IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v48y2012i2p107-114.html
   My bibliography  Save this article

A unifying framework for the problem of adjudicating conflicting claims

Author

Listed:
  • 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.

Suggested Citation

  • Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 107-114.
  • Handle: RePEc:eee:mateco:v:48:y:2012:i:2:p:107-114
    DOI: 10.1016/j.jmateco.2012.01.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406812000067
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmateco.2012.01.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    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.
    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, April.
    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," MSAP Working Paper Series 05_2010, University of Copenhagen, Department of Food and Resource 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," Discussion Papers 10-16, University of Copenhagen. Department of Economics.
    13. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    14. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
    15. 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.
    16. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    17. 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.
    18. 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.
    19. Diego Dominguez, 2007. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Working Papers 0705, Centro de Investigacion Economica, ITAM.
    20. 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.
    21. 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.
    22. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Moreno-Ternero, Juan D. & Vidal-Puga, Juan, 2021. "Aggregator operators for dynamic rationing," European Journal of Operational Research, Elsevier, vol. 288(2), pages 682-691.
    3. Vito Fragnelli & Ewa Kiryluk-Dryjska, 2019. "Rationing methods for allocating the European Union’s rural development funds in Poland," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 36(1), pages 295-322, April.
    4. 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.
      • 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," Discussion Papers 10-16, University of Copenhagen. Department of Economics.
    5. Duro, Juan Antonio & Giménez-Gómez, José-Manuel & Vilella, Cori, 2020. "The allocation of CO2 emissions as a claims problem," Energy Economics, Elsevier, vol. 86(C).
    6. 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.
    7. Cano Berlanga, Sebastian & Giménez Gómez, José M. (José Manuel) & Vilella Bach, Misericòrdia, 2015. "Enjoying cooperative games: The R package GameTheory," Working Papers 2072/247653, Universitat Rovira i Virgili, Department of Economics.
    8. 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.
    9. Andrea Gallice, 2019. "Bankruptcy problems with reference-dependent preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 311-336, March.
    10. 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.
    11. Giménez Gómez, José M. (José Manuel) & Blanco Gil, Carmen & Sánchez García, Juan Francisco, 2016. "New insights on empirical conflicting claims problems," Working Papers 2072/261530, Universitat Rovira i Virgili, Department of Economics.
    12. Juan D. Moreno-Ternero, 2017. "A Talmudic approach to bankruptcy problems," LIDAM Reprints CORE 2914, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Ju, Biung-Ghi & Kim, Min & Kim, Suyi & Moreno-Ternero, Juan D., 2021. "Fair international protocols for the abatement of GHG emissions," Energy Economics, Elsevier, vol. 94(C).
    14. 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 School of Economics.
    15. Giménez-Gómez, José-Manuel & Osório, Antonio, 2015. "Why and how to differentiate in claims problems? An axiomatic approach," European Journal of Operational Research, Elsevier, vol. 241(3), pages 842-850.
    16. Moreno-Ternero, Juan D., 2013. "A new analysis of a simple model of fair allocation," Economics Letters, Elsevier, vol. 118(2), pages 393-395.
    17. Gaertner, Wulf & Xu, Yongsheng, 2020. "Loss sharing: Characterizing a new class of rules," Mathematical Social Sciences, Elsevier, vol. 107(C), pages 37-40.
    18. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2021. "Broadcasting revenue sharing after cancelling sports competitions," MPRA Paper 109736, University Library of Munich, Germany.
    19. Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2021. "Constrained welfare egalitarianism in surplus-sharing problems," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 45-51.
    20. Pere Timoner Lledó & Josep Maria Izquierdo Aznar, 2015. "Generalized rationing problems and solutions," UB Economics Working Papers 2015/329, Universitat de Barcelona, Facultat d'Economia i Empresa, UB School of Economics.
    21. Dominik Karos, 2015. "Stable partitions for games with non-transferable utilities and externalities," Economics Series Working Papers 741, University of Oxford, Department of Economics.
    22. Dominik Karos, 2016. "Stable partitions for games with non-transferable utility and externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 817-838, November.
    23. Harless, Patrick, 2017. "Wary of the worst: Maximizing award guarantees when new claimants may arrive," Games and Economic Behavior, Elsevier, vol. 105(C), pages 316-328.
    24. Cano-Berlanga, Sebastián & Giménez-Gómez, José-Manuel & Vilella, Cori, 2017. "Enjoying cooperative games: The R package GameTheory," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 381-393.
    25. Timoner, Pere & Izquierdo, Josep M., 2016. "Rationing problems with ex-ante conditions," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 46-52.

    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Christopher P. Chambers & Juan D. Moreno-Ternero, 2017. "Taxation and poverty," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 153-175, January.
    10. Koster, Maurice & Boonen, Tim J., 2019. "Constrained stochastic cost allocation," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 20-30.
    11. Biung-Ghi Ju & Juan D. Moreno-Ternero, 2006. "Progressivity, Inequality Reduction, and Merging-Proofness in Taxation," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200603, University of Kansas, Department of Economics, revised Feb 2006.
    12. Harless, Patrick, 2017. "Wary of the worst: Maximizing award guarantees when new claimants may arrive," Games and Economic Behavior, Elsevier, vol. 105(C), pages 316-328.
    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. Andrea Gallice, 2019. "Bankruptcy problems with reference-dependent preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 311-336, March.
    15. Emin Karagözoğlu, 2014. "A noncooperative approach to bankruptcy problems with an endogenous estate," Annals of Operations Research, Springer, vol. 217(1), pages 299-318, June.
    16. 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.
    17. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    18. Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
    19. William Thomson, 2014. "Compromising between the proportional and constrained equal awards rules," RCER Working Papers 584, University of Rochester - Center for Economic Research (RCER).
    20. 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.

    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:eee:mateco:v:48:y:2012:i:2:p:107-114. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.