The Butterfly Effect in LLM Social Simulations: From Architecture Sensitivity to Robustness Audits
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
| Perturbation | Metric | GPT-5.2 | Claude Haiku 4.5 | Gemini 2.5 Flash | DeepSeek |
| Repeated Prisoner’s Dilemma (Two-Agent): | |||||
| Persona format R | Average payoff | 1.48*** | 1.49*** | 0.79*** | 0.14** |
| Cooperation rate (pp) | 75.2*** | 77.7*** | 36.0*** | 7.7** | |
| Game framing R | Average payoff | 0.42*** | 0.09* | 0.19 | 0.15*** |
| Cooperation rate (pp) | 19.3*** | 3.3* | 9.0 | 8.8*** | |
| Memory representation R | Average payoff | 0.10*** | 0.05 | 0.29 | 0.01 |
| 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) . | |
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- , 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- 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. |
| 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. |
| 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 Tabular | +1.467*** | +1.223*** | -0.010 | -0.127 |
| Plain Descriptive | -1.478*** | -1.487*** | -0.777*** | -0.013* | ||
| Plain Tabular | -0.012 | -0.263*** | -0.787*** | -0.140** | ||
| Persona | Cooperation rate (pp) | Descriptive Tabular | +74.000*** | +63.333*** | -0.333 | -6.333 |
| Plain Descriptive | -75.167*** | -77.667*** | -35.667*** | -1.333* | ||
| Contrast | GPT-5.2 | Claude Haiku 4.5 | Gemini 2.5 Flash | DeepSeek V3.2 |
|---|---|---|---|---|
| Persona format | ||||
| Plain vs Descriptive | = 0.271 = 0.752 = +0.481 [+0.327, +0.622] Amplification | = 0.315 = 0.777 = +0.462 [+0.376, +0.529] Amplification | = 0.070 = 0.357 = +0.287 [+0.190, +0.387] Amplification | = 0.101 = 0.013 = -0.087 [-0.108, -0.066] Attenuation |
| Plain vs Tabular | = 0.589 = 0.012 = -0.578 [-0.602, -0.556] Attenuation | = 0.429 = 0.143 = -0.286 [-0.341, -0.223] Attenuation | = 0.074 = 0.360 = +0.286 [+0.192, +0.384] Amplification | = 0.055 = 0.077 = +0.022 [-0.050, +0.121] No detectable difference |
| Descriptive vs Tabular | = 0.318 = 0.740 = +0.422 [+0.295, +0.546] Amplification | = 0.244 = 0.633 = +0.389 [+0.291, +0.481] Amplification | = 0.004 = 0.003 = -0.001 [-0.006, +0.013] No detectable difference | = 0.054 = 0.063 = +0.009 [-0.057, +0.102] No detectable difference |
| Game framing | ||||
| Canonical vs Moralized | = 0.117 = 0.193 = +0.077 [+0.024, +0.127] Amplification | = 0.058 = 0.008 = -0.050 [-0.067, -0.007] Attenuation | = 0.025 = 0.090 = +0.065 [-0.022, +0.143] No detectable difference | = 0.016 = 0.022 = +0.006 [-0.021, +0.017] No detectable difference |
| 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 | ||||
| Metric | GPT-5.2 | Claude Haiku 4.5 | Gemini 2.5 Flash | DeepSeek V4 Flash |
| Activation probability: | ||||
| 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: 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] |
| Perturbation | TRAILS | Context relevance | Outcome sensitivity | Interpretation |
| Repeated Prisoner’s Dilemma | ||||
| Persona format | TRAILS-R | Irrelevant | pp | Cooperation depended strongly on persona formatting. |
| Game framing | TRAILS-R | Relevant | pp | Framing conditions should qualify the claim. |
| Memory representation | TRAILS-R | Irrelevant | pp | Smaller but significant change; assess claim preservation against the tolerance. |
| Echo-chamber simulation | ||||
| Persona representation | TRAILS-R | Irrelevant | Estimated collective structure depended on persona representation. | |
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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