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A unifying framework for the problem of adjudicating conflicting claims

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  • Jens L. Hougaard

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

  • Juan D. Moreno-Ternero

    ()
    (Department of Economics, Universidad Pablo de Olavide; CORE, Université catholique de Louvain)

  • Lars P. Osterdal

    ()
    (Department of Business and Economics, University of Southern Denmark)

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 Universidad Pablo de Olavide, Department of Economics in its series Working Papers with number 12.01.

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Length: 23 pages
Date of creation: Sep 2012
Date of revision:
Handle: RePEc:pab:wpaper:12.01

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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, Elsevier, 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. Diego Dominguez & William Thomson, 2006. "A new solution to the problem of adjudicating conflicting claims," Economic Theory, Springer, Springer, vol. 28(2), pages 283-307, 06.
  3. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521887427.
  4. Juan de Dios Moreno Ternero & Antonio Villar Notario, 2003. "The Talmud Rule And The Securement Of Agents? Awards," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2003-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. 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.
  6. 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.
  7. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, Elsevier, vol. 44(2), pages 321-335, April.
  8. 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.
  9. 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.
  10. MORENO-TERNERO, Juan D. & VILLAR, Antonio, . "The TAL-family or rules for bankruptcy problems," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1897, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521681599.
  12. HOUGAARD, Jean Leth & MORENO-TERNERO, Juan D. & OSTERDAL, Lars Peter, . "Rationing in the presence of baselines," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -2470, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  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. 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.
  15. 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).
  16. 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.
  17. 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).
  18. 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.
  19. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, Econometric Society, vol. 68(3), pages 643-684, May.
  20. 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.
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Citations

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Cited by:
  1. Juan D. Moreno-Ternero, 2012. "A new analysis of a simple model of fair allocation," Working Papers, Universidad Pablo de Olavide, Department of Economics 12.10, Universidad Pablo de Olavide, Department of Economics.
  2. 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.
  3. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," Discussion Papers 10-16, University of Copenhagen. Department of Economics.
  4. HOUGAARD, Jean Leth & MORENO-TERNERO, Juan D. & OSTERDAL, Lars Peter, . "Rationing in the presence of baselines," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -2470, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. 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).
  6. 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.

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