Mean-field modelling of opinion polarization and structural misinformation susceptibility in online communities

This paper develops a mean-field framework for modelling opinion polarization and correlated opinion alignment in online communities, with particular attention to the structural conditions under which misinformation-prone environments arise. Rather than tracking the propagation of specific false content, the framework identifies the interaction regimes in which a platform’s aggregation mechanism becomes structurally unable to recover an accurate global opinion signal, which is the condition under which misinformation becomes consequential. We consider a population divided into interacting groups, where individuals hold binary opinions and influence one another through a coupling matrix that captures both within-community and cross-community interactions. Using ideas from statistical mechanics, the model describes collective opinion formation through an energy-based formulation and an associated Gibbs measure. We study the behaviour of the system in the limit of large populations and analyse the resulting community-level opinion margins. Optimal aggregation weights are derived by minimizing the expected discrepancy between the true global opinion and its approximation based on community-level signals. The analysis identifies three regimes of behaviour: weak coupling, the critical regime, and strong coupling, each leading to different macroscopic outcomes. In the weak-coupling regime, opinions are only weakly correlated, and the optimal weights are uniquely determined by a linear system involving the correlation structure. In the strong-coupling regime, the system exhibits either collective alignment or complete polarization, and the optimal weights are no longer uniquely defined. We also distinguish between cooperative and antagonistic interaction structures and show how they lead to consensus formation, echo chambers, or polarized states. These results show how the strength and sign of inter-community coupling determine whether platforms converge toward consensus, fragment into echo chambers, or become irreducibly polarized, and how the resulting aggregation breakdown, in turn, creates the structural conditions under which misinformation thrives.