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The Butterfly Effect in LLM Social Simulations: From Architecture Sensitivity to Robustness Audits

Jinyi Ye, Lei Cao, Ding Chen, Emilio Ferrara

arXiv:2610.28981v1cs.MA

TL;DR

LLM social simulations can be sensitive to implementation choices, complicating inference about the social processes they model. The paper audits controlled perturbations across repeated Prisoner’s Dilemma and echo-chamber simulations, finding that sensitivity varies across models and interaction settings. It introduces TRAILS and the Social Simulation Audit Card to connect robustness evidence with the scope of scientific claims.

  • Problem

    Realism and empirical grounding do not establish whether simulation conclusions remain stable across reasonable alternative configurations, leaving uncertain whether findings reflect modeled processes or implementation choices.

    Source: §1 · p. 2

  • Method

    The study varies selected representation and design choices across repeated Prisoner’s Dilemma and echo-chamber simulations, and organizes audit dimensions in TRAILS.

    Source: §1 · p. 2, §5 · p. 7

  • Results

    Sensitivity varied across perturbations, models, and outcomes; reciprocal interaction amplified or attenuated persona-representation effects, while echo-chamber representation changes were associated with differences in targeting and collective structure.

    Source: §1 · p. 2, §4.2 · p. 7, §6 · p. 9

  • Takeaways & Limitations

    Scientific claims from simulated societies can be scoped to the configurations, models, and interaction conditions for which robustness evidence is available.

    Source: §6 · p. 10

    The findings cover two simulation regimes, selected perturbations, four model families, and fixed interaction horizons, so the observed patterns should not be assumed to generalize to other settings.

    Source: §6 · p. 9

Abstract

from arXiv · show

A butterfly effect occurs when a local perturbation propagates through a system and produces divergence in its collective outcome. In LLM social simulations, this creates a particular challenge for scientific inference: sensitivity to implementation choices can enter agent interactions and alter the collective outcomes on which scientific claims are based. We study this problem through a repeated Prisoner's Dilemma and a social-media echo chamber, spanning representation- and design-level perturbations across four LLM families. We find that controlled perturbations can substantially alter collective outcomes, with sensitivity varying across both perturbations and models. In the Prisoner's Dilemma, changing only the representation of a matched persona shifts two-agent cooperation by 75.2 percentage points for GPT-5.2, while game framing and memory representation produce smaller or less consistent effects. Multi-agent interaction further reshapes representation sensitivity, producing amplification or attenuation depending on the model and perturbation. In the echo-chamber simulation, persona representation changes interaction targeting and is accompanied by divergence in collective interaction structure, extending representation sensitivity from agent behavior to network-level outcomes. These results show that robustness cannot be inferred from a single simulation configuration and that local sensitivity can change as it propagates through interaction. We introduce TRAILS (Taxonomy for Robustness Audits In LLM Simulations) and the Social Simulation Audit Card as a framework for systematically auditing these dependencies and calibrating the scope of scientific claims to the robustness evidence that supports them.

1 INTRODUCTION

LLM social simulations are increasingly used to explain social processes and inform decisions, but realism alone does not establish robustness. The paper tests how implementation choices affect outcomes and argues that scientific claims should be calibrated to robustness evidence.

1 INTRODUCTION

  • Realism, empirical correspondence, theory grounding, and human evaluation do not establish whether conclusions remain stable across reasonable alternative configurations.Without robustness tests, a finding may reflect either the modeled social process or the choices used to implement it.Source: §1 · pp. 1–2
  • A persona-format change shifted GPT-5.2 cooperation by 75.2 percentage points in an otherwise matched 10-round Prisoner’s Dilemma.The broader sensitivity patterns varied across perturbations and models, and reciprocal interaction amplified or attenuated representation effects depending on the model.Source: Figure 1 · p. 2, §1 · p. 2
  • Small representational changes can alter decisions that enter later interactions, memories, or social signals, compounding or attenuating differences in collective outcomes.The paper calls this interaction-mediated propagation of behavioral sensitivity the butterfly effect.Source: §1 · p. 2
  • The study compares a repeated Prisoner’s Dilemma under fixed-opponent and reciprocal LLM interaction with an echo-chamber simulation tracing agent choices to network structure.Both regimes span four LLM families and vary representation or design choices while holding other components fixed.Source: §1 · p. 2
  • TRAILS and the Social Simulation Audit Card organize robustness audits so claims can be scoped to the configurations, models, and interaction conditions covered by evidence.The framework connects audit results to the scope of scientific claims.Source: §1 · p. 2

2 RELATED WORK

Prior validation work assesses whether LLM social simulations plausibly represent their targets, while robustness asks whether conclusions persist under reasonable implementation alternatives. This paper examines controlled perturbations across two complementary collective-behavior settings.

