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

Jinyi Ye; Lei Cao; Ding Chen; Emilio Ferrara

cs.MAOct 20, 2026

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

Authors: Jinyi Ye, Lei Cao, Ding Chen, Emilio Ferrara

Organizations: University of Southern California

Abstract

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.

Figures & tables

Figure 1: The butterfly effect in LLM social simulations. Two representations of the same strategic persona produce a $75.2$ -percentage-point difference in cooperation in an otherwise matched 10-round Prisoner’s Dilemma ( gpt-5.2 , $N=30$ paired seeds, Holm-corrected $p<.001$ ). We study how such local sensitivity changes across perturbations, models, and multi-agent interaction, and use TRAILS to connect robustness audits to the scope of scientific claims.

Figure 2: Effect of persona format on Prisoner’s Dilemma outcomes ( gpt-5.2 ). Left: single-agent (fixed-opponent); right: two-agent (LLM–LLM). Bars show means with SD error bars; heatmaps show pairwise differences, with color indicating significance ( $p<.05$ ) and gray non-significance.

Perturbation	Metric	GPT-5.2	Claude Haiku 4.5	Gemini 2.5 Flash	DeepSeek
Repeated Prisoner’s Dilemma (Two-Agent): $\max\|\Delta\|$
Persona format R	Average payoff	1.48***	1.49***	0.79***	0.14**
Persona format R	Cooperation rate (pp)	75.2***	77.7***	36.0***	7.7**
Game framing R	Average payoff	0.42***	0.09*	0.19	0.15***
Game framing R	Cooperation rate (pp)	19.3***	3.3*	9.0	8.8***
Memory representation R	Average payoff	0.10***	0.05	0.29	0.01

Table 1: Outcome sensitivity across perturbations and models.

\Delta

denotes the difference in outcome means between two perturbation conditions.

Figure 3: Interaction reshapes persona-representation sensitivity in the repeated Prisoner’s Dilemma. Plain vs. Descriptive , $N=30$ paired seeds. (a) Cooperation-rate sensitivity under fixed-opponent and LLM–LLM interaction. (b) Interaction effect gap $A=S^{\mathrm{LLM}}-S^{\mathrm{fixed}}$ ; positive values indicate amplification and negative values attenuation. (c) Round-wise effect gap $A_{t}$ . Intervals and bands show paired-bootstrap 95% CIs.

Figure 4: Persona-representation sensitivity across interaction levels in the echo-chamber simulation. Prose vs. Bullet , $N=30$ paired seeds. (a) Agreement in action type and interaction target. (b) Cross-group targeting difference $\Delta_{\mathrm{target},t}$ ; positive values indicate more cross-group targeting under Prose . (c) Weighted stance-assortativity difference $\Delta_{r,t}$ ; negative values indicate lower assortativity under Prose . Error bars and bands show 95% CIs.

Level	Dimension	Description	Examples
TRAILS-R: Representation-level perturbations
	Representational format	Alternative encodings of a matched agent or task specification, including prose, lists, tables, and structured formats; persona format	Salinas and Morstatter (2024) ; Sclar et al. (2024) .
	Instruction hierarchy	Instruction order, placement, grouping, and authority across prompt components	Salinas and Morstatter (2024) ; Sclar et al. (2024) .
	Linguistic framing	Alternative wording or labels while other simulation components are held fixed; game-instruction framing	Salinas and Morstatter (2024) ; Sclar et al. (2024) .
	Context representation	Alternative representations or encodings of the same interaction history and contextual information; memory representation	Park et al. (2023) ; Salinas and Morstatter (2024) .
	Interaction sequencing	Presentation or ordering of otherwise matched interactions	Mou et al. (2024) .

Table 2: TRAILS: Taxonomy for Robustness Audits in LLM Simulations. TRAILS distinguishes representation-level perturbations (TRAILS-R), which vary how a fixed simulation specification or context is presented to LLM agents, from design-level perturbations (TRAILS-D), which vary components of the simulated system itself. Bolded examples indicate perturbations examined in our case studies.

