The Spread of Opinions via Boolean Networks

Opinion diffusion models the spread of information among agents whose connections are given by a social network. We study opinion diffusion via Boolean networks, in which agents update their (binary) opinion according to a Boolean function that we assume is compactly represented as a propositional formula. The classical threshold models, where opinion updates depend on the proportion of an agent’s influencers having a differing opinion, are a special case of our model. Boolean networks are a well-studied mathematical model for biology, and in this paper we analyse it through the lens of opinion diffusion. Most notably, we analyse the computational complexity of deciding if opinions converge from a given initial point, the existence of an asynchronous update that maximises the global agreement among the agents, and we explore connections with delegative voting