A Comparison of Group Criticality Notions for Simple Games

We analyze two independent efforts to extend the notion of criticality in simple games that measure the influence of a player in conjunction with others: the notion of rank of d-criticality given by Beisbart (2010) and the order of criticality in Dall'Aglio et al. (2016) and Aleandri et al. (2021). The aim is to get elements from both works and define measures of group criticality that take the best of both approaches.