A Network Model for Polarization of Political Opinion

We propose and study a simple model for the evolution of political opinion through a population. The model includes a nonlinear term that causes individuals with more extreme views to be less receptive to external influence. Such a term was suggested in 1981 by Loren Cobb in the context of a scalar-valued diffusion equation, and recent empirical studies support this modelling assumption. Here, we use the same philosophy in a network-based model. This allows us to incorporate the pattern of pairwise social interactions present in the population. We show that the model can admit two distinct stable steady states. This bi-stability property is seen to support polarization, and can also make the long-term behavior of the system extremely sensitive to the initial conditions and to the precise connectivity structure. Computational results are given to illustrate these effects.
This work addresses the important topic of political polarization in networked societies. A key feature of the proposed model is that like-minded individuals can reinforce the opinions of their adjacent neighbors and produce extreme views. The paper explores the bifurcations of the model to show how opinions of the network of participants can change according to their locality. The stability of the model under different parameterizations is explored to shed insight into how a group of people can separate into different fractions away from a global center.