Thursday December 15, 2022 at 10am. (room Espace One, Paris Dauphine)
Michele Aleandri (Sapienza Univeristy of Rome)
Title: Lexicographic Ranking based on Minimal Winning Coalitions
(joint work with V.Fragnelli and S.Moretti)
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  and the criticality-based ranking . 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, 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.
 Holler, M.J. (1982) Forming coalitions and measuring voting power. Political
Studies, 30, 262–271.
 Aleandri, M., Dall’Aglio, M., Fragnelli, V., Moretti, S. (2021) Minimal winning
coalitions and orders of criticality. Annals of Operations Research.