An Adaptive Voter Model in Heterogeneous Environments

In human social systems, it is natural to assume that individuals’ opinions influence and are influenced by their interactions. Mathematically, it is common to represent such systems as networks, where nodes are individuals and edges between them denote a connection. Adaptive network models explore the dynamic relationship between node properties and network topology. In the context of opinion dynamics, these models often take the form of adaptive voter models, where there are two mechanisms through which network changes can take place. Through homophily, an edge forms between two individuals who already agree. Through social learning, an individual adopts a neighbor’s opinion. Central to these models is assortative mixing, the notion that individuals more frequently attach to those who are similar to them, thus facilitating the formation of sub-communities of like-minded individuals. However, it is not always the case that individuals want to cluster into homogeneous groups. Instead, they might attempt to surround themselves with those who both agree and disagree with them to attain a balance of inclusion and distinctiveness in their social environments. In this work, we explore the effects that such heterogeneous preferences have on the dynamics of the adaptive voter model.