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

arXiv: https://arxiv.org/abs/2603.20248 · HTML: https://mlsanity.com/paper/2603.20248/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 47 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 9 of 9)

- [Closing the AI Accountability Gap: Defining an End-to-End Framework for Internal Algorithmic Auditing](https://mlsanity.com/paper/2001.00973/) (2020)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- ["I'm Not Sure, But...": Examining the Impact of Large Language Models' Uncertainty Expression on User Reliance and Trust](https://mlsanity.com/paper/2405.00623/) (2024)
- [COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution](https://mlsanity.com/paper/1507.02293/) (2015)
- [Algorithms and Decision-Making in the Public Sector](https://mlsanity.com/paper/2106.03673/) (2021)
- [A Tutorial on Hawkes Processes for Events in Social Media](https://mlsanity.com/paper/1708.06401/) (2017)
- [Novel Multidimensional Models of Opinion Dynamics in Social Networks](https://mlsanity.com/paper/1505.04920/) (2015)
- [Generative AI is already widespread in the public sector](https://mlsanity.com/paper/2401.01291/) (2024)
- [Trust in the CODA model: Opinion Dynamics and the reliability of other agents](https://mlsanity.com/paper/1304.3518/) (2013)

## Abstract (arXiv)

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.