Predicting the scale limits of social mechanisms in agent societies
Organizations: University of Osaka Osaka, Japan
Abstract
Societies of interacting language-model agents offer a controllable and repeatable way to study collective behaviour at scales that would be difficult to test with people. Their scientific value, however, depends on whether a social mechanism that works in a small group still operates when thousands of agents interact, and testing this directly requires costly large-scale runs. Here we introduce an audit that predicts a mechanism's fate as a population grows. It asks how often the mechanism can act, whether agents use the information it supplies, and whether the measurement itself creates apparent scale effects. Controlled experiments show that a single structural term can decide whether reciprocity, consensus or punishment survives scaling. For gossip, the population at which the mechanism fails is set by the reach and lifetime of its messages. In language-model societies, agents respond not only to social information but to how it is expressed: counts and percentages led to different scale behaviour. Predictions made before execution held on third-party code and a second model family, while a failed prediction exposed the boundary of the finding. The audit provides a prospective way to decide which social mechanisms can be interpreted across population scales.
Figures & tables
Appendix figures & tables23 assets
Supplementary material from the paper’s appendix.
Appendix
| Code | Name | Rule and diagnostic | Use in predictions |
| C1 | Scale-comparable observable | The observable must have an -comparable interpretation. Extensive counts and whole-population conjunctions, such as , carry mechanical size dependence and require normalisation or a separate null model | prediction undefined if violated |
| C2 | Activatability | Mechanism must activate at the reference scale or under exogenous seeding. Zero ignition only at large is a positive A2-class result, zero ignition everywhere is an invalid test | validity gate |
| C3 | Causal neighbourhood | Neighbourhood within the measurement horizon must clear the boundary and stay locally isomorphic across . On rings this reduces to . Globally coupled systems need separate argument | validity gate for small |
| C4 | Endgame isolation | Final rounds of known horizons excluded or reported separately | measurement window |
| C5 | Dynamic range | No ceilings or floors. Saturated cells are retuned and excluded from adjudication | measurement window |
| E1 | Identity-indexed input | Decision function indexed by the identity of the object | routes to A2 coverage audit |
| Code | Name | Rule and diagnostic | Use in predictions |
| A1 | Re-encounter probability | Pair re-interaction probability, under random matching . Diagnostic: count the pair generator | decay or transition of |
| A2 | Targeted coverage | Probability that a decision point holds information about the current object, . Diagnostic: measure the informed fraction | decay or transition of |
| A3 | Monitoring reach | Probability that behaviour is observed by a potential sanctioner. Diagnostic: count observation edges | decay or transition of |
| A4 | Time budget | Convergence time against a fixed horizon . Diagnostic: measure , discriminate by extending | decay or transition of |
| A5 | Update-step dilution | A factor inside the update step of a global aggregate. Diagnostic: read the update rule | decay or transition of |
| I1 | Memory-flux lifetime | , harmonic mean-field approximation under independent hazards | shifts turning scale only |
| System | Path | Input (E) | (source) | (source) | Codes | Filed class | Outcome |
|---|---|---|---|---|---|---|---|
| Pair A, direct (anchor) | remembered re-encounter | partner identity (E1) | under random matching (code) | full conditional defection (code) | A1 | transition | collapse at – at threshold |
| Pair A, network | neighbour clustering | neighbour payoffs | -independent local structure (code) | imitation of best neighbour (code) | – | flat | share stable near to |
