Coupling Gain: Measuring When Emergent Consensus Is Real in LLM Agent Societies

Code and per-run logs for the paper:

When Is Emergent Consensus Real? A Measured Coupling Gain and a Validity Diagnostic for LLM Agent Societies Dongxu Yang (DeepLethe). Preprint, 2026. arXiv: to be added.

We replace demonstration with measurement. The central quantity is the coupling gain gamma — a per-agent susceptibility measured directly from an LLM by counterfactually perturbing a neighbour's stated opinion. From gamma (plus a backfire coefficient beta and a modality-matched group coupling p_ft) we organise the macro outcome of an agent society into consensus, pluralism, and (induced) polarization, and we supply a (slope, bias) validity diagnostic that separates a genuine social dynamic from a model-prior artifact.

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Setup

Python 3.9+ and an OpenRouter API key.

pip install -r requirements.txt          # only matplotlib, for the figures
cp .env.example .env                      # then put your real key in .env
# .env contents:  OPENROUTER_API_KEY=sk-or-v1-...

The model client (or_client.py) reads the key from .env; the key is never hard-coded. Everything except figure rendering is standard-library only — bootstrap CIs and permutation tests are hand-rolled (no scipy/numpy).

Running the live probes calls paid LLM APIs. If you only want to re-derive the numbers in the paper, the results/*.log files are the raw per-run records and the analysis scripts below read straight from them — no API calls needed.

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Reproducing the paper

The committed results/*.log are the actual per-run logs the paper is built from. Re-run an analysis (no API needed):

Paper claim	Analysis script	Reads / writes
gamma table + bootstrap 95% CIs (Fig. 1)	bootstrap_ci.py	results/gamma_reps.log
Open-weight replication of gamma	open_gamma.py, open_gamma_one.py	results/open_gamma*.log
Social-neighbour vs numeric-anchor control	sycophancy_control.py	results/sycophancy_control.log
No spontaneous backfire (beta <= 0)	backfire.py	(live probe)
Induced polarization, t(4)=23.5	induced_reps.py	results/induced_reps.log
(slope, bias) authenticity diagnostic	prop_authenticity.py, authenticity_reps.py	results/authenticity_reps.log
Boundary-censoring confound ruled out	censoring_control.py	results/censoring_control.log
Interior-fact control (Table 2)	interior_measure_ci.py, interior_demo.py	results/interior_*.log
Chuang et al. (2023) re-analysis	run_debunk.py	(live probe)
Independent prior-p calibration	p_calibration.py	results/p_calibration.log
Free-text group pull p_ft	transfer_group_ft.py	results/transfer_group_ft.log
Society convergence (clean)	transfer_converge_clean.py	results/transfer_converge_clean.log
p_ft -> final spread, r=-0.70, perm p=0.008 (n=16)	correlate.py	results/transfer_*
gamma <-> p_ft anti-correlation + leave-one-out (Prop. 4)	correlate_gp.py	results/gamma_reps.log, open_gamma*.log, transfer_group_ft.log
Per-(model, condition) separation	analyze_clean.py	results/transfer_converge_clean.log
Figures 1-7	make_figures.py	results/* -> fig*.pdf

Core engine: or_client.py (OpenRouter client), jot.py (durable append-only logging used by every probe), society.py / network.py (multi-agent loop).

Example:

python correlate.py          # p_ft <-> spread correlation, permutation test
python correlate_gp.py       # gamma <-> p_ft, with leave-one-model-out
python bootstrap_ci.py       # gamma bootstrap CIs
python make_figures.py       # regenerate fig1..fig7

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Data integrity

An early version of the society loop had a silent-freeze bug: when an API call returned no content, the agent's stance was silently kept, fabricating a spurious "hold". We fixed it (retry + fallback-parse, and we discard runs with any true failure rather than fabricate data — genuine holds are kept, distinguished by fails == 0, not by a frozen trajectory), re-ran the affected cells, and audited every convergence log. audit_frozen.py is that audit, and both the contaminated and the clean logs are committed so the fix is verifiable (results/transfer_converge.log vs results/transfer_converge_clean.log).

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Citation

@misc{yang2026coupling,
  title         = {When Is Emergent Consensus Real? A Measured Coupling Gain and
                   a Validity Diagnostic for LLM Agent Societies},
  author        = {Yang, Dongxu},
  year          = {2026},
  eprint        = {XXXX.XXXXX},
  archivePrefix = {arXiv},
  primaryClass  = {cs.CL}
}

(Update eprint with the arXiv id once posted.)

License

MIT.