Opinion formation models with heterogeneous persuasion and zealotry

In this work an opinion formation model with heterogeneous agents is proposed. Each agent is supposed to have different power of persuasion, and besides its own level of zealotry, that is, an individual willingness to being convinced by other agent. In addition, our model includes zealots or stubborn agents, agents that never change opinions. We derive a Bolzmann-like equation for the distribution of agents on the space of opinions, which is approximated by a transport equation with a nonlocal drift term. We study the long-time asymptotic behavior of solutions, characterizing the limit distribution of agents, which consists of the distribution of stubborn agents, plus a delta function at the mean of their opinions, weighted by they power of persuasion. Moreover, explicit bounds on the rate of convergence are given, and the time to convergence is shown to decrease when the number of stubborn agents increases. This is a remarkable fact observed in agent based simulations in different works.