Figure 5: The Social Simulation Audit Card. The five-step workflow connects perturbation selection and sensitivity analysis to the scope of scientific claims. GPT-5.2 examples illustrate two interpretations of sensitivity: a context-irrelevant persona-format change reveals implementation dependence in the repeated Prisoner’s Dilemma, whereas context-relevant network homophily bounds the conditions under which echo-chamber-like interaction structure is supported.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Level	Dimension	What to perturb
Micro	Model substrate	Model family, model size, base vs. instruction-tuned models, alignment, temperature, top- $p$ , random seed, safeguards.
	Agent specification	Demographics, ideology, personality, goals, prior beliefs, real-data-grounded vs. synthetic personas, relationship attributes.
	Internal state and cognition	Beliefs, attitudes, emotions, needs, moral values, reasoning style, reflection rules, belief updating, preference updating.
	Memory and temporality	last- $k$ memory, summarized memory, episodic memory, retrieval rules, forgetting, reflection frequency, temporal granularity.
Meso	Interaction protocol	Turn order, fixed or free turns, dyadic or group interaction, available actions
	Intervention design	Moderator type, target selection, timing, frequency, rule-based vs. LLM-based intervention.

Appendix

Table 3: TRAILS-D: Design-level perturbations

Category	Perturbation	Example
Representational format	Formatting	Narrative prose vs. bullet points; paragraph vs. table; bolded keywords; numbered lists.
	Delimiter choice	Conversation history enclosed in code blocks, XML tags, JSON, or plain text.
	Output schema	Free-form paragraph vs. short reply vs. JSON with rationale.
Instruction hierarchy	Instruction order	“Update your opinion, then write a reply” vs. “Write a reply, then update your opinion.”
	Role/message placement	The same instruction placed in the system message vs. the user message.
Linguistic framing	Agent naming	Agent A/B vs. Alice/Bob.

Appendix

Table 4: TRAILS-R: Representation-level perturbations

Perturbation	Outcome	Contrast	GPT-5.2	Claude Haiku 4.5	Gemini 2.5 Flash	DeepSeek V3.2
Repeated Prisoner’s Dilemma (Two-Agent)
Persona	Average payoff	Descriptive $\rightarrow$ Tabular	+1.467***	+1.223***	-0.010	-0.127
		Plain $\rightarrow$ Descriptive	-1.478***	-1.487***	-0.777***	-0.013*
		Plain $\rightarrow$ Tabular	-0.012	-0.263***	-0.787***	-0.140**
Persona	Cooperation rate (pp)	Descriptive $\rightarrow$ Tabular	+74.000***	+63.333***	-0.333	-6.333
		Plain $\rightarrow$ Descriptive	-75.167***	-77.667***	-35.667***	-1.333*

Appendix

Table 5: Pairwise contrasts in the Prisoner’s Dilemma experiment across perturbations, representations, and models.

\Delta

denotes the difference in outcome means between two perturbation conditions.

