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Lexicographic Ranking Based on Minimal Winning Coalitions

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Power and Responsibility

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Abstract

In this paper, we consider the consistency of the desirability relation with the ranking of the players in a simple game provided by some well-known solutions, in particular the Public Good Index Holler (1982) and the criticality-based ranking Aleandri et al. (2021). We define a new ranking solution, the Lexicographic Ranking based on Minimal winning coalitions (LRM), strongly related to the Public Good Index being rooted in the minimal winning coalitions of the simple game, proving that it is monotonic with respect to the desirability relation Isbell (1958), when it holds. A suitable characterization of the LRM solution is provided. Finally, we investigate the relation among the LRM solution and the criticality-based ranking, referring to the dual game.

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Acknowledgements

The authors want to thank professor Marco Dall’Aglio for the valuable discussions and the anonymous referee for the useful comments. S. Moretti gratefully acknowledges the support of the ANR project THEMIS (ANR-20-CE23-0018).

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Authors and Affiliations

  1. Luiss University, Viale Romania, 32, 00197, Rome, Italy

    M. Aleandri

  2. Department of Sciences and Innovative Technologies (DISIT), University of Eastern Piedmont, Viale T. Michel 11, 15121, Alessandria, Italy

    V. Fragnelli

  3. LAMSADE, CNRS, Université Paris-Dauphine, Université PSL, 75016, Paris, France

    S. Moretti

Authors
  1. M. Aleandri
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  2. V. Fragnelli
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  3. S. Moretti
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Corresponding author

Correspondence to V. Fragnelli .

Editor information

Editors and Affiliations

  1. Pforzheim University of Applied Sciences, Pforzheim, Germany

    Martin A. Leroch

  2. Kutaisi International University, Kutaisi, Georgia

    Florian Rupp

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Aleandri, M., Fragnelli, V., Moretti, S. (2023). Lexicographic Ranking Based on Minimal Winning Coalitions. In: Leroch, M.A., Rupp, F. (eds) Power and Responsibility. Springer, Cham. https://doi.org/10.1007/978-3-031-23015-8_13

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