IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v44y2008i11p1057-1071.html
   My bibliography  Save this article

On properties of division rules lifted by bilateral consistency

Author

Listed:
  • Hokari, Toru
  • Thomson, William

Abstract

We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is "lifted" if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number of properties that are lifted, such as equal treatment of equals, resource monotonicity, composition down and composition up, and show that continuity, anonymity and self-duality are not lifted. However, each of these three properties is lifted if the rule is resource monotonic.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1057-1071
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4068(08)00002-5
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
    2. Oscar Volij & Nir Dagan, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 11-25.
    3. Dagan, Nir & Serrano, Roberto & Volij, Oscar, 1997. "A Noncooperative View of Consistent Bankruptcy Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 55-72, January.
    4. Dagan, Nir & Volij, Oscar, 1993. "The bankruptcy problem: a cooperative bargaining approach," Mathematical Social Sciences, Elsevier, vol. 26(3), pages 287-297, November.
    5. 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.
    6. William Thomson, 2007. "On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach," Review of Economic Design, Springer;Society for Economic Design, vol. 11(3), pages 225-251, November.
    7. 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.
    8. 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.
    9. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
    10. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    11. 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.
    12. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    13. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 241-261, March.
    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. 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.
    2. 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.
    3. William Thomson, 2007. "On the existence of consistent rules to adjudicate conflicting claims: a constructive geometric approach," Review of Economic Design, Springer;Society for Economic Design, vol. 11(3), pages 225-251, November.
    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. 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.
    6. Rodrigo Velez, 2014. "Consistent strategy-proof assignment by hierarchical exchange," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 125-156, May.
    7. 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.
    8. Rahmi İlkılıç & Çağatay Kayı, 2014. "Allocation rules on networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 877-892, December.
    9. William Thomson, 2012. "Lorenz rankings of rules for the adjudication of conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 547-569, August.
    10. 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.
    11. 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.
    12. Thomson, William, 2013. "A characterization of a family of rules for the adjudication of conflicting claims," Games and Economic Behavior, Elsevier, vol. 82(C), pages 157-168.
    13. Marieke Quant & Peter Borm, 2011. "Random conjugates of bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 249-266, February.
    14. 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.
    15. 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.
    16. William Thomson, 2014. "Compromising between the proportional and constrained equal awards rules," RCER Working Papers 584, University of Rochester - Center for Economic Research (RCER).
    17. 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).

    More about this item

    Keywords

    Claims problems Consistency Lifting Constrained equal awards rule Constrained equal losses rule;

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

    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:44:y:2008:i:11:p:1057-1071. 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: (Dana Niculescu). 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 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.