| Pair B, local (anchor) | convergence within budget | neighbour opinions | outruns fixed (measured) | majority adoption (code) | A4 | transition | frozen from |
| Pair B, global | mean-field sampling | sampled opinions | -independent (code) | same (code) | – | flat | flat to |
| Pair C, sequential (anchor) | informative decisions | public record | saturates near four (measured) | cascade adoption (code) | – | flat below analytic anchor | pinned near vs |
| Pair C, independent | private signals | own signal | grows with (code) | majority count (code) | – | growth |
| System | Path | Input (E) | (source) | (source) | Codes | Filed class | Outcome |
|---|---|---|---|---|---|---|---|
| Count channel | targeted report | report count (E3, probed) | stated not consumed, no dilution path (probes) | give on targeted report. Dose per (probes) | E3 | flat in stated | no detected stated-size dependence, four engines |
| Percentage channel | stated ratio | explicit percentage (E3, probed) | report always delivered in probes; its stated ratio falls with | threshold (Firth ) or graded ( ) response to the ratio (probes) | E3 | decay in stated | negative interactions, both model families |
| Composed mechanism | ignition, transmission, sanction | identity marks (E1) | fired at . Zero ignition at over decisions | probe values above | A2, C2, C4 | window-qualified composition | residual zero in window. Whole-run verdicts failed on final round |
| Third-party library | within-match re-encounter | partner identity (E1) | repeat turns per opponent fall under per-capita budget (code) | strategy payoff structure (code) | A1, A4 | sign flip in – | filed quantities exact |
| Engine (as reported) | Resolved identity | Access | Notes and run dates |
|---|---|---|---|
| Primary engine, early probes | claude-sonnet-4-6 | vendor CLI | targeted, placebo, count and proportion probes and wording robustness (2026-07-12). Envelopes not logged in this early batch |
| Primary engine, later runs | claude-sonnet-5 | vendor CLI | confirmatory rerun, count lattice, factor separations, cross-model-family test, percentage lattice (2026-07-13 to 07-20). Full envelopes. Provider fixes sampling temperature |
| Opus family | claude-opus-4-8 | vendor CLI | cross-model probes (2026-07-12) and factor-separation reruns (2026-07-19) |
| GPT-5.5 | gpt-5.5 via the codex agent CLI | vendor CLI | cross-model probes (2026-07-12) and count lattice (2026-07-22). Reasoning-capable configuration |
| Gemini | gemini-3.5-flash | public API | cross-family probes, count lattice, temperature sweep at (2026-07-19 to 07-22) |
| DeepSeek | deepseek-v4-flash | public API | accessed with reasoning mode on (reasoner) and off (chat) over fixed weights. Percentage and count lattices, cross-model-family test (2026-07-19 to 07-22) |
| 0.708 (24) | 0.500 (24) | 0.583 (24) | |
| 0.958 (24) | 0.917 (24) | 1.000 (24) | |
| 0.875 (24) | 0.625 (24) | 0.792 (24) | |
| 0.750 (24) | 0.708 (24) | 0.792 (24) |
| 0.667 (24) | 0.750 (24) | 0.875 (24) | |
| 0.333 (24) | 0.500 (24) | 0.292 (24) | |
| 0.167 (24) | 0.250 (24) | 0.174 (23) | |
| 0.208 (24) | 0.500 (24) | 0.167 (24) |
| 1.000 (24) | 1.000 (24) | 1.000 (24) | |
| 0.917 (24) | 1.000 (24) | 0.708 (24) | |
| 0.292 (24) | 0.458 (24) | 0.250 (24) | |
| 0.083 (24) | 0.208 (24) | 0.208 (24) |
| 0.958 (24) | 1.000 (24) | 0.917 (24) | |
| 0.833 (24) | 0.792 (24) | 0.833 (24) | |
| 0.667 (24) | 0.625 (24) | 0.792 (24) | |
| 0.583 (24) | 0.458 (24) | 0.708 (24) |
| 0.833 (24) | 0.708 (24) | 0.583 (24) | |
| 1.000 (24) | 1.000 (24) | 1.000 (24) | |
| 1.000 (24) | 1.000 (24) | 1.000 (24) | |
| 0.000 (24) | 0.958 (24) | 1.000 (24) |
| 0.833 (24) | 0.458 (24) | 0.583 (24) | |
| 0.667 (24) | 0.958 (24) | 0.625 (24) | |
| 0.304 (23) | 0.750 (24) | 0.792 (24) | |
| 0.042 (24) | 0.333 (24) | 0.542 (24) |
| No information | 0.833 (24) | 0.833 (24) | 0.792 (24) | 0.750 (24) |
|---|---|---|---|---|
| Proportion-format report ( ) | 0.000 (24) | 0.500 (24) | 0.708 (24) | 0.875 (24) |
| No information | 1.000 (24) | 0.958 (24) | 0.792 (24) | 0.792 (24) |
