Diversity mitigates polarization and consensus in opinion dynamics

TL;DR

This work introduces a Kuramoto-inspired model of opinion dynamics in which opinions are circular phases and interactions are governed by two thresholds, $A$ and $B$, yielding attractive, repulsive, or neutral couplings. Through numerical simulations and an Ott-Antonsen reduction, the authors identify explosive transitions from scattered states to $π$-bipolarization and then to consensus, along with robust multistability and hysteresis, which are moderated by the population diversity encoded in the width $γ$ of the conviction distribution. The framework reveals distinct dynamical states—scattered, bipolarized ($π$), tri-polarised, and consensus—and highlights how neutral regions or stubborn neutrality can drastically alter tipping points and irreversibility, sometimes suppressing consensus or promoting persistence of diversity. The model is validated on real data by applying it to language assimilation in India, showing that the degree and nature of neutral attitudes critically influence assimilation dynamics and reversibility. Collectively, the results offer insights into mitigating polarization by tuning interaction ranges and the behavior of undecided individuals, with broader implications for sociophysical contexts and language dynamics.

Abstract

We study the opinion dynamics in a population by considering a variant of Kuramoto model where the phase of an oscillator represents the opinion of an individual on a single topic. Two extreme phases separated by $π$ represent opposing views. Any other phase is considered as an intermediate opinion between the two extremes. The interaction (or attitude) between two individuals depends on the difference between their opinions and can be positive (attractive) or negative (repulsive) based on the defined thresholds. We investigate the opinion dynamics when these thresholds are varied. We observe explosive transition from a bipolarized state to a consensus state with the existence of scattered and tri-polarized states at low values of threshold parameter. The system exhibits multistability between various states in a sizeable parameter region. These transitions and multistability are studied in populations with different degrees of diversity represented by the width of conviction distribution. We found that a more homogeneous population has greater tendency to exhibit bipolarized, tri-polarized and clustered states while a diverse population helps mitigate polarization among individuals by reaching to a consensus sooner. Ott-Antonsen analysis is used to analyse the system's long term macroscopic behaviour and verify the numerical results. We also study the effects of neutral individuals that do not interact with others or do not change their attitude on opinion formation, nature of transitions and multistability. Furthermore, we apply our model to language data to study the assimilation of diverse languages in India and compare the results with those obtained from model equations.

Figures (17)

• Figure 1: Pictorial representation of limiters $A$ and $B$ for assigning attractive and repulsive couplings (a) without and (b) with the neutral region on the phase cycle.
• Figure 2: Block diagram outlining the steps followed to calculate order parameters numerically from Eqs. \ref{['eq:eq1']}-\ref{['eq:eq4']} for dependent and independent runs.
• Figure 3: Variation of order parameter $R$ with increase in $A$ without neutral region ($A=B$) shown for different conviction width, (a) $\gamma$=0.05, (b) $\gamma$=0.10, (c) $\gamma$=0.15, and (d) $\gamma$=0.20. The numerical results obtained by integrating Eq. \ref{['eq:eq1']} are plotted with blue triangles while the analytical predictions from Ott-Antonsen analysis (from Eqs. \ref{['eq:eq19']}- \ref{['eq:eq24']} ) are plotted with red solid lines.
• Figure 4: Average weighted order parameter, $S$ (Eq. \ref{['eq:eq25']}) is plotted as a function of $A$ for the case when there is no neutral region ($A=B$) for different values of conviction spread: (a) $\gamma$=0.05, (b) $\gamma$=0.1, (c) $\gamma$=0.15, and (d) $\gamma$=0.2. The results obtained by numerically integrating Eq. \ref{['eq:eq1']} are shown with blue triangles and the theoretical predictions are shown with red solid lines (from Eqs. \ref{['eq:eq19']}-\ref{['eq:eq25']}).
• Figure 5: Order parameter, $R$ is plotted with varying $A$ ($A=B$) in the forward and backward directions for the dependent runs at different values of distribution width: (a) $\gamma$=0.05, (b) $\gamma$=0.10, (c) $\gamma$=0.15, and (d) $\gamma$=0.20. The numerical results obtained from Eqs. \ref{['eq:eq1']}- \ref{['eq:eq4']} are shown with blue circles (forward run) and red triangles (backward run). The theoretical values (from Eqs. \ref{['eq:eq19']}- \ref{['eq:eq24']} ) are shown with green solid lines (forward run) and black dashed lines (backward run).