Extremism, segregation and oscillatory states emerge through collective opinion dynamics in a novel agent-based model

Using mathematics to model the evolution of opinions among interacting agents is a rich and growing field. We present a novel agent-based model that enhances the explanatory power of existing theoretical frameworks, corroborates experimental findings in social psychology, and reflects observed phenomena in contemporary society. Bespoke features of the model include: a measure of pairwise affinity between agents; a memory capacity of the population; and a generalized confidence bound called the interaction threshold, which can be dynamical and heterogeneous. Moreover, the model is applicable to opinion spaces of any dimensionality. Through analytical and numerical investigations, we study the opinion dynamics produced by the model and examine the effects of various model parameters. We prove that as long as every agent interacts with every other, the population will reach an opinion consensus regardless of the initial opinions or parameter values. When interactions are limited to be among agents with similar opinions, segregated opinion clusters can be formed. An opinion drift is also observed in certain settings, leading to collective extremisation of the whole population, which we quantify using a rigorous mathematical measure. We find that collective extremisation is likely if agents cut off connections whenever they move away from the neutral position, effectively isolating themselves from the population. When a population fails to reach a steady state, oscillations of a neutral majority are observed due to the influence exerted by a small number of extreme agents. By carefully interpreting these results, we posit explanations for the mechanisms underlying socio-psychological phenomena such as emergent cooperation and group polarization.