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On properties of division rules lifted by bilateral consistency

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  • 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
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    4. 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.
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    9. 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.
    10. 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.
    11. 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.
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    10. William Thomson, 2014. "Compromising between the proportional and constrained equal awards rules," RCER Working Papers 584, University of Rochester - Center for Economic Research (RCER).
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    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).

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    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

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