Emergence of polarization on dynamical directed social networks

Polarization has been widely observed in social media for controversial topics. Both social relationship adjustments and opinion dynamics are crucial for polarization. Yet, it is challenging to capture the emergence of polarization in such co-evolutionary dynamics due to the curse of dimensionality. In this work, we propose a discrete three-opinion voter-like model on dynamical directed social networks, and successfully derive the polarization probability by solving a partial differential equation (PDE) under fast rewiring. It is found that if all the directed links are broken with the same probability, the polarization probability is proportional to the number of extreme opinions. If the breaking probabilities are slightly different, the polarization probability is not only determined by the total fraction of extreme opinions, but also by the product of the fraction of extreme opinions. Furthermore, we find that if extreme opinions are the majority initially, the polarization probability increases via extending the duration time of individuals who have the same opinion. If extreme opinions are the minority initially, the polarization probability decreases via extending the duration time of individuals who have the same opinion. Our work can be insightful for quantitatively understanding the emergence of polarization.