Cultural, Structural, and Mediated Routes to Polarization in a Nonlinear Mean-Field Model

Abstract

Collective polarization can arise through mechanisms acting at different stages of social communication, but similar polarized outcomes need not imply dynamically equivalent processes. We introduce a nonlinear two-group mean-field model that distinguishes three routes to polarization: individual content filtering, assortativity, and receiver-side message tailoring. Sender-side reformulation is included as a complementary mediation process that transforms source signals before they are mixed. These message transformations are motivated by AI-mediated cultural transmission, in which intermediaries can reformulate messages or adapt them to receivers. Using common and difference coordinates, we derive general conditions for instabilities toward consensus and balanced polarization and analyze the resulting stationary branches in the full two-dimensional phase plane. Individual filtering can generate polarization through state-dependent updating, assortativity can preserve group differences in the social field, and receiver tailoring can create a polarizing feedback even under complete mixing. By contrast, sender-side reformulation affects the polarization mode only when assortativity preserves differentiated source signals. Although these mechanisms can produce identical local instability conditions or balanced-branch amplitudes, they remain distinguishable through transverse stability, asymmetric equilibria, multistability, and basin geometry. In particular, balanced polarization may emerge as a saddle before becoming a stable attractor, while asymmetric saddles organize the boundary between consensus and polarization basins. These results show that collective polarization depends not only on feedback strength, but also on where feedback enters the communication process.