From Ground Truth to Measurement: A Statistical Framework for Human Labeling

Data quality now matters as much as compute for training language models. Much training data comes from human annotation of text, and interpretive annotation has no ground truth that could settle what is "accurate". Two lines of work respond to this. One combines annotators into a "ground truth" and measures how well they agree with each other; the other treats their disagreement as a signal. Both compare different people at one point in time. We measure something else: how well one reader reproduces their own reading of the same text over time. One expert human reader and three LLM families segmented three Sumerian myths and labelled the causal function of each segment with one of seven states. Across runs months apart, the human cut the text in much the same places but named the segments differently, in every myth. The models show no such consistent pattern: their gap between the two layers is positive in some myths and negative in others, and its size varies. The human's label changes are not random: the runs go through much the same functions but start them one step apart, while model runs start them at the same places. We argue that this pattern is a usable measure of data quality and a contamination check: a "human" annotation whose labels are as stable as its boundaries, and whose functions start in sync, looks like a model's.

An increasing number of scholars use AI to measure variables they subsequently include in downstream analyses. Although AI-measured variables are often analyzed as if observed without error, ignoring prediction errors in automated measurement leads to substantial bias and invalid confidence intervals in downstream analyses, even if AI measurement accuracy is high, e.g., above 90%. Existing solutions, such as design-based supervised learning and prediction-powered inference, combine error-prone AI-based measurements with gold-standard labels, which may be costly and difficult to obtain in some application areas. In this paper, we propose debiased inference with multiple imperfect measurements (DMM), a framework that combines multiple error-prone AI measurements to enable valid downstream inference without gold-standard labels. Building on the established results on CP decomposition, DMM assumes that these measurements are independent conditional on the latent true label and observed unit-level features, such as text features represented by embeddings. This framework allows for unknown misclassification rates to vary across annotation methods (e.g., large language models) and across units of annotation (e.g., texts). Under this assumption, we use semiparametric inference theory to prove that the DMM estimator is consistent and asymptotically normal, enabling valid inference for a wide range of downstream statistical analyses common in the social sciences. Our simulation results show that DMM yields valid inference and that adding accurate, though imperfect, measurements can improve efficiency. Focusing on common applications of large language model annotations, we also develop diagnostics to assess the conditional independence assumption.

High-quality labeled data is essential for training robust machine learning models, yet obtaining annotations at scale remains expensive. AI-assisted annotation has therefore become standard in large-scale labeling workflows. However, in tasks where model predictions carry two independent components, a class label and spatial boundaries, a model may classify an object with high confidence while mislocalizing it. Existing AI-assisted workflows offer annotators no signal about where spatial errors are most likely. Without such guidance, humans may systematically underinspect subtly misplaced boxes. We address this by studying the effect of visualizing spatial uncertainty via a purpose-built interface. In a controlled study with 120 participants, those receiving uncertainty cues achieve higher label quality while being faster overall. A box-level analysis confirms that the cues redirect annotator effort toward high-uncertainty predictions and away from well-localized boxes. These findings establish localization uncertainty as a lever to improve human-in-the-loop annotation. Code is available at https://mos-ks.github.io/MUHA/.