Robust Clustering in Generalized Bounded Confidence Models

Bounded confidence models add a critical theoretical ingredient to the explanation of opinion clustering, opinion polarisation, and the persistence of opinion diversity, assuming that individuals are only influenced by others who are sufficiently similar and neglect actors with too different views. However, despite its enormous recognition in the literature, the bounded confidence assumption has been criticized for being able to explain diversity only when implemented in a very strict and unrealistic way. The model is unable to explain patterns of opinion diversity when actors are sometimes influenced also by others who hold distant views, even when these deviations from the bounded-confidence assumption are rare and random. Here, we echo this criticism but we also show that the model's ability to explain opinion diversity can be regained when another assumption is relaxed. Building on modeling work from statistical mechanics, we include that actors' opinion changes do not only result from social influence. When other influences are modelled as random, uniformly distributed draws, then robust patterns of opinion clustering emerge also with the relaxed implementations of bounded confidence. The results holds under both communication regimes: the updating to the average of all acceptable opinions as in the model of Hegselmann and Krause (2002) and random pair-wise communication as in the model of Deffuant et al. (2000). We discuss implications for future modelling work and point to gaps in empirical research on influence.