Title:Chaotic Dynamics in Multi-LLM Deliberation

Abstract:Collective AI systems increasingly rely on multi-LLM deliberation, but their stability under repeated execution remains poorly characterized. We model five-agent LLM committees as random dynamical systems and quantify inter-run sensitivity using an empirical Lyapunov exponent ($\hat{\lambda}$) derived from trajectory divergence in committee mean preferences. Across 12 policy scenarios, a factorial design at $T=0$ identifies two independent routes to instability: role differentiation in homogeneous committees and model heterogeneity in no-role committees. Critically, these effects appear even in the $T=0$ regime where practitioners often expect deterministic behavior. In the HL-01 benchmark, both routes produce elevated divergence ($\hat{\lambda}=0.0541$ and $0.0947$, respectively), while homogeneous no-role committees also remain in a positive-divergence regime ($\hat{\lambda}=0.0221$). The combined mixed+roles condition is less unstable than mixed+no-role ($\hat{\lambda}=0.0519$ vs $0.0947$), showing non-additive interaction. Mechanistically, Chair-role ablation reduces $\hat{\lambda}$ most strongly, and targeted protocol variants that shorten memory windows further attenuate divergence. These results support stability auditing as a core design requirement for multi-LLM governance systems.

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