LLM social simulation and the validation gap

  • Existing validation approaches assess plausibility, empirical correspondence, grounding, and human evaluation, while systematic analysis across representation, interaction, and design choices remains less developed.The paper frames robustness as whether conclusions persist under reasonable alternative implementations.Source: §2 · p. 3

From local LLM sensitivity to multi-agent propagation

  • Prior work documents sensitivity in LLM inputs and persona construction, but leaves open how controlled representation perturbations change in magnitude as agents interact.The study measures amplification or attenuation under reciprocal LLM–LLM interaction and traces sensitivity across behavioral and collective outcomes in networked interaction.Source: §2 · p. 3

Controlled testbeds for collective sensitivity

  • Repeated Prisoner’s Dilemma isolates comparison across fixed-opponent and reciprocal interaction, while echo chambers connect interaction choices to emergent network structure.The experiments isolate selected perturbations while holding non-targeted components fixed.Source: §2 · p. 3

3 METHOD

The method defines sensitivity through controlled changes to a simulation configuration, then measures how effects appear in repeated strategic interaction and networked social interaction. Across both testbeds, selected perturbations are compared while other components are held fixed.

3.1 CONCEPTUAL FRAMEWORK

  • A controlled perturbation changes one component of a simulation configuration while holding the remaining components fixed, and sensitivity measures the associated outcome change.The framework distinguishes representation changes in how a fixed specification is presented from design changes to the simulated system itself.Source: §3.1 · pp. 3–4

3.2 REPEATED PRISONER’S DILEMMA

  • The Prisoner’s Dilemma uses 10 rounds, four fixed opponent policies for single-agent play, and matched LLM agents for two-agent play, with persona format, game framing, and memory representation varied.Cooperation rate is the primary outcome and average per-round payoff the secondary outcome; each condition has 30 runs.Source: §3.2 · p. 4

3.3 SOCIAL-MEDIA ECHO CHAMBER

  • The echo-chamber test uses 100 agents over 15 rounds with fixed stances and varies persona representation plus five design dimensions.It measures cross-group targeting and collective network structure, compares action-type and target agreement across paired runs, and uses 30 independent runs per condition unless otherwise specified.Source: §3.3 · pp. 4–5

4 RESULTS

Across both simulation regimes, sensitivity varies by perturbation and model, and interaction can reshape how persona-representation differences develop. Effects range from shifted cooperation to changes in targeting and collective network structure.

4.1 SENSITIVITY VARIES ACROSS PERTURBATIONS AND MODELS

  • 75.2 percentage points: GPT-5.2 cooperation fell from 98.2% under PLAIN to 23.0% under DESCRIPTIVE in two-agent interaction.The matched-persona contrast also decreased average payoff by 1.48 points per round.Source: §4.1 · pp. 5–6
  • Persona format significantly shifted two-agent cooperation across all four model families, with largest contrasts from 7.7 percentage points for deepseek-v3.2 to 77.7 for claude-haiku-4-5.Game framing shifted cooperation significantly for a subset of models; memory representation did so only for GPT-5.2.Source: §4.1 · p. 6, Table 1 · p. 6
  • In the echo chamber, persona representation significantly changed same-group edge ratio across all four models and stance assortativity for two; activation probability affected both outcomes across all four.Memory window significantly affected both outcomes for three models, while recommendation feed size had smaller, more selective effects.Source: §4.1 · p. 6, Table 1 · p. 6

