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Baseline Rationing

Author

Listed:
  • Jens Leth Hougaard

    (Department of Food and Resource Economics, University of Copenhagen)

  • Juan D. Moreno-Ternero

    (Department of Economics, Universidad de Malaga and Pablo de Olavide)

  • Lars Peter Østerdal

    (Department of Economics, University of Copenhagen)

Abstract

The standard problem of adjudicating conflicting claims describes a situation in which a given amount of a divisible good has to be allocated among agents who hold claims against it exceeding the available amount. This paper considers more general rationing problems in which, in addition to claims, there exist baselines (to be interpreted as objective entitlements, ideal targets, or past consumption) that might play an important role in the allocation process. The model we present is able to accommodate real-life rationing situations, ranging from resource allocation in the public health care sector to international protocols for the reduction of greenhouse emissions, or water distribution in drought periods. We define a family of allocation methods for such general rationing problems - called baseline rationing rules - and provide an axiomatic characterization for it. Any baseline rationing rule within the family is associated with a standard rule and we show that if the latter obeys some properties reflecting principles of impartiality, priority and solidarity, the former obeys them too.

Suggested Citation

  • 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.
  • Handle: RePEc:foi:msapwp:05_2010
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    File URL: http://okonomi.foi.dk/workingpapers/MSAPpdf/MSAP2010/MSAP_WP05_2010.pdf
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    References listed on IDEAS

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    1. 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.
    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. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
    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. Kaminski, Marek M., 2006. "Parametric rationing methods," Games and Economic Behavior, Elsevier, vol. 54(1), pages 115-133, January.
    7. 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.
    8. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    9. 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.
    10. 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.
    11. John E. Roemer, 1986. "Equality of Resources Implies Equality of Welfare," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 751-784.
    12. 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.
    13. Fleurbaey, Marc & Roemer, John E., 2011. "Judicial precedent as a dynamic rationale for axiomatic bargaining theory," Theoretical Economics, Econometric Society, vol. 6(2), May.
    14. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    15. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
    16. 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.
    17. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    18. 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.
    19. 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.
    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. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284, Elsevier.
    22. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    23. 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.
    24. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
    25. Juan Moreno-Ternero & Antonio Villar, 2006. "New characterizations of a classical bankruptcy rule," Review of Economic Design, Springer;Society for Economic Design, vol. 10(2), pages 73-84, August.
    26. 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.
    27. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
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    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. 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.

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    More about this item

    Keywords

    rationing; baselines; claims; priority; solidarity;
    All these keywords.

    JEL classification:

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

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