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Ranking objects from a preference relation over their subsets

Author

Listed:
  • Giulia Bernardi

    (Politecnico di Milano)

  • Roberto Lucchetti

    (Politecnico di Milano)

  • Stefano Moretti

    (Université Paris Dauphine, PSL Research University, CNRS, LAMSADE)

Abstract

In many everyday situations, we need to rank individuals or single items having the possibility to observe the behavior of groups. In this paper we propose a way to get this ranking over the elements of a set X, starting from an arbitrary preference relation over the subsets of X and taking into account the information provided by this ranking over the subsets. To this purpose, we use a very common approach in the social choice framework: we single out some properties that a general solution should satisfy, and we prove that these properties characterize a unique solution. Given the generality of the approach, we believe that this paper is only a starting point for a more extended analysis. In particular, it is clear that different contexts can suggest other properties, thus identifying alternative ranking methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:52:y:2019:i:4:d:10.1007_s00355-018-1161-1
    DOI: 10.1007/s00355-018-1161-1
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    References listed on IDEAS

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    1. Josep Freixas, 2010. "On ordinal equivalence of the Shapley and Banzhaf values for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 513-527, October.
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    7. Roberto Lucchetti & Stefano Moretti & Fioravante Patrone, 2015. "Ranking sets of interacting objects via semivalues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 567-590, July.
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    Cited by:

    1. 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.
    2. 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.
    3. Michele Aleandri & Marco Dall’Aglio & Vito Fragnelli & Stefano Moretti, 2022. "Minimal winning coalitions and orders of criticality," Annals of Operations Research, Springer, vol. 318(2), pages 787-803, November.
    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).
    5. 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.
    6. Ritu Dutta & Rajnish Kumnar & Surajit Borkotokey, 2023. "How to choose a Compatible Committee?," Papers 2308.03507, arXiv.org.
    7. Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2021. "A Core-partition solution for coalitional rankings with a variable population domain," Working Papers 2021-06, CRESE.

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