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This research introduces a mathematical framework to model the stability of AI governance by coupling public opinion dynamics with controversy intensity processes. The study reveals counterintuitive findings, such as high-trust systems potentially being structurally fragile and demonstrating that resilience depends more on information environment architecture than absolute trust levels. These insights are critical for policymakers aiming to design robust institutional safeguards against cascading failures in algorithmic decision-making ecosystems.
Stability of AI Governance Systems: A Coupled Dynamics Model of Public Trust and Social Disruptions
arXiv:2603.20248v2 Announce Type: replace-cross Abstract: AI systems are increasingly entrenched in public governance, yet scholarship lacks formal tools to determine when deviations of public trust in algorithmic institutions dissipate and when they grow into collapse. Stability refers here to asymptotic recovery from finite state perturbations under fixed structural parameters. We address this gap by developing a mathematical framework for institutional trust stability that couples a Friedkin-Johnsen opinion dynamics process with a Hawkes-inspired intensity process for AI controversies. Motivated by the Computers-Are-Social-Actors literature and recent studies of trust in large language models, this bidirectional coupling reveals that governance stability depends on the structural architecture of the information environment rather than absolute trust levels. We derive an exact spectral stability criterion delineating resilience from collapse, demonstrating how event self-excitation and memory persistence systematically narrow the stable parameter regime. Our structural analysis yields four counterintuitive structural implications: high-trust systems can be structurally fragile, low-trust environments can be structurally stable, dynamical stability neither measures nor guarantees algorithmic fairness or legitimacy, and network topology reshapes equilibrium heterogeneity while its effect on spectral stability is uniformly bounded in an explicit memory-dominated regime. Governance assessment should therefore pair normative evaluation of harms and fairness with structural analysis of recoverability, rather than treating either as a proxy for the other.
Abstract:AI systems are increasingly entrenched in public governance, yet scholarship lacks formal tools to determine when deviations of public trust in algorithmic institutions dissipate and when they grow into collapse. Stability refers here to asymptotic recovery from finite state perturbations under fixed structural parameters. We address this gap by developing a mathematical framework for institutional trust stability that couples a Friedkin-Johnsen opinion dynamics process with a Hawkes-inspired intensity process for AI controversies. Motivated by the Computers-Are-Social-Actors literature and recent studies of trust in large language models, this bidirectional coupling reveals that governance stability depends on the structural architecture of the information environment rather than absolute trust levels. We derive an exact spectral stability criterion delineating resilience from collapse, demonstrating how event self-excitation and memory persistence systematically narrow the stable parameter regime. Our structural analysis yields four counterintuitive structural implications: high-trust systems can be structurally fragile, low-trust environments can be structurally stable, dynamical stability neither measures nor guarantees algorithmic fairness or legitimacy, and network topology reshapes equilibrium heterogeneity while its effect on spectral stability is uniformly bounded in an explicit memory-dominated regime. Governance assessment should therefore pair normative evaluation of harms and fairness with structural analysis of recoverability, rather than treating either as a proxy for the other.
Computers and Society (cs.CY); Artificial Intelligence (cs.AI); Human-Computer Interaction (cs.HC); Multiagent Systems (cs.MA)
arXiv:2603.20248 [cs.CY]
(or arXiv:2603.20248v2 [cs.CY] for this version)
https://doi.org/10.48550/arXiv.2603.20248 Focus to learn more arXiv-issued DOI via DataCite
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