Consensus and Factual Dynamics in Large Populations of Interacting Language Models

LLM "agent societies" are studied via demonstrations of emergent consensus or polarization -- with no measurable control parameter, no theory of when each regime appears, and no test of whether an outcome is a genuine social dynamic or a model artifact. We introduce the coupling gain gamma, measured per-agent by counterfactually perturbing a neighbour's stated opinion. (i) gamma is stable and model-distinguishing -- across five frontier models it spans 0.15-0.43 (n=20, 95% CIs <= 0.025), paraphrase-invariant; social-neighbour gamma roughly equals numeric-anchor gamma, so gamma is evidence-coupling, not uniquely social. (ii) Classical dynamics with measured (not assumed) coefficients organise the regime: Friedkin-Johnsen for consensus/pluralism, signed-Laplacian/structural-balance for polarization. (iii) Frontier LLMs do not spontaneously backfire (beta <= 0), so default societies do not self-polarize -- polarization is always induced; the beta>0 branch arises only in the FJ surrogate, never in the agents. (iv) A randomized-initial-condition diagnostic -- the (slope, bias) of final vs. initial opinion -- separates genuine averaging from model-prior artifacts (boundary-censoring ruled out by construction via interior-valued facts); applied to a published "emergent consensus" result (Chuang et al. 2023) it reveals a model-specific conflation: averaging on debatable claims, prior-artifact on settled facts. (v) Coupling is context-dependent: pairwise gamma does not predict multi-neighbour outcomes -- it can order them backwards -- whereas a modality-matched group coupling does (sixteen closed+open models, Pearson r=-0.70, permutation p=0.008). The regime laws take this matched coupling, not the single-neighbour gamma: emergent consensus must be read from coupling in the target interaction. We contribute a measurement protocol and a validity instrument, not new theory.

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.

Decentralized populations of Large Language Model (LLM) agents can spontaneously reach consensus on shared conventions, yet the microscopic mechanisms by which their internal stochasticity shapes macroscopic ordering remain unexplored. We study a minimal LLM Naming Game in which the listener's decision is a single-token LLM call at decoding temperature $T$, replacing the inventory check of the deterministic Naming Game. Each interaction decomposes into an in-inventory and an out-inventory channel with conditional rates $π(T)\!\equiv\!P(\text{YES}\mid w\in P_j)$ and $φ(T)\!\equiv\!P(\text{YES}\mid w\notin P_j)$, whose balance controls an ordering-disordering drift. A mean-field theory of the two-rate dynamics yields an analytical ordering condition that generalizes the consensus threshold of the stochastic Naming Game to a critical line in the $(π,φ)$ plane. Across three open-weight architectures, consensus is always reached, but through three distinct listener regimes: permissive (repaint-noise dominated), near-deterministic, and conservative (missed-collapse dominated). The effective finite-size exponent $β(T)$ in $t_{\rm conv}\!\sim\!N^β$ shifts with temperature, and the temperature-sensitivity $α$ in $t_c\!\sim\!e^{αT}$ ranges from ${\approx}\,0.67$ to ${\approx}\,0$ across architectures. Decoding temperature thus emerges as an architecture-dependent control parameter for decentralized LLM populations, quantitatively characterized by the statistical-physics toolkit.