4.2 MULTI-AGENT INTERACTION RESHAPES REPRESENTATION SENSITIVITY

  • For GPT-5.2, cooperation sensitivity rose from Sfixed = 0.271 to SLLM = 0.752, giving A = 0.481; reciprocal interaction amplified sensitivity for Claude and Gemini but attenuated it for DeepSeek.Round-wise trajectories also differed across models.Source: §4.2 · p. 7, Figure 3 · p. 7
  • In GPT-5.2’s echo-chamber simulation, PROSE increased cross-group targeting by 5.15 percentage points and accompanied 0.194 lower cumulative stance assortativity by round 15.Action agreement was 99.7%, versus 55.1% target agreement; final assortativity differences were not statistically significant for Claude and DeepSeek.Source: §4.2 · p. 7

5 FROM ARCHITECTURE SENSITIVITY TO ROBUSTNESS AUDITS

The paper introduces TRAILS to organize robustness audits of LLM social simulations and the Social Simulation Audit Card to connect those audits to the scope of scientific claims.

5 FROM ARCHITECTURE SENSITIVITY TO ROBUSTNESS AUDITS

  • TRAILS organizes audit choices into representation-level perturbations (TRAILS-R) and design-level perturbations (TRAILS-D).TRAILS-D covers substantive simulation changes across eight dimensions and three levels; TRAILS-R covers five dimensions of how a fixed specification or context is presented.Source: §5 · pp. 7–8, Table 2 · p. 8
  • The Social Simulation Audit Card guides five steps, from stating a claim and mapping perturbations to defining the claim’s scope.It distinguishes context-relevant conditions, which help scope where a claim holds, from context-irrelevant choices, whose sensitivity indicates implementation dependence.Source: §5 · p. 9, Figure 5 · p. 9
  • The audit classifies outcomes as Robust, Scope-limited, Implementation-sensitive, or Inconclusive, bounded by the conditions audited.TRAILS covers the simulation system; measurement and evaluation sensitivity belong to the downstream evaluation pipeline.Source: §5 · pp. 8–9

6 CONCLUSIONS

Sensitivity varies across perturbations, models, and interaction regimes, and can extend from agent behavior to network structure. The authors conclude that robustness evidence from one configuration or model does not establish robustness of the scientific claim.

6 CONCLUSIONS

  • Persona representation shifts outcomes across several settings, while other perturbations have smaller or more selective effects and multi-agent interaction can amplify or attenuate sensitivity.In networked interaction, representation sensitivity appears in targeting and, for some models, collective network structure.Source: §6 · p. 9
  • The findings cover two simulation regimes, selected perturbations, four model families, and fixed interaction horizons, so their sensitivity patterns should not be assumed to generalize.The echo-chamber analysis holds stances fixed and does not establish a causal pathway from targeting differences to network divergence; robustness to implementation choices is only one dimension of simulation validity.Source: §6 · p. 9
  • TRAILS and the Social Simulation Audit Card provide a vocabulary and reporting structure for matching audit coverage to the claim and simulation context.The authors argue that claims can then be scoped to the configurations, models, and interaction conditions for which robustness evidence is available.Source: §6 · pp. 9–10

RELATIONSHIP TO EARLIER WORK

The present study extends an earlier position paper that introduced the robustness-audit perspective and TRAILS. Its extensions include systematic comparisons, measurement of interaction effects, and analysis of networked outcomes.

RELATIONSHIP TO EARLIER WORK

  • An earlier position paper introduced the robustness-audit perspective and TRAILS, using selected results from the same simulation settings as motivating examples.The present study extends that work through systematic comparisons across perturbations and models, explicit measurement of interaction amplification and attenuation, and analysis of behavioral and collective outcomes in networked interaction.Source: RELATIONSHIP TO EARLIER WORK · p. 14

A TRAILS (TAXONOMY FOR ROBUSTNESS AUDITS IN LLM SIMULATIONS)

TRAILS organizes audit choices across representation and design dimensions, while the paper situates audits in complementary strategic and open-ended social simulation settings. Audit coverage depends on the intended claim, the simulation’s openness, and the stakes of use.

