When Is Emergent Consensus Real? A Measured Coupling Gain and a Validity Diagnostic for LLM Agent Societies
For researchers studying LLM agent societies, the paper provides a measurement protocol and validity diagnostic to distinguish genuine social dynamics from model artifacts, addressing a critical methodological gap.
The paper introduces a measurable coupling gain gamma to diagnose whether emergent consensus in LLM agent societies reflects genuine social dynamics or model artifacts. Across five frontier models, gamma ranges 0.15–0.43 with narrow confidence intervals, and a randomized-initial-condition diagnostic reveals that a published 'emergent consensus' result conflates genuine averaging with prior artifacts on settled facts.
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.