, 2010. "The Economics of Clusters: Lessons from the French Experience," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199592203, October.
  9. Juan Moreno-Ternero & Antonio Villar, 2006. "The TAL-Family of Rules for Bankruptcy Problems," Social Choice and Welfare, Springer, Springer, vol. 27(2), pages 231-249, October.
  10. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521715348.
  11. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, Elsevier, vol. 45(3), pages 249-297, July.
  12. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, Elsevier, 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.
  13. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 195-213, August.
  14. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521681599.
  15. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, Elsevier, vol. 44(2), pages 321-335, April.
  16. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 418, University of Rochester - Center for Economic Research (RCER).
  17. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers, Rice University, Department of Economics 2001-06, Rice University, Department of Economics.
  18. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, Elsevier, vol. 132(1), pages 1-26, January.
  19. Toru Hokari & William Thomson, 2007. "On properties of division rules lifted by bilateral consistency," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 536, University of Rochester - Center for Economic Research (RCER).
  20. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, Econometric Society, vol. 68(3), pages 643-684, May.
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Citations

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Cited by:
  1. Jens L. Hougaard & Juan D. Moreno-Ternero & Lars P. Østerdal, 2011. "Baseline Rationing," Working Papers, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center 2011-04, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
  2. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing in the presence of baselines," Social Choice and Welfare, Springer, Springer, vol. 40(4), pages 1047-1066, April.
  3. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "Rationing with baselines: The composition extension operator," Discussion Papers of Business and Economics, Department of Business and Economics, University of Southern Denmark 23/2012, Department of Business and Economics, University of Southern Denmark.
  4. Moreno-Ternero, Juan D., 2013. "A new analysis of a simple model of fair allocation," Economics Letters, Elsevier, Elsevier, vol. 118(2), pages 393-395.
  5. Pere Timoner & Josep Maria Izquierdo, 2014. "Rationing problems with payoff thresholds," UB Economics Working Papers, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics 2014/311, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.
  6. William Thomson, 2013. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 578, University of Rochester - Center for Economic Research (RCER).

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