Emergent Relational Order in LLM Agent Societies: From Collective Affect to Authority Stratification

Simulating societies of many large language model (LLM) agents is expensive, yet the questions asked of such simulations are usually macroscopic: phase behaviour, stylised facts, and scaling with the number of agents $N$, not the cognition of any single agent. We turn a statistical-physics observation into a method: replace each LLM agent by a low-parameter model fitted from a few hundred to a few thousand cheap queries, then run the society at any $N$ on a laptop. Whether this works is decided before the simulation runs, chiefly by what each agent perceives. We introduce an [interaction order x memory] taxonomy that maps perception and memory to an effective theory and a predicted $N$-trend of the surrogate error. We validate it on a faithful reimplementation of the LLM macroeconomy EconAgent and seven further named LLM simulations, with agent decisions cloned from genuine LLM elicitations (primarily DeepSeek) for a few dollars; the predicted error trends hold cell by cell, and the two refuted predictions, both on a strongly saturating response and traced to its curvature, are themselves matched quantitatively by the theory with no free parameters.

Large language models (LLMs) are increasingly deployed in multi-agent environments. However, the processes by which beliefs form and propagate among interacting LLMs remain poorly understood. We introduce CoevolveSim, a framework for studying belief diffusion within networked LLM populations. CoevolveSim allows us to isolate and study three factors: domain specialization, social-role assignment, and social network structure. Within this framework, generalist and specialist LLM agents exchange and revise beliefs. In each round, an LLM agent observes a summary of its neighbors' beliefs before updating its own. We run 1,280 controlled simulations spanning four scenarios, two network structures, and 20 medical-indication statements. We find that persona-style role assignment and network structure reshape individual belief revision but have minimal effect on population-level consensus. In contrast, introducing (finetuned) specialist LLMs more than doubles the shift in consensus and gives rise to consistent asymmetries in exerted influence. We further show that simple persistence-based opinion-dynamics models reproduce collective outcomes in all-generalist LLM populations, whereas heterogeneous LLM populations require population-level belief composition to reproduce consensus and agent identity to predict individual belief transitions. Our results indicate that realistic simulation of belief diffusion in multi-agent LLM systems requires a diverse set of underlying LLMs, not persona prompting alone.

Large language models (LLMs) can simulate human-like reasoning and decision-making in individual agents. LLM-powered multi-agent systems (MAS) combine such agents to simulate population-scale social phenomena such as polarization, information cascades, and market panics. Such studies require attributing macro emergence to individual agents, but existing axiomatic methods scale combinatorially in $N$ and have been confined to $N \lesssim 10^3$, while the phenomena they explain occur at $N \geq 10^6$. We address this gap by adapting Aumann--Shapley path-integral attribution to LLM-powered MAS at million-agent scale; the resulting method satisfies all four axioms, runs three to five orders of magnitude faster than sampled Shapley on the same hardware, and extends feasible axiomatic attribution by over three orders of magnitude (a $1670\times$ jump). We use this method to test the scale gap empirically: across 14 days of public Bluesky data ($1{,}671{,}587$ active users, five topics), we compute the attribution at both full scale and the visibility-biased $N = 10^2$ convenience sample used by small-scale studies, and the two disagree structurally. At full scale the long tail and middle tier jointly carry the majority; the biased small panel shifts about twice that share onto the upper follower tiers ($48\%$ versus $24\%$). We then prove that the disagreement cannot in general be reduced by post-hoc rescaling: an Attribution Scaling Bias theorem shows that a reconciling global rescaling factor exists exactly when the macro indicator is linear over agents, and our nonlinear indicators give residuals of $0.10$--$0.98$. For such nonlinear indicators, full-scale attribution is therefore a requirement rather than a methodological choice.