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Mediation in claims problems

Author

Listed:
  • José-Manuel Giménez-Gómez
  • Josep Peris

Abstract

Mediation is a dispute resolution process whereby agents reach a mutually acceptable agreement among different proposals that satisfy a set of principles. This paper provides a natural way of coming to such agreements in claims problems. In our approach, mediation combines (i) a set of fair properties (legitimate principles); and (ii) a criterion for delimiting the admissible manners of distributing the endowment, that is determined by the mediator expressing the two (dual) points of view to face such problems: awards and losses. These dual views define a lower and an upper bounds on awards, which are used to implement the so-called Double Recursive Process. We find that this process concludes at the midpoint between the two dual points of view. Finally, we argue that the criterion of the mediator could be established throughout Lorenz domination. In so doing, we retrieve the average of old and well-known rules. Copyright The Author(s) 2014

Suggested Citation

  • José-Manuel Giménez-Gómez & Josep Peris, 2014. "Mediation in claims problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 5(4), pages 357-375, November.
    • Handle: RePEc:spr:series:v:5:y:2014:i:4:p:357-375
    DOI: 10.1007/s13209-014-0110-1
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 791-807, November.
    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. 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.
    5. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    6. 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.
    7. 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.
    8. José-Manuel Giménez-Gómez & M. Marco-Gil, 2014. "A new approach for bounding awards in bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 447-469, August.
    9. Diego Dominguez, 2007. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Working Papers 0705, Centro de Investigacion Economica, ITAM.
    10. Diego Dominguez, 2013. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 663-678, March.
    11. 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.
    12. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    13. 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.
    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. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 791-807, November.
    16. Sofia Grahn & Mark Voorneveld, 2002. "Population Monotonic Allocation Schemes in Bankruptcy Games," Annals of Operations Research, Springer, vol. 109(1), pages 317-329, January.
    17. 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.
    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.
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    Cited by:

    1. José-manuel Giménez-gómez & Cori Vilella, 2017. "Recursive methods for discrete claims problems," Economics Bulletin, AccessEcon, vol. 37(3), pages 1653-1665.
    2. 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.
    3. 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.
    4. Pedro Gadea-Blanco & José-Manuel Giménez-Gómez & M. Carmen Marco-Gil, 2016. "Compromising in bifocal distribution games: the average value," Theory and Decision, Springer, vol. 81(3), pages 449-465, September.

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    More about this item

    Keywords

    Claims problems; Midpoint; Bounds; Recursivity; Self-duality; C71; D63; D71;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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