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 exhibits a variety of qualitatively distinct stationary states, and we demonstrate that the final opinion structures are critically determined by the people's opinion weights.