Engineering polarization: How contradictory stimulation systematically undermines political moderation

TL;DR

This work addresses the fragility of political moderation under realistic, noisy information environments. It extends Marvel et al.'s deterministic model by incorporating a stochastic media drive $\zeta(t)$ and differential susceptibility with $\sigma_y>\sigma_x$, formulating Stratonovich SDEs and deriving effective deradicalization rates $u_A^{\text{eff}}$ and $u_B^{\text{eff}}$. The main contribution is showing a noise-induced phase transition: when $\sigma_y>\sigma_x$, conservatives collapse and moderates vanish due to the asymmetric pressure, driving liberal dominance; this occurs independently of content, through the architecture of information flow and cross-cutting interactions. The findings highlight that platform dynamics and information structure can systematically erode political centrism, motivating resilience-focused approaches—education, civil dialogue spaces, and epistemic agency—over centralized control to preserve democratic resilience in high-noise environments.

Abstract

Political moderation, a key attractor in democratic systems, proves highly fragile under realistic information conditions. We develop a stochastic model of opinion dynamics to analyze how noise and differential susceptibility reshape the political spectrum. Extending Marvel et al.'s deterministic framework, we incorporate stochastic media influence $ζ(t)$ and neuropolitically-grounded sensitivity differences ($σ_y > σ_x$). Analysis reveals the moderate population -- stable in deterministic models -- undergoes catastrophic collapse under stochastic forcing. This occurs through an effective deradicalization asymmetry ($u_{B}^{\text{eff}} = u + σ_y^2/2 > u_{A}^{\text{eff}}$) that drives conservatives to extinction, eliminating cross-cutting interactions that sustain moderates. The system exhibits a phase transition from multi-stable coexistence to liberal dominance, demonstrating how information flow architecture -- independent of content -- systematically dismantles the political center. Our findings reveal moderation as an emergent property highly vulnerable to stochastic perturbations in complex social systems.

Figures (4)

• Figure 1: Deterministic baseline: Population equilibria under nonsocial deradicalization. Shows how moderate populations (black squares) persist only within a specific range of media influence $u,$ while conservatives (blue triangles) are driven to extinction beyond a critical threshold $u_{cr},$ destabilizing the political ecosystem. Parameters: $n_{A_c}(0)=p,$$n_{B}(0)=1-p$ with $p=5/100,$$n_{AB}(0)=0$ and $n_{A}(0)=0,$$u_{cr}=\frac{11}{10}-\sqrt{\frac{3}{5}}\approx0.325$.
• Figure 2: Differential susceptibility in deterministic framework: Equilibrium populations as a function of conservative sensitivity $u_B$ for varying liberal sensitivities $u_A$. Clockwise from top-left: $u_A=\frac{1}{100}, \frac{1}{10}, \frac{1}{2}, 1$. The key insight reveals that lower liberal susceptibility to media influences (smaller $u_A$) systematically reduces equilibrium moderate populations (black squares), establishing the foundational asymmetry exploited in our stochastic extension. This demonstrates how inherent differences in media responsiveness can predispose the system to center collapse under noisy conditions.
• Figure 3: Stochastic collapse of political moderation: Quasi-stationary probability density functions for the moderate population under differential noise susceptibility. (Top) For low conservative sensitivity ($\sigma_x=0.6$, $\sigma_y=0.25$), the distribution maintains a peak away from zero, indicating viable moderate coexistence. (Bottom) For high conservative sensitivity ($\sigma_x=0.6$, $\sigma_y=0.75$), the distribution undergoes catastrophic collapse to a peak at zero, demonstrating moderator extinction. This visualizes the central finding of our study---a noise-induced phase transition where the political center becomes unsustainable under asymmetric contradictory stimulation.
• Figure 4: Emergent liberal dominance following center collapse: Quasi-stationary probability density functions for the liberal population. (Top) $\sigma_x=0.6$, $\sigma_y=0.25$; (Bottom) $\sigma_x=0.6$, $\sigma_y=0.75$. As conservative sensitivity to contradictory stimulation increases, the liberal distribution shifts rightward and sharpens, indicating demographic dominance. Crucially, this liberal expansion occurs not through conversion of moderates but through the collapse of the cross-cutting interaction network that sustained the political center, revealing the ecosystem-level consequences of asymmetric noise susceptibility.