Analysing Opinion Dynamics via a Cognitive Model of Structured Beliefs

Opinion dynamics models can help explain observed social phenomena that emerge from social interaction, such as echo chambers or polarisation, by using computational and numerical methods. However, to make them mathematically tractable, many such models are based on simplistic and unrealistic assumptions that do not align with the knowledge from the empirical cognitive science field. A significant exception is a recent multidimensional opinion model proposed by Mueller and Tan, which was able to reproduce opinion divergence and group polarisation by establishing a need for consistency between related beliefs that restricts the space of allowed combinations of opinions. Although this contribution is promising in closing the gap between the cognitive sciences and opinion dynamics models, the authors only provided a limited set of experiments to show the behaviour of the model and a more in–depth understanding is lacking. Here, we provide a concise mathematical analysis and a more thorough numerical analysis of the cognitive model of opinion dynamics proposed by Mueller and Tan and show that the outcomes of opinion divergence and group polarisation only emerge under some regimes of the parameter space: medium–term dynamics, a moderate number of topics discussed upon interaction, with opinion divergence emerging under sparse belief spaces and group polarisation under large, dense belief spaces. These scenarios should be contrasted with real–life cases to confirm whether the assumptions of the constrained belief space are enough to explain the observed phenomena or whether additional ingredients should be added for a more realistic representation of social behaviour.