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Lexicographic solutions for coalitional rankings based on individual and collective performances

Author

Listed:
  • Sylvain Béal

    (CRESE EA3190, Univ. Bourgogne Franche-Comté, F-25000 Besançon, France)

  • Eric Rémila

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France)

  • Philippe Solal

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France)

Abstract

A coalitional ranking describes a situation where a finite set of agents can form coalitions that are ranked according to a weak order. A social ranking solution on a domain of coalitional rankings assigns an individual ranking, that is a weak order over the agent set, to each coalitional ranking of this domain. We introduce two lexicographic solutions for a variable population domain of coalitional rankings. These solutions are computed from the individual performance of the agents, then, when this performance criterion does not allow to decide between two agents, a collective performance criterion is applied to the coalitions of higher size. We provide parallel axiomatic characterizations of these two solutions.

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2021. "Lexicographic solutions for coalitional rankings based on individual and collective performances," Working Papers 2021-07, CRESE.
    • Handle: RePEc:crb:wpaper:2021-07
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    References listed on IDEAS

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    1. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    2. Zhengxing Zou & René Brink & Youngsub Chun & Yukihiko Funaki, 2021. "Axiomatizations of the proportional division value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 35-62, July.
    3. Giulia Bernardi & Roberto Lucchetti & Stefano Moretti, 2019. "Ranking objects from a preference relation over their subsets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 589-606, April.
    4. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    5. René Brink & Yukihiko Funaki & Yuan Ju, 2013. "Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 693-714, March.
    6. Encarnación Algaba & Stefano Moretti & Eric Rémila & Philippe Solal, 2021. "Lexicographic solutions for coalitional rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 817-849, November.
    7. Zou, Zhengxing & van den Brink, René & Funaki, Yukihiko, 2021. "Compromising between the proportional and equal division values," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    8. Encarnación Algaba & Stefano Moretti & Eric Rémila & Philippe Solal, 2021. "Lexicographic solutions for coalitional rankings," Post-Print hal-03422945, HAL.
    9. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    10. Zhengxing Zou & Rene van den Brink, 2020. "Sharing the Surplus and Proportional Values," Tinbergen Institute Discussion Papers 20-014/II, Tinbergen Institute.
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    Cited by:

    1. Felix Fritz & Stefano Moretti & Jochen Staudacher, 2023. "Social Ranking Problems at the Interplay between Social Choice Theory and Coalitional Games," Mathematics, MDPI, vol. 11(24), pages 1-22, December.
    2. Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2023. "A Core-Partition Ranking Solution to Coalitional Ranking Problems," Group Decision and Negotiation, Springer, vol. 32(4), pages 965-985, August.

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    More about this item

    Keywords

    Coalitional rankings; converse consistency; individual performance; lexicographic criteria; path monotonocity;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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