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Social Ranking Problems at the Interplay between Social Choice Theory and Coalitional Games

Author

Listed:
  • Felix Fritz

    (LAMSADE, CNRS, Université Paris-Dauphine, Université PSL, 75016 Paris, France)

  • Stefano Moretti

    (LAMSADE, CNRS, Université Paris-Dauphine, Université PSL, 75016 Paris, France)

  • Jochen Staudacher

    (Fakultät Informatik, Hochschule Kempten, 87435 Kempten, Germany)

Abstract

This paper reviews the recent literature on the “social ranking problem”, that is, the problem of converting group rankings into individual rankings. We introduce and categorize existing social ranking methods and we briefly explain their attributes. Three main categories of social ranking methods are identified: lexicographic social rankings, methods based on voting mechanisms, and those inspired by the theory of coalitional games. An open-source R package called socialranking for computing the majority of the existing social rankings is also presented and discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4905-:d:1296576
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
    4. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    5. 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).
    6. Rodolfo Metulini & Giorgio Gnecco, 2023. "Measuring players’ importance in basketball using the generalized Shapley value," Annals of Operations Research, Springer, vol. 325(1), pages 441-465, June.
    7. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    8. Carreras, Francesc & Freixas, Josep, 2008. "On ordinal equivalence of power measures given by regular semivalues," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 221-234, March.
    9. 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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