Opinion dynamics with disagreement and modulated information

Opinion dynamics concerns social processes through which populations or groups of individuals agree or disagree on specific issues. As such, modelling opinion dynamics represents an important research area that has been progressively acquiring relevance in many different domains. Existing approaches have mostly represented opinions through discrete binary or continuous variables by exploring a whole panoply of cases: e.g. independence, noise, external effects, multiple issues. In most of these cases the crucial ingredient is an attractive dynamics through which similar or similar enough agents get closer. Only rarely the possibility of explicit disagreement has been taken into account (i.e., the possibility for a repulsive interaction among individuals’ opinions), and mostly for discrete or 1-dimensional opinions, through the introduction of additional model parameters. Here we introduce a new model of opinion formation, which focuses on the interplay between the possibility of explicit disagreement, modulated in a self-consistent way by the existing opinions’ overlaps between the interacting individuals, and the effect of external information on the system. Opinions are modelled as a vector of continuous variables related to multiple possible choices for an issue. Information can be modulated to account for promoting multiple possible choices. Numerical results show that extreme information results in segregation and has a limited effect on the population, while milder messages have better success and a cohesion effect. Additionally, the initial condition plays an important role, with the population forming one or multiple clusters based on the initial average similarity between individuals, with a transition point depending on the number of opinion choices.

💡 Research Summary

Opinion dynamics studies how individuals in a population adjust their views through social interaction, leading either to consensus or persistent disagreement. Most existing models treat opinions as either binary states or one‑dimensional continuous variables and rely on attractive (convergent) interactions: agents with sufficiently similar opinions become even more alike. Explicit repulsive interactions—where agents deliberately move apart—have been explored only in limited settings, typically for discrete or scalar opinions, and usually require additional ad‑hoc parameters. Moreover, external information (media, campaigns, policy messages) is often modeled as a static field that uniformly pushes all agents toward a target opinion, ignoring the fact that real individuals process information differently depending on how it aligns with their current beliefs.

The present paper introduces a novel framework that simultaneously incorporates (i) multi‑option continuous opinions, (ii) a self‑consistent repulsion/attraction mechanism governed by the overlap of the interacting agents’ opinion vectors, and (iii) an external information source whose influence is modulated by each agent’s current overlap with the message.

Model specification
Each agent (i) carries an opinion vector (\mathbf{x}_i = (x_i^1,\dots,x_i^M)) with components in (