Political Polarization as a Convergence Condition of Democratic Systems Controlled by Dynamic Social Networks

This paper presents a control systems framework for analyzing political polarization, a phenomenon that has become increasingly prevalent worldwide. Specifically, it examines the conditions under which a democratic system controlled by a social network converges to a progressive or a regressive state. The social network is modeled as a directed graph, and the democratic system is represented by a finite-state machine. Transitions toward more equal or more unequal states occur by majority rule, based on the choices of individual agents. To describe decision convergence, the study introduces the notion of a strongly divided network, which captures political polarization. Under the assumption that the network is strongly divided, the paper derives the conditions under which the democratic system controlled by that network eventually converges to either a progressive or a regressive state.