Modelling Public Opinion Dynamics: The Spiral of silence in clustered homophilic networks

Public discourse emerges from the interplay between individuals’ willingness to voice their opinions and the structural features of the social networks in which they are embedded. In this work we investigate how choice homophily and triadic closure shape the emergence of the spiral of silence, the phenomenon whereby minority views are progressively silenced due to fear of isolation. We advance the state of the art in three ways. First, we integrate a realistic network formation model, where homophily and triadic closure co-evolve, with a mean-field model of opinion expression. Second, we perform a bifurcation analysis of the associated Q-learning dynamics, revealing conditions for hysteresis and path dependence in collective expression. Third, we validate our theoretical predictions through Monte Carlo simulations, which highlight the role of finite-size effects and structural noise. Our results show that moderate triadic closure can foster minority expression by reinforcing local cohesion, whereas excessive closure amplifies asymmetries and entrenches majority dominance. These findings provide new insights into how algorithmic reinforcement of clustering in online platforms can either sustain diversity of opinion or accelerate its suppression. • Coupled dynamics of opinion expression and social network evolution. • Game-theoretic and Q-learning models of the Spiral of Silence. • Hysteresis and path dependence emerge in public expression. • Clustering can enhance silence in opinion expression dynamics. • Saddle bifurcations explain irreversible collective transitions.