Manipulation in Communication Structures of Graph-Restricted Weighted Voting Games

Weighted voting games are an important class of compactly representable simple games that can be used to model collective decision-making processes. The influence of players in weighted voting games is measured by power indices such as the Shapley-Shubik and the Penrose-Banzhaf power indices. Previous work has studied how such power indices can be manipulated via actions such as merging or splitting players [1,1.2], adding or deleting players [13], or tampering with the quota [21]. We study graph-restricted weighted voting games [8,9,18], a model in which weighted voting games are embedded into a communication structure (i.e., a graph). We investigate to what extent power indices in such games can be changed by adding or deleting edges in the underlying communication structure and we study the resulting problems in terms of their computational complexity.