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Extended proportionality in division problems with multiple references

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  • M. Hinojosa
  • A. Mármol
  • F. Sánchez

Abstract

We consider an extension of the classic problem of division with claims to situations in which the characteristics of the agents are multi-dimensional. The proportional rule is the most prominent in the one-dimensional case, however there is no obvious way to define proportionality for the extended model. In this paper we introduce a property which generalizes proportionality, identify the family of rules satisfying it, and characterize a particular rule within this family on the basis of a property of symmetry. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • M. Hinojosa & A. Mármol & F. Sánchez, 2013. "Extended proportionality in division problems with multiple references," Annals of Operations Research, Springer, vol. 206(1), pages 183-195, July.
  • Handle: RePEc:spr:annopr:v:206:y:2013:i:1:p:183-195:10.1007/s10479-013-1388-2
    DOI: 10.1007/s10479-013-1388-2
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    References listed on IDEAS

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    1. Carlos González-Alcón & Peter Borm & Ruud Hendrickx, 2007. "A composite run-to-the-bank rule for multi-issue allocation situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 339-352, April.
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    9. Brânzei, R. & Dimitrov, D.A. & Pickl, S. & Tijs, S.H., 2002. "How to Cope with Division Problems under Interval Uncertainty of Claims?," Discussion Paper 2002-96, Tilburg University, Center for Economic Research.
    10. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Hendrickx, R.L.P., 2005. "Balanced Contributions for Multi-Issue Allocation Situations," Discussion Paper 2005-93, Tilburg University, Center for Economic Research.
    11. M. Hinojosa & A. Mármol & F. Sánchez, 2012. "A consistent talmudic rule for division problems with multiple references," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 661-678, October.
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    Cited by:

    1. A. M. Mármol & M. A. Hinojosa, 2020. "A Two-Step Proportional Rule for Division with Multiple References," Group Decision and Negotiation, Springer, vol. 29(1), pages 127-141, February.
    2. J. Sánchez-Pérez, 2023. "New results for multi-issue allocation problems and their solutions," Review of Economic Design, Springer;Society for Economic Design, vol. 27(2), pages 313-336, June.

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