Opinion Copulas, Homophily and Multimodal Marginals

An empirically founded and widely established driving force in opinion dynamics is homophily i.e. the tendency of "birds of a feather" to "flock together". The closer our opinions are the more likely it is that we will interact and converge. Models using these assumptions are called bounded confidence models (BCM) as they assume a tolerance threshold after which interaction is unlikely. They are known to produce one or more clusters, depending on the size of the bound, with more than one cluster being possible only in the deterministic case. Introducing noise, as is likely to happen in a stochastic world, causes BCM to produce consensus which leaves us with the open problem of explaining the emergence and sustainance of opinion clusters and polarisation. We investigate the role of heterogeneous priors in opinion formation, introduce the concept of opinion copulas, argue that it is well supported by findings in Social Psychology and use it to show that the stochastic BCM does indeed produce opinion clustering without the need for extra assumptions.