|---|---|---|---|---|
| Proportion-format report ( ) | 0.583 (24) | 1.000 (24) | 1.000 (24) | 1.000 (24) |
| No information | 1.000 (24) | 1.000 (24) | 1.000 (24) |
|---|---|---|---|
| Targeted report | 0.000 (24) | 0.000 (24) | 0.000 (24) |
| Count report, | 0.000 (24) | 0.000 (24) | 0.000 (24) |
| Half | Area | Submissions | Reviews | Clust. |
|---|---|---|---|---|
| D | alignment, fairness, safety, privacy, and societal co… | 1048 | 4225 | 0.586 |
| D | applications to computer vision, audio, language, and… | 1373 | 5528 | 0.594 |
| D | applications to physical sciences (physics, chemistry… | 543 | 2204 | 0.592 |
| D | applications to robotics, autonomy, planning | 244 | 973 | 0.624 |
| D | generative models | 1063 | 4278 | 0.603 |
| D | learning theory | 365 | 1460 | 0.609 |
| Venue | Roots | Reviews | Official figure | Note |
|---|---|---|---|---|
| ICLR 2024 | 7,404 | 28,028 | 7,262 submissions reported | reviewed forums equal official count exactly |
| ICLR 2025 | 11,672 | 46,748 | 11,672 / 11,603 | roots minus desk = 11,602, Fact Sheet 11,603 |
| ICLR 2026 | 19,814 | 75,859 | 19,525 valid; 779 desk | API desk count 908 at extraction; enforcement continued |
| TMLR | 7,576 | 21,454 | about 4,026 searchable | invitation enumeration more complete |
| Format | Engine | Fit | |||||
|---|---|---|---|---|---|---|---|
| count | sonnet (primary) | GLM | 288 | ||||
| count | reasoner | GLM | 287 | ||||
| count | gemini | Firth | 288 | ||||
| count | gpt-5.5 | GLM | 288 | ||||
| pct | reasoner | GLM | 287 | ||||
| pct | sonnet | Firth | 288 |
| Pool | Arm | Payoff advantage per turn | |
|---|---|---|---|
| II Grudger | per-capita budget | 6 | |
| II Grudger | per-capita budget | 12 | |
| II Grudger | per-capita budget | 24 | |
| II Grudger | per-capita budget | 48 | |
| II Grudger | per-capita budget | 96 | |
| II Grudger | fixed match length | 6 |
| Registered criterion | Graded arm | Flatness arm |
|---|---|---|
| Give rate strictly monotone in | pass | – |
| Anchor: give at | pass | – |
| Anchor: give at | pass | – |
| Interior: at | pass | – |
| Interior: at | pass | – |
| Give-rate rise of at least across the tested range | pass | – |
| Registered criterion | gemini-3.5-flash | gpt-5.5 | deepseek-reasoner |
|---|---|---|---|
| (i) dose effect , | pass | pass | fail |
| (ii) 95% CI for contains | pass | pass | pass |
| (iii) anti-diagonal give-rate spread | pass | pass | pass |
| Engine | B | T | X | Count | Pct 8 | Pct 1000 |
|---|---|---|---|---|---|---|
| claude-sonnet-4-6 | 1.00 | 0.00 | 1.00 | 0.00 | 0.96 | – |
| claude-opus-4-8 | 1.00 | 0.50 | 1.00 | 0.75 | 0.96 | – |
| gpt-5.5 | 0.92 | 0.00 | 0.96 | 0.00 | 0.00 | 0.17 |
| gemini-3.5-flash | 1.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.04 |
| deepseek-chat | 1.00 | 1.00 | 0.96 | 0.25 | 0.83 | 0.96 |
| deepseek-reasoner | 0.92 | 0.00 | 0.75 | 0.00 | 0.17 | 0.88 |
| Outcome | What followed |
|---|---|
| Exponent test failed under bounded memory (slope ) | memory turnover identified as a candidate violated assumption. A separately registered amendment using unbounded memory and an absolute threshold passed with slope , without isolating which change accounted for the difference |
| Aggregate verdict inconclusive in the routing pair | mandatory component metrics and the path decomposition step |
| Flatness failed at the smallest population | causal neighbourhood condition. Registered retest above threshold passed with spread |
| Registered sign prediction failed in the early gossip design | sign treated as implementation property, demonstrated by the refusal variant |
| Two composed-system verdicts failed on the final round | endgame isolation rule for live runs |
| A registered interpretation was refuted by its own control cell | the format account of proportion framing |
Large Language Model-Based Social Simulation
Large language model-based social simulation studies how language-model agents represent people and interact to produce social behavior.
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