Multi-Dimensional Opinion Formation

Abstract: In this paper we propose and investigate a multi-dimensional opinion dynamics model where people are characterised by both opinions and importance weights across these opinions. Opinion changes occur through binary interactions, with a novel coupling mechanism: the change in one topic depends on the weighted similarity across the full opinion vector. We state the kinetic equation for this process and derive its mean-field partial differential equation to describe the overall dynamics. Analytical computations and numerical simulations confirm that this model generates complex stationary states, and we demonstrate that the final opinion structures are critically determined by the peoples' opinion weights.