IDEAS home Printed from https://ideas.repec.org/p/pab/wpaper/12.01.html
   My bibliography  Save this paper

A unifying framework for the problem of adjudicating conflicting claims

Author

Listed:
  • 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.

Suggested Citation

  • Jens L. Hougaard & Juan D. Moreno-Ternero & Lars P. Osterdal, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Working Papers 12.01, Universidad Pablo de Olavide, Department of Economics.
    • Handle: RePEc:pab:wpaper:12.01
    as

    Download full text from publisher

    File URL: http://www.upo.es/serv/bib/wps/econ1201.pdf
    File Function: First version, 2012
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521715348, September.
    2. Juan Moreno-Ternero & Antonio Villar, 2006. "The TAL-Family of Rules for Bankruptcy Problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 231-249, October.
    3. 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.
    4. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    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. Thomson, William & Yeh, Chun-Hsien, 2008. "Operators for the adjudication of conflicting claims," Journal of Economic Theory, Elsevier, vol. 143(1), pages 177-198, November.
    7. H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
    8. Juan D Moreno-Ternero & John E Roemer, 2006. "Impartiality, Priority, and Solidarity in the Theory of Justice," Econometrica, Econometric Society, vol. 74(5), pages 1419-1427, September.
    9. 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.
    10. 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.
    11. 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.
    12. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," Discussion Papers 10-16, University of Copenhagen. Department of Economics.
      • Jens L. Hougaard & Juan D. Moreno-Ternero & Lars P. Østerdal, 2011. "Baseline Rationing," Working Papers 2011-04, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
      • 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.
    13. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    14. 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.
    15. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
    16. Huriot,Jean-Marie & Thisse,Jacques-François (ed.), 2009. "Economics of Cities," Cambridge Books, Cambridge University Press, number 9780521118279, September.
    17. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing in the presence of baselines," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1047-1066, April.
    18. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    19. 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.
    20. Diego Dominguez & William Thomson, 2006. "A new solution to the problem of adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 283-307, June.
    21. Diego Dominguez, 2007. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Working Papers 0705, Centro de Investigacion Economica, ITAM.
    22. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2011. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 2, number 2.
    23. 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.
    24. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
    25. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    2. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," Discussion Papers 10-16, University of Copenhagen. Department of Economics.
    3. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing with baselines: the composition extension operator," Annals of Operations Research, Springer, vol. 211(1), pages 179-191, December.
    4. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing in the presence of baselines," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1047-1066, April.
    5. Long, Yan & Sethuraman, Jay & Xue, Jingyi, 2021. "Equal-quantile rules in resource allocation with uncertain needs," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. Bas Dietzenbacher & Yuki Tamura & William Thomson, 2024. "Partial-implementation invariance and claims problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 203-229, August.
    7. Sanchez-Soriano, Joaquin, 2021. "Families of sequential priority rules and random arrival rules with withdrawal limits," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 136-148.
    8. Jaume García-Segarra & Miguel Ginés-Vilar, 2023. "Additive adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 93-116, March.
    9. Patrick Harless, 2017. "Endowment additivity and the weighted proportional rules for adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 755-781, March.
    10. 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.
    11. René Brink & Juan D. Moreno-Ternero, 2017. "The reverse TAL-family of rules for bankruptcy problems," Annals of Operations Research, Springer, vol. 254(1), pages 449-465, July.
    12. José-Manuel Giménez-Gómez & M. Marco-Gil, 2014. "A new approach for bounding awards in bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 447-469, August.
    13. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 667-692, December.
    14. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    15. William Thomson, 2014. "Compromising between the proportional and constrained equal awards rules," RCER Working Papers 584, University of Rochester - Center for Economic Research (RCER).
    16. Moreno-Ternero, Juan D. & Roemer, John E., 2012. "A common ground for resource and welfare egalitarianism," Games and Economic Behavior, Elsevier, vol. 75(2), pages 832-841.
    17. Biung-Ghi Ju & Juan Moreno-Ternero, 2011. "Progressive and merging-proof taxation," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 43-62, February.
    18. Siwei Chen, 2015. "Systematic favorability in claims problems with indivisibilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 283-300, February.
    19. José-Manuel Giménez-Gómez & Josep E. Peris & María-José Solís-Baltodano, 2023. "Resource allocations with guaranteed awards in claims problems," Review of Economic Design, Springer;Society for Economic Design, vol. 27(3), pages 581-602, September.
    20. Moreno-Ternero, Juan D., 2011. "Voting over piece-wise linear tax methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 29-36, January.

    More about this item

    Keywords

    rationing; operators; baselines; composition; claims;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pab:wpaper:12.01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Publicación Digital - UPO (email available below). General contact details of provider: https://edirc.repec.org/data/deupoes.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.