A TRAILS (TAXONOMY FOR ROBUSTNESS AUDITS IN LLM SIMULATIONS)

  • TRAILS presents separate taxonomies for design-level and representation-level perturbations.The supplied tables are titled “TRAILS-D: Design-level perturbations” and “TRAILS-R: Representation-level perturbations.”Source: Table 3 · p. 15, Table 4 · p. 15

B.1 LLM-BASED SOCIAL SIMULATIONS

  • The paper focuses on collective human behavior arising from interacting LLM agents, distinguishing it from individual simulations, non-human or aggregate actors, and task-completion systems.Its testbeds contrast goal-structured scenarios with explicit incentives and rules against open-ended scenarios where repeated communication and engagement produce collective patterns.Source: §B.1 · p. 16
  • Audit requirements depend on the claim, simulation openness, and stakes: exploratory findings call for prompt, seed, and model checks, while mechanism and policy claims require broader coverage.Open-ended simulations expose more choices about communication, memory, and platform feedback, expanding the perturbation space.Source: §B.1 · p. 16

B.2 REPEATED PRISONER’S DILEMMA AS A GOAL-STRUCTURED TESTBED

  • Repeated Prisoner’s Dilemma offers a controlled testbed for cooperation and adaptation, with fixed actions, payoffs, and horizon enabling comparisons across fixed-opponent and reciprocal LLM–LLM interaction.The perturbations test whether matched persona content, alternative descriptions of the same payoff structure, and different history representations yield stable behavior.Source: §B.2 · p. 16

B.3 ECHO CHAMBERS AS AN OPEN-ENDED SOCIAL SIMULATION TESTBED

  • Echo-chamber simulations provide an open-ended setting where collective structure emerges from local engagement, allowing sensitivity to be traced from interaction targeting to the resulting network.The setting complements strategic interaction organized around a shared payoff.Source: §B.3 · p. 16
  • The echo-chamber audit varies persona presentation while preserving persona information, then tests participation, recent context, visible exposure, initial homophily, and which stance group occupies highly connected positions.The structural contrasts preserve the degree sequence for hub assignment and provide context-relevant conditions for the Audit Card.Source: §B.3 · p. 16

C ADDITIONAL EXPERIMENTAL DETAILS

This appendix details the Prisoner’s Dilemma and echo-chamber simulations, their outcome measures, controlled perturbations, and analyses, and explains how to interpret estimated perturbation differences, memory-condition abbreviations, and significance shading.

C.1.1 SETUP AND CONFIGURATIONS

  • The Prisoner’s Dilemma tests single-agent play against four fixed policies and matched two-agent play across four LLMs, using 10-round episodes and 30 runs per condition.Actions are simultaneous, with payoffs of (C, C) = (3, 3), (C, D) = (0, 5), (D, C) = (5, 0), and (D, D) = (1, 1).Source: §C.1.1 · p. 17

C.1.2 OUTCOME MEASURES

  • Cooperation rate is the primary outcome for comparing representation sensitivity across interaction regimes, while average payoff captures outcomes under the game’s incentives.Cooperation rate is the fraction of rounds an agent chooses C; average payoff is mean per-round reward.Source: §C.1.2 · p. 17

C.1.3 PERTURBATION DETAILS

  • Prisoner’s Dilemma perturbations vary matched persona format, game-instruction framing, and history presentation, including table or narrative formats with or without summary statistics.The memory design uses four variants; two-agent histories are role-specific, mapping “You” and “Other agent” to the appropriate player.Source: §C.1.3 · pp. 17–19

C.1.4 INTERACTION-AMPLIFICATION MEASURES

  • Interaction amplification compares representation effects in reciprocal LLM play with effects across fixed opponents, preserving opponent-specific differences in effect direction.Uncertainty uses 10,000 paired bootstrap replicates over 30 matched seeds, with percentile 95% confidence intervals; effects are also computed by round.Source: §C.1.4 · p. 20

C.2.1 SETUP AND CONFIGURATIONS

  • The echo-chamber simulation uses 100 agents over 15 rounds, with fixed stances, neighbor-based feeds, and POST, REPOST, REPLY, or DO NOTHING actions.Networks reuse a fixed heavy-tailed degree sequence with target mean degree 8 and exponent 2.4; conditions generally have 30 runs.Source: §C.2.1 · p. 20

C.2.2 OUTCOME MEASURES

  • Echo-chamber sensitivity is measured through paired action and target agreement, weighted stance assortativity, and the weighted same-group edge ratio.Assortativity distinguishes within-stance from cross-stance interaction relative to observed marginals; the edge ratio measures interaction volume within stance groups.Source: §C.2.2 · pp. 20–21

