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Stability of AI Governance Systems: A Coupled Dynamics Model of Public Trust and Social Disruptions

Jiaqi Lai, Hou Liang, Weihong Huang

Abstract

As artificial intelligence (AI) is increasingly deployed in high-stakes public decision-making (from resource allocation to welfare distribution), public trust in these systems has become a critical determinant of their legitimacy and sustainability. Yet existing AI governance research remains largely qualitative, lacking formal mathematical frameworks to characterize the precise conditions under which public trust collapses. This paper addresses that gap by proposing a rigorous coupled dynamics model that integrates a discrete-time Hawkes process -- capturing the self-exciting generation of AI controversy events such as perceived algorithmic unfairness or accountability failures -- with a Friedkin-Johnsen opinion dynamics model that governs the evolution of institutional trust across social networks. A key innovation is the bidirectional feedback mechanism: declining trust amplifies the intensity of subsequent controversy events, which in turn further erode trust, forming a self-reinforcing collapse loop. We derive closed-form equilibrium solutions and perform formal stability analysis, establishing the critical spectral condition rho(J_{2nt}) < 1 that delineates the boundary between trust resilience and systemic collapse. Numerical experiments further reveal how echo chamber network structures and media amplification accelerate governance failure. Our core contribution to the AI governance field is a baseline collapse model: a formal stability analysis framework demonstrating that, absent strong institutional intervention, even minor algorithmic biases can propagate through social networks to trigger irreversible trust breakdown in AI governance systems.

Stability of AI Governance Systems: A Coupled Dynamics Model of Public Trust and Social Disruptions

Abstract

As artificial intelligence (AI) is increasingly deployed in high-stakes public decision-making (from resource allocation to welfare distribution), public trust in these systems has become a critical determinant of their legitimacy and sustainability. Yet existing AI governance research remains largely qualitative, lacking formal mathematical frameworks to characterize the precise conditions under which public trust collapses. This paper addresses that gap by proposing a rigorous coupled dynamics model that integrates a discrete-time Hawkes process -- capturing the self-exciting generation of AI controversy events such as perceived algorithmic unfairness or accountability failures -- with a Friedkin-Johnsen opinion dynamics model that governs the evolution of institutional trust across social networks. A key innovation is the bidirectional feedback mechanism: declining trust amplifies the intensity of subsequent controversy events, which in turn further erode trust, forming a self-reinforcing collapse loop. We derive closed-form equilibrium solutions and perform formal stability analysis, establishing the critical spectral condition rho(J_{2nt}) < 1 that delineates the boundary between trust resilience and systemic collapse. Numerical experiments further reveal how echo chamber network structures and media amplification accelerate governance failure. Our core contribution to the AI governance field is a baseline collapse model: a formal stability analysis framework demonstrating that, absent strong institutional intervention, even minor algorithmic biases can propagate through social networks to trigger irreversible trust breakdown in AI governance systems.
Paper Structure (50 sections, 43 equations, 8 figures, 1 table)

This paper contains 50 sections, 43 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Conceptualizing and Quantifying Trust in the Context of Artificial Intelligence
  4. Modeling the Diffusion of Trust in Social Networks
  5. Formal Models of Social Event Emergence and Propagation
  6. AI Governance and Institutional Trust
  7. Interdependencies Between Public Trust and Social Events: Toward a Bidirectional Framework
  8. Co-evolution of Trust and Opinion
  9. Modeling Social Events and Information Shocks
  10. Current Gaps and Contributions of This Work
  11. Model
  12. Trust Update Equation
  13. Controversy Event Update Equation
  14. Theoretical Analysis
  15. Equilibrium Analysis
  16. ...and 35 more sections

Figures (8)

  • Figure 1: Coupled dynamics between trust and perceived event intensity
  • Figure 2: Simulation with time step=50
  • Figure 3: Simulation with time step=5
  • Figure 4: Sensitivity analysis of $\alpha$ ($\beta=0.4$, $\gamma=0.5$). The system remains stable ($\rho(J_{2n}) < 1$) throughout the scanned range $\alpha \in [0, 0.5]$, as shown in the right panel.
  • Figure 5: Sensitivity analysis of $\beta$ ($\gamma=0.5$, $\alpha=0.05$). The dashed red line marks the stability boundary $\rho(J_{2n})=1$ at $\beta^* \approx 0.50$; the shaded region indicates parameter values for which the system diverges. The right panel shows the spectral radius $\rho(J_{2n})$ as a function of $\beta$.
  • ...and 3 more figures