Orders of Criticality in Voting Games

Abstract

The authors focus on the problem of investigating the blackmail power of players in simple games, which is the possibility of players of threatening coalitions to cause them loss using arguments that are (apparently) unjustified. To this purpose, the classical notion of the criticality of players has been extended, in order to characterize situations where players may gain more power over the members of a coalition thanks to collusion with other players. (original abstract)