Leader-Follower Opinion Dynamics: Socio-Economic Factors and Optimal Control

Overview

In recent years the study of many-agent social systems and leader-follower opinion formation dynamics in particular have received growing attention. Mathematical methods from kinetic theory provide a powerful approach to study these phenomena. Voter demographics and socio-economic factors play an important role in opinion formation. We discuss recent attempts to include voter demographics and socio-economic factors in leader-follower models of opinion formation and show simulation results for recent general elections in the United Kingdom.

Such modelling naturally sparks curiosity how leaders can optimise their behaviour, e.g. position themselves optimally to attract a mass of followers. We discuss the partial differential equation-constrained optimal control for a leader-follower opinion formation model and derive first-order optimality conditions. We then solve the resulting optimality system of coupled nonlinear partial differential equations employing a gradient-type sweeping algorithm and present numerical results of finite elements based simulations.