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Lexicographic solutions for coalitional rankings

Author

Listed:
  • Encarnación Algaba

    (Camino de los Descubrimientos, s/n)

  • Stefano Moretti

    (LAMSADE, CNRS, Université Paris-Dauphine, Université PSL)

  • Eric Rémila

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

  • Philippe Solal

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

Abstract

In many real world situations, the design of social rankings over agents or items from a given raking over groups or coalitions, to which these agents or items belong to, is of big interest. With this aim, we revise the lexicographic excellence solution and introduce two novel solutions which, moreover, take into account the size of the groups. We present some desirable axioms which are interpreted in this context. Next, a comparable axiomatization of these three solutions is established, revealing the main differences among the two new social rankings and the lexicographic excellence solution. Finally, we apply the three social rankings under study to a real scenario. Specifically, the performance of some football players of Paris Saint-Germain during the UEFA Champions League according to these three rules is analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:57:y:2021:i:4:d:10.1007_s00355-021-01340-z
    DOI: 10.1007/s00355-021-01340-z
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    References listed on IDEAS

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    1. László Csató, 2019. "UEFA Champions League Entry Has Not Satisfied Strategyproofness in Three Seasons," Journal of Sports Economics, , vol. 20(7), pages 975-981, October.
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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.
    3. Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2021. "A Core-partition solution for coalitional rankings with a variable population domain," Working Papers 2021-06, CRESE.
    4. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2022. "Lexicographic solutions for coalitional rankings based on individual and collective performances," Journal of Mathematical Economics, Elsevier, vol. 102(C).

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