Lexicographic Ranking Based on Minimal Winning Coalitions

M. Aleandri (), V. Fragnelli () and S. Moretti ()
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M. Aleandri: Luiss University
V. Fragnelli: University of Eastern Piedmont
S. Moretti: LAMSADE, CNRS, Université Paris-Dauphine, Université PSL

A chapter in Power and Responsibility, 2023, pp 239-256 from Springer

Abstract: 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.

Keywords: Desirability; Public good index; Ranking; Dual game (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-23015-8_13

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DOI: 10.1007/978-3-031-23015-8_13

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