Estimating the prevalence of a category in a population using imperfect measurement devices (diagnostic tests, classifiers, or large language models) is fundamental to science, public health, and online trust and safety. Standard approaches correct for known device error rates but assume these rates remain stable across populations. We show this assumption fails under covariate shift and that multicalibration, which enforces calibration conditional on the input features rather than just on average, is sufficient for unbiased prevalence estimation under such shift. Standard calibration and quantification methods fail to provide this guarantee. Our work connects recent theoretical work on fairness to a longstanding measurement problem spanning nearly all academic disciplines. A simulation confirms that standard methods exhibit bias growing with shift magnitude, while a multicalibrated estimator maintains near-zero bias. While we focus the discussion mostly on LLMs, our theoretical results apply to any classification model. Two empirical applications -- estimating employment prevalence across U.S. states using the American Community Survey, and classifying political texts across four countries using an LLM -- demonstrate that multicalibration substantially reduces bias in practice, while highlighting that calibration data should cover the key feature dimensions along which target populations may differ.
LLM-as-a-Judge evaluation has become a standard tool for assessing base model performance. However, characterizing performance via the naive estimator, i.e., raw judge outputs, is systematically biased. Recent work has proposed estimators to correct this bias, but their reliability depends critically on judge quality and, for model comparisons, on calibration stability. Sharing calibration across compared models is practically attractive but can introduce severe bias, including cases where the comparison estimate points in the wrong direction with high apparent confidence. We study these failure modes through analytical results, simulations over judge quality (J) and cross-model calibration instability (ΔJ), and a real-data MMLU-Pro case study with sign reversal. We propose J and ΔJ as diagnostics for when corrected estimates, especially shared-calibration comparisons, are likely unreliable, and provide reporting guidance for LaaJ evaluation.
Large language models (LLMs) are increasingly used in social science as scalable measurement tools for converting unstructured text into variables that can enter standard empirical designs. Measurement validity demands more than high average accuracy, which requires well calibrated confidence that faithfully reflects the empirical probability of each measurement being correct. This paper studies the model miscalibration in LLM-based social science measurement. We begin with a case study on FOMC and show that confidence based filtering can change downstream regression estimates when LLM confidence is miscalibrated. We then audit calibration across 14 social science constructs covering both proprietary models, including GPT-5-mini, DeepSeek-V3.2, and open source models. Across tasks and model families, reported confidence is poorly aligned with tolerance-based correctness. As a simple mitigation, we propose a soft label distillation pipeline for calibrating Bert with LLM. The method converts an LLM score and its verbalized confidence into a soft target distribution, then trains a smaller discriminative classifier on encoder models for these targets. Averaged across datasets, this approach reduces ECE by 43.2% and Brier by 34.0%. These results suggest that LLM-based social science pipelines should treat calibration as part of measurement validity, rather than as an optional post-processing concern.
A key factor in deciding whether to trust an automatic prediction is its confidence score, which should be calibrated to match the actual probability of the prediction being correct. Most confidence calibration metrics target binary or multi-class tasks, while multi-label calibration remains largely underexplored. Multi-label classification tasks, such as assigning medical codes to clinical notes or determining news topics, are usually dominated by a large number of negatives, i.e., labels that do not apply. We show that existing binning schemes to compute label-wise expected calibration error either underestimate the error, simply reflect label frequency, or suffer from many bins with very few instances. To achieve trustworthy label-wise calibration errors, we propose a new binning scheme that gives equal weight to positive and negative label assignments. Our empirical study demonstrates that in contrast to existing binning schemes, our new scheme results in meaningful estimates of calibration error in hierarchical and in extreme multi-label classification. We also show that calibrating confidence scores of large language models for multi-label predictions is an open challenge. Our detailed analysis lays the foundation for further research by providing a solid evaluation metric for measuring calibration in multi-label classification.
Sophie Henning, Georg Hofmann, Alexander Schulte +2