Rise of the centrist: from binary to continuous opinion dynamics

TL;DR

This paper introduces a continuous opinion dynamics model extending binary Sznajd-Weron rules, incorporating disagreement, memory, and centrist propagation, with simulations showing how these factors influence opinion variance over time.

Contribution

It develops a symmetric continuum extension of binary opinion models that includes disagreement, memory effects, and centrist influence, providing new insights into opinion dynamics.

Findings

Memory effects significantly influence opinion variance.

Centrist propagation alters opinion distribution.

Binary models differ markedly from multi-opinion models in long-term behavior.

Abstract

We propose a model that extends the binary ``united we stand, divided we fall'' opinion dynamics of Sznajd-Weron to handle continuous and multi-state discrete opinions. Disagreement dynamics are often ignored in continuous extensions of the binary rules, so we make the most symmetric continuum extension of the binary model that can treat the consequences of agreement (debate) and disagreement (confrontation) within a population of agents. We use the continuum extension as an opportunity to develop rules for persistence of opinion (memory). Rules governing the propagation of centrist views are also examined. Monte Carlo simulations are carried out. We find that both memory effects and the type of centrist significantly modify the variance of average opinions in the large timescale limits of the models. Finally, we describe the limit of applicability for Sznajd-Weron's model of binary opinions as the continuum limit is approached. By comparing Monte Carlo results and long time-step limits, we find that the opinion dynamics of binary models are significantly different to those where agents are permitted more than 3 opinions.