C.2.3 PERTURBATION DETAILS

  • Echo-chamber perturbations vary persona presentation and five design factors: network homophily, hub assignment, activation probability, memory window, and recommendation-feed size.Persona information is presented as bullets or prose; other comparisons include activation probabilities 0.3 and 0.5, memory windows of 2 and 4 rounds, and feeds of up to 5 or 10 posts.Source: §C.2.3 · pp. 21–22

C.2.4 PROPAGATION MEASURES

  • Propagation measures track cross-group targeting effects and sensitivity over time, alongside behavioral and collective-network effects, to locate where persona-representation sensitivity develops.Paired runs also compare action-type and interaction-target agreement.Source: §C.2.4 · p. 22
  • Cooperation differences use percentage points, payoff differences use native units, and Holm-corrected significance is marked by asterisks; memory contrasts use NR, NS, TR, and TS.Unshaded cells are not statistically significant; NR = Narrative-Raw, NS = Narrative+Stats, TR = Table-Raw, and TS = Table+Stats.Source: §C.2.4 · p. 23

D EXTENDED EXPERIMENTAL RESULTS

The extended results report pairwise Prisoner’s Dilemma contrasts, echo-chamber representation and design sensitivity, and network-structure dependencies on homophily and hub assignment.

Prisoner’s Dilemma results

  • Table 6 reports interaction-amplification results for prespecified Prisoner’s Dilemma representation contrasts, with A defined as SLLM − Sfixed.Sfixed summarizes effects across four fixed opponents; SLLM is the effect under reciprocal LLM–LLM interaction.Source: D EXTENDED EXPERIMENTAL RESULTS · pp. 23–24, Table 6 · p. 23

Network homophily and hub assignment

  • Figure 8 shows that echo-chamber interaction structure depends on initial network homophily and hub-group assignment, even when reassignment preserves the degree sequence.These context-relevant dependencies qualify the structural conditions under which an echo-chamber claim holds.Source: D EXTENDED EXPERIMENTAL RESULTS · p. 24

Echo-chamber results

  • Tables 7 and 8 report echo-chamber representation and design contrasts, respectively, across 30 paired seeds, with collective outcomes cumulative through round 15.Table 7 compares PROSE with BULLET; Table 8 compares higher with lower design conditions.Source: D EXTENDED EXPERIMENTAL RESULTS · p. 23, Table 7 · p. 25, Table 8 · p. 25
  • The design-sensitivity figures report round-wise targeting differences and cumulative assortativity contrasts with pointwise, unadjusted bootstrap confidence intervals.Assortativity is undefined in round 1 without eligible edges; these trajectories are not causal mediation or interaction-amplification estimates.Source: D EXTENDED EXPERIMENTAL RESULTS · p. 25

E THE SOCIAL SIMULATION AUDIT CARD

The Social Simulation Audit Card operationalizes TRAILS by linking a stated scientific claim to selected perturbations, evidence, and a bounded verdict. It distinguishes context-relevant sensitivity from implementation dependence.

Context relevance

  • TRAILS distinguishes context-relevant perturbations, which reveal conditions under which a claim holds, from context-irrelevant choices, which reveal implementation dependence.The Audit Card applies this claim-specific judgment alongside evidentiary role, simulation openness, and intended-use stakes.Source: E THE SOCIAL SIMULATION AUDIT CARD · p. 25

Audit procedure

  • The audit begins by stating the claim, evidentiary role, intended scope, and property that must be preserved.The preservation property may be a phenomenon’s presence, effect direction, or a quantitative effect within a stated tolerance.Source: E THE SOCIAL SIMULATION AUDIT CARD · p. 25

Sensitivity figures

  • The design-sensitivity figures compare round-wise targeting and cumulative assortativity under specified conditions, with pointwise bootstrap intervals.Figure 7 omits round 1 because assortativity is undefined without eligible edges; its trajectories are not causal mediation estimates.Source: Figure 6 · p. 26, Figure 7 · p. 26

