Conformity, anticonformity and polarization of opinions: insights from a mathematical model of opinion dynamics

Understanding and quantifying polarization in social systems is important because of many reasons. It could for instance help to avoid segregation and conflicts in the society or to control polarized debates and predict their outcomes. In this paper we present a version of the $q$-voter model of opinion dynamics with two types of response to social influence: conformity (like in original $q$-voter model) and anticonformity. We put the model on a social network with the double-clique topology in order to check how the interplay between those responses impacts the opinion dynamics in a population divided into two antagonistic segments. The model is analyzed analytically, numerically and by means of Monte Carlo simulations. Our results show that the systems undergoes two bifurcations as the number of cross-links between cliques changes. Below the first critical point consensus in the entire system is possible. Thus two antagonistic cliques may share the same opinion only if they are loosely connected. Above that point the system ends up in a polarized state.