You might expect that running the same AI committee on the same problem twice would produce the same answer. It doesn't — even at temperature zero.
Shimao, Khern-am-nuai, and Kim model five-agent LLM committees as random dynamical systems and measure their divergence using an empirical Lyapunov exponent. The finding: there are two independent routes to instability — role differentiation (giving agents titles like “Chair”) and model heterogeneity (mixing different LLMs). Both produce positive divergence at T=0, where practitioners assume deterministic behavior.
The interaction between these routes is the interesting part. Mixed models with no roles are the most unstable (lambda-hat = 0.0947). Mixed models with roles are less unstable (0.0519). The Chair role doesn't add instability — it absorbs it. Removing the Chair increases divergence more than any other ablation. The hierarchy is a stabilizer, not a source of chaos.
This inverts the standard worry about centralized control in multi-agent systems. The concern has always been that hierarchical structure concentrates failure. But in deliberative systems, hierarchy concentrates divergence into a single predictable node rather than distributing it across the network. The Chair doesn't prevent instability — it localizes it.
The practical implication is that “stability auditing” should be a design requirement for any multi-LLM governance system. The instability exists before the temperature knob is even touched. It's structural, not stochastic.