Influencing the dynamics of correlated opinions in the voter model on multiplex networks

Processes of opinion formation have found much attention in the recent literature on complex systems and networks [2]. Whereas many studies have considered the spread of opinions on a single network, recognition of, in particular, the multi-relational structure of online activities [6] has led to an increased interest in spreading processes on multi-layer networks, where ignoring the existence of different types of connections can have important consequences for our ability to model such systems [7, 5]. Here, building on previous work on opinion propagation in the voting dynamics [4, 8] we are interested in maximizing influence on a multi-layer network. Different to previous work [9], we study influence maximization for multiple correlated opinions, where opinions about different issues spread on different layers of a multiplex network. As an example, consider how people discuss different topics with their friends in offline and online social networks. Yet, holding a particular opinion about one topic may change the individuals’ susceptibility to adopt opinions about other topics, thus effectively coupling different network layers through opinion correlations. Studying influence maximization in such settings allows for a gradual control of the population, as has been observed in real-world scenarios [3]. For instance, we can first prime a population by spreading a particular attitude, which then allows for an easier propagation of our desired opinion. In this paper we formalize a model of such correlated opinion dynamics on multiplex networks, develop an algorithm for optimizing influence on controlled opinions, and provide analysis of different scenarios of optimal control in the presence of an adversary.