Minimal winning coalitions and orders of criticality

Abstract In this paper, we analyze the order of criticality in simple games, under light minimal winning coalitions. The a player game is based on number other players that have to leave so question becomes pivotal. We show definition can be formulated referring cardinality blocking coalitions or hitting sets for family coalitions; moreover, are related dual game. Finally, propose rank all lexicographically accounting which they critical each order, and characterize ranking using four independent axioms.