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Lexicographic Ranking Based on Minimal Winning Coalitions

In: Power and Responsibility

Author

Listed:
  • M. Aleandri

    (Luiss University)

  • V. Fragnelli

    (University of Eastern Piedmont)

  • S. Moretti

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

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.

Suggested Citation

  • M. Aleandri & V. Fragnelli & S. Moretti, 2023. "Lexicographic Ranking Based on Minimal Winning Coalitions," Springer Books, in: Martin A. Leroch & Florian Rupp (ed.), Power and Responsibility, pages 239-256, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-23015-8_13
    DOI: 10.1007/978-3-031-23015-8_13
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