IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20160108.html
   My bibliography  Save this paper

The Reverse TAL-family of Rules for Bankruptcy Problems

Author

Listed:
  • René van den Brink

    (VU University Amsterdam, The Netherlands)

  • Juan D. Moreno-Ternero

    (Universidad Pablo de Olavide, Spain, and Université Catholique de Louvain, Belgium)

Abstract

This paper analyzes a family of rules for bankruptcy problems that generalizes the so-called reverse Talmud rule and encompasses both the constrained equal-awards rule and the constrained equal-losses rule. The family, introduced by van den Brink et al., [Characterization of the reverse Talmud bankruptcy rule by exemption and exclusion properties, European Journal of Operational Research 228 (2013), 413-417], is a counterpart to the so-called TAL-family of rules, introduced and studied by Moreno-Ternero and Villar [The TAL-family of rules for bankruptcy problems, Social Choice and Welfare 27 (2006) 231-249], and it is included within the so-called CIC-family of rules introduced by Thomson [Two families of rules for the adjudication of conflicting claims, Social Choice and Welfare 31 (2008) 667-692]. We provide a systematic study of the structural properties of the rules within the family, as well as its connections with the existing related literature.

Suggested Citation

  • René van den Brink & Juan D. Moreno-Ternero, 2016. "The Reverse TAL-family of Rules for Bankruptcy Problems," Tinbergen Institute Discussion Papers 16-108/II, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20160108
    as

    Download full text from publisher

    File URL: http://papers.tinbergen.nl/16108.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. JU, Biung-Ghi & MORENO-TERNERO, Juan, 2014. "Fair allocation of disputed properties," CORE Discussion Papers 2014024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
    3. 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.
    4. 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.
    5. Moreno-Ternero, Juan D., 2011. "Voting over piece-wise linear tax methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 29-36, January.
    6. William Thomson, 2015. "For claims problems, compromising between the proportional and constrained equal awards rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 495-520, November.
    7. 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.
    8. repec:eee:matsoc:v:89:y:2017:i:c:p:43-49 is not listed on IDEAS
    9. 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.
    10. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    11. repec:wsi:igtrxx:v:09:y:2007:i:02:n:s0219198907001497 is not listed on IDEAS
    12. Chun-Hsien Yeh, 2006. "Protective Properties and the Constrained Equal Awards Rule for Claims Problems: A Note," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 221-230, October.
    13. 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.
    14. Juan D. Moreno-Ternero, 2010. "A coalitional procedure leading to a family of bankruptcy rules," Working Papers 10.15, Universidad Pablo de Olavide, Department of Economics.
    15. Huijink, S. & Borm, P.E.M. & Kleppe, J. & Reijnierse, J.H., 2015. "Bankruptcy and the per capita nucleolus: The claim-and-right rules family," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 15-31.
    16. 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.
    17. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    18. Chambers, Christopher P., 2006. "Asymmetric rules for claims problems without homogeneity," Games and Economic Behavior, Elsevier, vol. 54(2), pages 241-260, February.
    19. 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.
    20. Giménez-Gómez, José-Manuel & Peris, Josep E., 2014. "A proportional approach to claims problems with a guaranteed minimum," European Journal of Operational Research, Elsevier, vol. 232(1), pages 109-116.
    21. 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.
    22. 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.
    23. 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.
    24. William Thomson, 2015. "For claims problems, another compromise between the proportional and constrained equal awards rules," RCER Working Papers 592, University of Rochester - Center for Economic Research (RCER).
    25. M. Pulido & P. Borm & R. Hendrickx & N. Llorca & J. Sánchez-Soriano, 2008. "Compromise solutions for bankruptcy situations with references," Annals of Operations Research, Springer, vol. 158(1), pages 133-141, February.
    26. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
    27. Juan D. Moreno-Ternero, 2007. "Erratum: "Bankruptcy Rules And Coalitional Manipulation"," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 411-424.
    28. Chambers, Christopher P. & Thomson, William, 2002. "Group order preservation and the proportional rule for the adjudication of conflicting claims," Mathematical Social Sciences, Elsevier, vol. 44(3), pages 235-252, December.
    29. Flores-Szwagrzak, Karol, 2015. "Priority classes and weighted constrained equal awards rules for the claims problem," Journal of Economic Theory, Elsevier, vol. 160(C), pages 36-55.
    30. 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.
    31. Carmen Herrero & Antonio Villar, 2002. "Sustainability in bankruptcy problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 261-273, December.
    32. Timoner, Pere & Izquierdo, Josep M., 2016. "Rationing problems with ex-ante conditions," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 46-52.
    33. Casas-Méndez, Balbina & Fragnelli, Vito & García-Jurado, Ignacio, 2011. "Weighted bankruptcy rules and the museum pass problem," European Journal of Operational Research, Elsevier, vol. 215(1), pages 161-168, November.
    34. Juan D. Moreno-Ternero & Antonio Villar, 2006. "On the Relative Equitability of a Family of Taxation Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(2), pages 283-291, May.
    35. Manuel Pulido & Joaquín Sánchez-Soriano & Natividad Llorca, 2002. "Game Theory Techniques for University Management: An Extended Bankruptcy Model," Annals of Operations Research, Springer, vol. 109(1), pages 129-142, January.
    36. 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.
    37. repec:wsi:igtrxx:v:09:y:2007:i:01:n:s0219198907001308 is not listed on IDEAS
    38. Huijink, S. & Borm, P.E.M. & Reijnierse, J.H. & Kleppe, J., 2013. "Bankruptcy and the Per Capita Nucleolus," Discussion Paper 2013-059, Tilburg University, Center for Economic Research.
    39. Bergantinos, Gustavo & Lorenzo, Leticia, 2008. "The equal award principle in problems with constraints and claims," European Journal of Operational Research, Elsevier, vol. 188(1), pages 224-239, July.
    40. 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.
    41. van den Brink, René & Funaki, Yukihiko & van der Laan, Gerard, 2013. "Characterization of the Reverse Talmud bankruptcy rule by Exemption and Exclusion properties," European Journal of Operational Research, Elsevier, vol. 228(2), pages 413-417.
    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. Juan D. Moreno-Ternero, 2017. "A Talmudic Approach to Bankruptcy Problems," Working Papers 17.01, Universidad Pablo de Olavide, Department of Economics.

    More about this item

    Keywords

    Bankruptcy problems; Reverse TAL-family; Reverse Talmud rule; Equal awards; Equal losses;

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tin:wpaper:20160108. 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: (Tinbergen Office +31 (0)10-4088900). General contact details of provider: http://edirc.repec.org/data/tinbenl.html .

    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 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.

    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.