Why More Agents Do Not Always Help: Empirical Power Laws of Coordination in LLM Agent Societies

LLM multi-agent systems are increasingly deployed as interacting agent societies, yet scaling often yields diminishing or unstable returns whose cause remains poorly understood. We present the first large-scale empirical study of coordination dynamics in LLM multi-agent systems, introducing an atomic event-level formulation that reconstructs reasoning as cascades of coordination. Analyzing over 1.5 million interactions across tasks, topologies, and scales, we uncover three coupled empirical coordination laws: coordination follows heavy-tailed cascades, concentrates via reinforced routing into influence elites, and produces increasingly large extreme events as system size grows. We show that these regularities are linked by a structural mechanism: an integration bottleneck, in which coordination expansion scales with system size while consolidation does not, producing large but weakly integrated reasoning processes. To test this mechanism, we introduce Deficit-Triggered Integration (DTI), which selectively increases integration under imbalance. DTI improves performance precisely where coordination fails, without suppressing large-scale reasoning. Together, our results identify coordination structure as a measurable and previously underexplored axis for understanding and improving scalable multi-agent intelligence. Code: https://anonymous.4open.science/r/mas-elites-0645/