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 (λ) 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 (λ=0.0541 and 0.0947, respectively), while homogeneous no-role committees also remain in a positive-divergence regime (λ=0.0221). The combined mixed+roles condition is less unstable than mixed+no-role (λ=0.0519 vs 0.0947), showing non-additive interaction. Mechanistically, Chair-role ablation reduces λ 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.

Reproductions