Chaotic Dynamics in Multi-LLM Deliberation

• URL: http://arxiv.org/abs/2603.09127v1
• Date: Tue, 10 Mar 2026 02:59:11 GMT
• Title: Chaotic Dynamics in Multi-LLM Deliberation
• Abstract summary: We quantify inter-run sensitivity using an empirical Lyapunov exponent ($hat$) derived from trajectory divergence in committee mean preferences.<n>We identify two independent routes to instability: role differentiation in homogeneous committees and model heterogeneity in no-role committees.<n>These results support stability auditing as a core design requirement for multi-LLM governance systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 ($\hatλ$) 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 ($\hatλ=0.0541$ and $0.0947$, respectively), while homogeneous no-role committees also remain in a positive-divergence regime ($\hatλ=0.0221$). The combined mixed+roles condition is less unstable than mixed+no-role ($\hatλ=0.0519$ vs $0.0947$), showing non-additive interaction. Mechanistically, Chair-role ablation reduces $\hatλ$ 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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