Mean-field analysis for cognitively-grounded opinion dynamics with confirmation bias

Understanding how individuals' beliefs and attitudes evolve within a population is crucial for explaining social phenomena such as polarization and consensus formation. We explore a persuasive arguments model incorporating confirmation bias, where individuals preferentially accept information aligning with their existing beliefs. By employing a mean-field approach, widely used in statistical physics, we simplify complex processes of argument exchange within the population. Our analysis proceeds by projecting the model onto continuous opinion dynamics and further reducing it through mean-field reasoning. The findings highlight the robustness of mean-field predictions and their compatibility with agent-based simulations, capturing the transition from consensus to polarization induced by confirmation bias.