🤖 AI Summary
This study addresses the absence of formal frameworks for characterizing when public trust in algorithmic governance institutions stabilizes or collapses. By coupling Friedkin–Johnsen opinion dynamics with a Hawkes-type intensity process modeling AI controversy events, the authors construct a bidirectional interaction model and derive precise spectral stability criteria through spectral graph theory and dynamical systems analysis. The analysis uncovers counterintuitive phenomena—such as highly trusted systems exhibiting structural fragility and low-trust environments proving more stable—and demonstrates that self-excitation of events and persistent memory substantially narrow the parameter regime permitting stability. Although network topology can reshape equilibrium heterogeneity, its influence on spectral stability is provably bounded above in memory-dominated regimes. Crucially, the work establishes that system stability is not equivalent to fairness or legitimacy.
📝 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.