Signal or Spurious Cue? A Randomized Audit of Survey-Country Metadata in LLM Social Inference

Large language models (LLMs) are increasingly used to simulate social survey responses, yet their outputs exhibit systematic biases: marginal distributions are skewed, response variance is poorly calibrated, and predictor-outcome relationships are attenuated. We ask a simple question: given a small pilot sample of human responses, can an LLM recover the statistical characteristics of a broader population? We decompose recovery along three axes: structural fidelity, marginal fidelity, and individual fidelity. Using a COVID-19 misinformation survey as a case study, we benchmark three families of approaches: prompting, rectification, and fine-tuning. The findings suggest that fine-tuning on small pilot samples offers a balanced approach for achieving multiple forms of fidelity, but the levels of such fidelity can vary across subsamples, potentially threatening pluralistic alignment.

Survey research faces mounting structural challenges: declining response rates, sample bias, block-wise missingness among at-risk respondents, and AI-assisted fraudulent completions in online panels. Large language models (LLMs) have been proposed as a remedy, yet rigorous evaluations across the full survey workflow remain scarce, particularly in disaster contexts where data quality matters most. We present and evaluate a five-stage framework for LLM integration covering questionnaire design, sample selection, pilot testing, missing-data imputation, and post-collection analysis, using the 2024 Hurricane Milton preparedness survey of Florida residents (n=946) as a shared empirical testbed. We introduce a Protection Motivation Theory (PMT)-constrained co-occurrence knowledge graph and develop seven LLM configurations spanning zero-shot inference, retrieval-augmented baselines, and novel theory-informed variants. Our proposed Anchored Marginal Theory-Informed LLM (A-TLM) outperforms all three classical imputation baselines (IPW/MI, MICE+PMM, missForest) on RMSE under disaster-relevant block-wise MNAR conditions (S4 RMSE 1.439 vs. 1.496 for the next-best), while achieving near-zero signed bias (-0.121) where the random-forest imputer produces the largest absolute bias (-0.631). Organizing retrieval around PMT causal structure and integrating all evidence in a single model call outperforms unstructured retrieval and staged sequential inference (MAE 0.993 vs. 1.097 for standard RAG). We document that near-zero aggregate bias can mask opposing subgroup errors and propose subgroup-stratified bias auditing as a reporting standard. A retrieval-constrained knowledge-graph chatbot demonstrates that hallucination is architecturally manageable through grounded refusal.

Large Language Models can generate synthetic survey responses at low cost, but their accuracy varies unpredictably across questions. We study the design problem of allocating a fixed budget of human respondents across estimation tasks when cheap LLM predictions are available for every task. Our framework combines three components. First, building on Prediction-Powered Inference, we characterize a question-specific rectification difficulty that governs how quickly the estimator's variance decreases with human sample size. Second, we derive a closed-form optimal allocation rule that directs more human labels to tasks where the LLM is least reliable. Third, since rectification difficulty depends on unobserved human responses for new surveys, we propose a meta-learning approach, trained on historical data, that predicts it for entirely new tasks without pilot data. The framework extends to general M-estimation, covering regression coefficients and multinomial logit partworths for conjoint analysis. We validate the framework on two datasets spanning different domains, question types, and LLMs, showing that our approach captures 61-79% of the theoretically attainable efficiency gains, achieving 11.4% and 10.5% MSE reductions without requiring any pilot human data for the target survey.