Do Agent Societies Develop Intellectual Elites? The Hidden Power Laws of Collective Cognition in LLM Multi-Agent Systems

Abstract

Large Language Model (LLM) multi-agent systems are increasingly deployed as interacting agent societies, yet scaling these systems often yields diminishing or unstable returns, the causes of which remain poorly understood. We present the first large-scale empirical study of coordination dynamics in LLM-based 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 laws: coordination follows heavy-tailed cascades, concentrates via preferential attachment into intellectual elites, and produces increasingly frequent extreme events as system size grows. We show that these effects are coupled through a single 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 establish quantitative laws of collective cognition and identify coordination structure as a fundamental, previously unmeasured axis for understanding and improving scalable multi-agent intelligence.

Figures (18)

• Figure 1: Heavy-tailed coordination cascades across observables. CCDFs show a power-law regime ($2 < \hat{\alpha} < 3$) with truncation at large $x$. Dashed lines indicate MLE fits above $x_{\min}$. Truncated power laws are favored over log-normal and exponential alternatives (Table \ref{['tab:global_tail_model_comparison']}).
• Figure 2: Finite-size stability of heavy-tailed coordination dynamics.(Left) Estimated tail exponents $\hat{\alpha}$ (MLE) vs. agent count $N$. Estimates fluctuate at small $N$ due to limited tail samples, then stabilize and converge beyond $N \approx 64$, indicating emergence of a consistent heavy-tailed regime. (Right) Mean maximum event size $\langle x_{\max} \rangle$ vs. $N$. The upper tail grows systematically across observables, with strongest expansion for TCE, showing that increasing system size expands the reachable coordination tail.
• Figure 3: Topology- and task-specific heavy-tailed coordination cascades in multi-agent LLM systems. Complementary cumulative distribution functions (CCDF) of coordination-event sizes $P(X \ge x)$ across four coordination observables: Delegation Cascade, Revision Wave, Contradiction Burst, and Total Coordination Effort (TCE) under four agent interaction topologies (Chain, Star, Hierarchical, and Dynamic Reputation) and four task families (Reasoning, Coding, QA, and Coordination). Each curve represents the empirical distribution of coordination-event sizes for a given task family within a topology. Across all settings, the distributions exhibit broad heavy-tailed behavior with estimated scaling exponents $2 < \hat{\alpha} < 3$ in the intermediate regime (values shown per panel), consistent with scale-free coordination dynamics. While the precise tail exponent varies modestly across tasks and architectures, the heavy-tailed form persists across all topologies, indicating that complex coordination in LLM multi-agent systems produces heterogeneous cascades spanning multiple scales. Deviations at the largest event sizes reflect finite-size truncation due to system constraints such as limited agent attention, bounded communication bandwidth, and task decomposition depth.
• Figure 4: Scale-dependent emergence of broad elite tiers.(a)(a) Top-$k$ active agents ($E^{\mathrm{active}}_{10}$, $E^{\mathrm{active}}_{25}$, $E^{\mathrm{active}}_{50}$) capture disproportionate shares of coordination effort relative to egalitarian baselines; $E^{\mathrm{all}}_{10}$ (dashed) confirms the result is not driven by inactive agents. of coordination effort relative to egalitarian baselines. (b) Excess concentration $\Delta^{\mathrm{active}}_k$ above equal participation increases with $N$, with strongest gains in the top decile and quartile. (c) Cumulative concentration curves vs $N$ increasingly bow above the equality line, indicating broader and more dominant elite tiers at scale.
• Figure 5: Preferential attachment is a core micro-mechanism behind heavy-tailed coordination and elite concentration in LLM agent societies. (a) The routing ratio $R(x,N)$ rises above the null baseline once a claim accumulates prior engagement, and the effect strengthens with system size $N$, revealing scale-dependent preferential amplification before saturating in the tail. (b) Estimated attachment slopes $\hat{\beta}$ vary systematically across topology and task type, with stronger reinforcement in star, fully connected, and modular societies than in tree or chain settings. (c) Event types differ in cascade-sustaining power: delegation and contradiction occupy the high-amplification, high-continuation region, while revision is intermediate and merge fan-in remains comparatively local. (d) Conditions with larger condition-level attachment slope $\hat{\beta}$ also exhibit larger top-10% effort share $E^{\mathrm{active}}_{10}$, linking local reinforcement directly to macro-level elite concentration.