A model of mutual influence is presented where the structure of individual’s beliefs and the social structure both matter. The model thus combines processes of belief change base on Thagard’s (Behav Brain Sci 12:435–467, 1989) theory of mental coherence with plausible processes of social network change. This combination of cognitive and social processes has outcomes that are qualitatively different from either only cognitive or only social pro- cesses, which shows the importance of studying these together. An illustration that moves towards representing the processes involved in Brexit is also exhibited to show the potential of this kind of simulation. Whilst only conceived of as an illustration of a kind of model, it is consistent with a number of observed patterns in opinion poll data, with some social and cognitive theories and only consists of plausible processes. This kind of model could also be used to relate and integrate different kinds of evidence into a coherent framework in the shape of more developed simulations.