Contrast	GPT-5.2	Claude Haiku 4.5	Gemini 2.5 Flash	DeepSeek V3.2
Persona format
Plain vs Descriptive	$S_{\mathrm{fixed}}$ = 0.271 $S_{\mathrm{LLM}}$ = 0.752 $A$ = +0.481 [+0.327, +0.622] Amplification	$S_{\mathrm{fixed}}$ = 0.315 $S_{\mathrm{LLM}}$ = 0.777 $A$ = +0.462 [+0.376, +0.529] Amplification	$S_{\mathrm{fixed}}$ = 0.070 $S_{\mathrm{LLM}}$ = 0.357 $A$ = +0.287 [+0.190, +0.387] Amplification	$S_{\mathrm{fixed}}$ = 0.101 $S_{\mathrm{LLM}}$ = 0.013 $A$ = -0.087 [-0.108, -0.066] Attenuation
Plain vs Tabular	$S_{\mathrm{fixed}}$ = 0.589 $S_{\mathrm{LLM}}$ = 0.012 $A$ = -0.578 [-0.602, -0.556] Attenuation	$S_{\mathrm{fixed}}$ = 0.429 $S_{\mathrm{LLM}}$ = 0.143 $A$ = -0.286 [-0.341, -0.223] Attenuation	$S_{\mathrm{fixed}}$ = 0.074 $S_{\mathrm{LLM}}$ = 0.360 $A$ = +0.286 [+0.192, +0.384] Amplification	$S_{\mathrm{fixed}}$ = 0.055 $S_{\mathrm{LLM}}$ = 0.077 $A$ = +0.022 [-0.050, +0.121] No detectable difference
Descriptive vs Tabular	$S_{\mathrm{fixed}}$ = 0.318 $S_{\mathrm{LLM}}$ = 0.740 $A$ = +0.422 [+0.295, +0.546] Amplification	$S_{\mathrm{fixed}}$ = 0.244 $S_{\mathrm{LLM}}$ = 0.633 $A$ = +0.389 [+0.291, +0.481] Amplification	$S_{\mathrm{fixed}}$ = 0.004 $S_{\mathrm{LLM}}$ = 0.003 $A$ = -0.001 [-0.006, +0.013] No detectable difference	$S_{\mathrm{fixed}}$ = 0.054 $S_{\mathrm{LLM}}$ = 0.063 $A$ = +0.009 [-0.057, +0.102] No detectable difference
Game framing
Canonical vs Moralized	$S_{\mathrm{fixed}}$ = 0.117 $S_{\mathrm{LLM}}$ = 0.193 $A$ = +0.077 [+0.024, +0.127] Amplification	$S_{\mathrm{fixed}}$ = 0.058 $S_{\mathrm{LLM}}$ = 0.008 $A$ = -0.050 [-0.067, -0.007] Attenuation	$S_{\mathrm{fixed}}$ = 0.025 $S_{\mathrm{LLM}}$ = 0.090 $A$ = +0.065 [-0.022, +0.143] No detectable difference	$S_{\mathrm{fixed}}$ = 0.016 $S_{\mathrm{LLM}}$ = 0.022 $A$ = +0.006 [-0.021, +0.017] No detectable difference

Appendix

Table 6: Interaction amplification across prespecified representation contrasts in the Prisoner’s Dilemma experiment.

	GPT-5.2	Claude Haiku 4.5	Gemini 2.5 Flash	DeepSeek V4 Flash
Paired behavioral agreement
Action agreement	0.997 [0.996, 0.998]	0.936 [0.932, 0.941]	0.850 [0.839, 0.860]	0.663 [0.649, 0.677]
Target agreement	0.551 [0.541, 0.560]	0.593 [0.585, 0.601]	0.610 [0.602, 0.618]	0.144 [0.137, 0.151]
Behavioral sensitivity
Cross-group targeting (pp)	+5.15 *** [4.22, 6.07]	-0.93 * [-1.62, -0.24]	+2.31 *** [1.49, 3.14]	-7.35 *** [-8.98, -5.72]
Collective network sensitivity at round 15

Appendix

Table 7: Representation sensitivity in the echo-chamber simulation. Results compare Prose with Bullet persona representations across

N=30

paired seeds. Differences are Prose - Bullet .

Metric	GPT-5.2	Claude Haiku 4.5	Gemini 2.5 Flash	DeepSeek V4 Flash
Activation probability: $0.5-0.3$
Stance assortativity	+0.068 *** [0.041, 0.095]	+0.103 *** [0.085, 0.121]	+0.108 *** [0.089, 0.127]	+0.107 *** [0.080, 0.134]
Same-group edge ratio	+0.032 *** [0.019, 0.045]	+0.060 *** [0.048, 0.072]	+0.061 *** [0.050, 0.073]	+0.070 *** [0.051, 0.089]
Memory window: $4-2$ rounds
Stance assortativity	-0.009 [-0.035, 0.018]	+0.063 *** [0.049, 0.076]	+0.080 *** [0.065, 0.094]	+0.092 *** [0.057, 0.127]
Same-group edge ratio	-0.011 [-0.021, -0.001]	+0.039 *** [0.031, 0.048]	+0.038 *** [0.028, 0.048]	+0.058 *** [0.040, 0.075]

Appendix

Table 8: Design sensitivity in the echo-chamber simulation. Signed differences compare the higher condition with the lower condition across

N=30

paired seeds. Outcomes are cumulative through round

15

Panel of Figure 6 — Figure 6: Design sensitivity in interaction targeting. Panels report round-wise cross-group targeting differences for (a) activation probability ( $0.5-0.3$ ), (b) memory window ( $4-2$ rounds), and (c) recommendation feed size ( $10-5$ posts), across four models and $N=30$ paired seeds. Models are GPT-5.2 (pink circles), Claude Haiku 4.5 (blue squares), Gemini 2.5 Flash (orange triangles), and DeepSeek V4 Flash (teal diamonds). Differences are higher minus lower condition, in percentage points; negative values indicate less cross-group targeting under the higher condition. Targeting is measured within each round, not cumulatively. Shaded bands are pointwise 95% paired-percentile-bootstrap confidence intervals from 10,000 seed resamples, not simultaneous or multiplicity-adjusted intervals.

