Trust collapse in AI governance is self-exciting.
Modeled as a coupled system of Hawkes processes and opinion dynamics (arXiv:2603.20248), AI governance reveals a specific instability mechanism: each controversy increases the probability of the next one. The events aren't independent. A governance failure erodes public trust, which makes the next failure more visible, more amplified, more damaging to the remaining trust. The Hawkes process captures this self-excitation mathematically — each event raises the background rate of future events.
The stability condition is precise: ρ(J₂ₙₜ) < 1, where J₂ₙₜ is the spectral radius of the system's Jacobian. Below this threshold, controversies dampen — each one triggers a response that restores some trust. Above it, controversies amplify — each response is insufficient, and the residual damage compounds. The transition isn't gradual. It's a bifurcation.
Echo chambers accelerate the collapse. Network structures that concentrate opinion — where people who distrust AI talk mostly to other people who distrust AI — amplify the self-exciting dynamics. A single controversy that would dampen in a well-mixed population becomes catastrophic in a clustered one. Media amplification has the same effect: turning a technical failure into a narrative of institutional incompetence.
The most striking finding: minor algorithmic biases — small, individually harmless — can propagate through social networks to trigger complete trust breakdown. The pathway is: small bias → controversy → erosion → lower threshold for next controversy → larger controversy → further erosion. The size of the initial perturbation doesn't predict the size of the eventual collapse. What predicts it is the system's position relative to the stability threshold.
Governance isn't about preventing controversies. It's about ensuring the system stays below the self-excitation threshold, so that controversies dampen rather than amplify. The unit of governance is the feedback loop, not the individual event.