Multi-Dimensional Opinion Formation

TL;DR

This paper introduces a multi-dimensional opinion dynamics model where individuals' opinions and importance weights influence how opinions evolve through binary interactions, leading to complex stationary states.

Contribution

The paper presents a novel multi-dimensional opinion model with a coupling mechanism based on weighted similarity, along with its kinetic and mean-field equations.

Findings

Complex stationary opinion states emerge from the model.

Final opinion structures depend critically on importance weights.

Numerical simulations validate the analytical results.

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.