Panel of Figure 7 — Figure 7: Design sensitivity in collective interaction structure. Panels use the same contrasts, models, and paired seeds as Figure 6 , and report signed differences in weighted stance assortativity computed from interaction edges accumulated through each round. Positive values indicate higher assortativity under the higher condition. Bands are pointwise 95% paired-percentile-bootstrap confidence intervals from 10,000 seed resamples. Round 1 is omitted because assortativity is undefined without eligible interaction edges. These trajectories describe collective sensitivity rather than a causal mediation or interaction-amplification estimate.

Figure 8: Effects of network homophily and hub assignment on echo-chamber outcomes. Left panels vary initial stance homophily; right panels vary hub assignment while holding the degree sequence fixed. Boxplots show run-level stance assortativity and weighted same-group edge ratio. Significant pairwise differences are based on paired t-tests with Holm correction ( $p<0.05$ ).

Perturbation	TRAILS	Context relevance	Outcome sensitivity	Interpretation
Repeated Prisoner’s Dilemma
Persona format	TRAILS-R	Irrelevant	$75.2^{***}$ pp	Cooperation depended strongly on persona formatting.
Game framing	TRAILS-R	Relevant	$19.3^{***}$ pp	Framing conditions should qualify the claim.
Memory representation	TRAILS-R	Irrelevant	$6.2^{***}$ pp	Smaller but significant change; assess claim preservation against the tolerance.
Echo-chamber simulation
Persona representation	TRAILS-R	Irrelevant	$\|\Delta r\|=0.194^{*}$ $\|\Delta H\|=0.051^{*}$	Estimated collective structure depended on persona representation.

Appendix

Table 9: Audited perturbations and claim-level interpretations for GPT-5.2. PD reports the maximum absolute cooperation-rate difference across contrasts, in percentage points (pp). EC reports absolute differences in stance assortativity (

r

) and weighted same-group edge ratio (

H

). Stars indicate

p<.001

; unmarked estimates were not statistically significant.

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Stop Drawing Scientific Claims from LLM Social Simulations Without Robustness Audits

Jinyi Ye, Lei Cao, Ding Chen, Emilio Ferrara

Thomas Lord Department of Computer Science, University of Southern California · Annenberg School for Communication and Journalism, University of Southern California · Marshall School of Business, University of Southern California

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The scientific claims drawn from LLM social simulations should be no stronger than the robustness audits that support them. Generative agents bring new expressive power to agent-based modeling, enabling simulations of collective social processes like cooperation, polarization, and norm formation. Yet they also introduce complexity through additional architectural choices, such as agent specification, memory representation, interaction protocols, and environment design. Small perturbations that appear minor to researchers can cascade into macro-level outcomes through repeated interaction, creating a "butterfly effect." Consequently, scientific claims drawn from LLM social simulations may reflect implementation artifacts rather than the social mechanisms being modeled. We support this position with two case studies: a repeated Prisoner's Dilemma and a social media echo chamber simulation. Across multiple models, minor perturbations in persona format and game-instruction framing shift cooperation rates by up to 76 percentage points, while network homophily and hub assignment produce significant and consistent shifts in polarization metrics. We also find that sensitivity is unevenly distributed across both architectural choices and model families: the same perturbation that produces the 76 pp shift in one frontier model only shifts another by 1 pp. Robustness is therefore a property that should be measured per claim and per model, not assumed. To address this validation gap, we introduce TRAILS (Taxonomy for Robustness Audits In LLM Simulations), a robustness-audit taxonomy spanning three levels of simulation design: agent (micro-level), interaction (meso-level), and system (macro-level). We call for robustness to become a first-order validation requirement before LLM social simulations are used to explain mechanisms, evaluate interventions, or inform decisions.

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Large Language Model-Based Social Simulation

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