Speaker: Michele Aleandri, Luiss
In this talk, I reconsider the order of criticality in simple games, originally introduced in Dall’Aglio et al. (2016), under the light of minimal winning coalitions. I propose a direct criterion to measure the order of criticality of any player in a simple game, based on the cardinality of the minimal hitting sets for the family of minimal winning coalitions, and I adapt an algorithm for the minimal hitting set generation to determine the order of criticality of the players. Exploiting the equivalence between blocking coalitions and winning coalitions in the dual game, I then provide a solution for ranking the players based on their power to block decisions in a simple game, alone or in conjunction with other players. Finally, I characterize this ranking by means of four independent axioms.