Audit procedure

  • Auditors map each perturbation to TRAILS-D or TRAILS-R and assess its context relevance, then register alternatives, constants, models, runs, and preservation criteria.Unaudited dimensions and uncertainty requirements are recorded before results are examined.Source: E THE SOCIAL SIMULATION AUDIT CARD · p. 26

Interpreting and scoping results

  • Report effect sizes and uncertainty against the registered criterion, then classify the claim as Robust, Scope-limited, Implementation-sensitive, or Inconclusive.Statistical significance alone does not determine robustness; verdicts are bounded by audited dimensions and tested ranges.Source: E THE SOCIAL SIMULATION AUDIT CARD · pp. 26–27

Audit limits

  • Audit sufficiency depends on covering consequential dimensions with precision appropriate to the decision rule, while human-behavior generalization requires external validation.Every verdict should state tested ranges, model coverage, and remaining uncertainty.Source: E THE SOCIAL SIMULATION AUDIT CARD · p. 27

E.1 AUDITING SCIENTIFIC CLAIMS IN THE TWO CASE STUDIES

The case studies apply the Audit Card to cooperation and echo-chamber claims, finding substantial sensitivity to persona representation and qualifying verdicts by tested conditions. The accompanying templates specify how agents, prompts, feeds, and outputs are represented.

E.1 AUDITING SCIENTIFIC CLAIMS IN THE TWO CASE STUDIES

  • The audits summarize GPT-5.2 results from 30 independent runs per condition with shared seeds, and verdicts apply to the reported model, interaction conditions, and outcomes.Table 9 maps perturbations to their audit interpretations.Source: §E.1 · p. 27, Table 9 · p. 28
  • Changing the matched persona from PLAIN to DESCRIPTIVE reduced two-agent cooperation by 75.2 percentage points and supported an Implementation-sensitive verdict.Game framing, a context-relevant perturbation, had a maximum cooperation difference of 19.3 percentage points; memory representation had a smaller significant maximum difference of 6.2 points, subject to the specified tolerance.Source: §E.1 · pp. 27–28, Table 9 · p. 28
  • In the echo-chamber audit, PROSE increased cross-group targeting by 5.15 percentage points and lowered cumulative stance assortativity by 0.194, while the phenomenon-presence verdict remained Inconclusive.Activation probability significantly changed both collective outcomes, whereas memory window and recommendation feed size produced smaller, non-significant differences; the verdict was bounded to the audited claim and conditions.Source: §E.1 · p. 28, Table 9 · p. 28

F.1.1 BASE PERSONA; F.1.2 BASE SINGLE-AGENT PROMPT TEMPLATE

  • The Prisoner’s Dilemma base persona directs the participant to maximize long-term payoff, while the single-agent prompt uses an unrevealed fixed external opponent and history-based decisions.The prompt specifies a repeated game and asks the model to choose an action each round.Source: §F.1.1 · p. 28, §F.1.2 · pp. 28–29

F.1.3 BASE TWO-AGENT PROMPT TEMPLATE

  • In the two-agent Prisoner’s Dilemma template, both model-driven players receive the same prompt structure with role-specific histories.The template assigns agent roles and specifies simultaneous choices against another model-driven player.Source: §F.1.3 · p. 29

F.1.4 OUTPUT SCHEMA AND PARSING INSTRUCTION

  • Prisoner’s Dilemma outputs use JSON action and reason fields; if parsing fails, the fallback action is Defect.The parser first attempts to extract a JSON object from unparseable raw text.Source: §F.1.4 · p. 29

F.2.1 AGENT PERSONA TEMPLATE

  • Echo-chamber personas include an agent ID, short bio, follower count, and fixed AI-regulation stance on a five-point scale from −2 to 2.The scale ranges from strong opposition to strong support.Source: §F.2.1 · pp. 29–30

F.2.2 ROUND DECISION PROMPT; F.2.3 VISIBLE FEED FORMAT; F.2.4 OUTPUT SCHEMA AND PARSING INSTRUCTION

  • Each activated echo-chamber agent sees its profile, neighbor count, and recent neighbor posts, then chooses an action and may target a numbered feed item.The feed is a numbered list when recent posts are available; output schema restricts actions and fixes stance throughout the run.Source: §F.2.2 · p. 30, §F.2.3 · p. 30, §F.2.4 · p. 31
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