Partial Identification from LLM Prompts

2026-06-12

AI Summary

This study addresses the challenge of identifying the prevalence θ of a latent binary variable when ground-truth labels are unobservable and only binary outputs from large language models (LLMs) are available, particularly under arbitrary error correlations across multiple LLMs. The authors model LLM responses via a two-component finite mixture framework, leveraging repeated prompting and multi-model responses. By incorporating external calibration scores and event-level constraints, they exploit the full distributional structure of scores—not merely their means—together with stochastic ordering constraints such as first-order dominance for partial identification. Theoretically, under weak assumptions, the identified set for θ collapses to the uninformative interval [0,1]; however, calibration information yields tight and informative bounds. This work is the first to demonstrate that consensus patterns, rather than simple majority voting, are crucial for identification, and it extends the approach to partial identification of regression coefficients.

Abstract

Large language models are increasingly used as binary classifiers when the true label is latent. We study partial identification of the prevalence $θ= P(X^* = 1)$ from panels of LLM reports whose errors may be arbitrarily dependent given the truth. The design of replication determines the observable, and hence the identifying content: repeated prompts to one model yield a count, several named models a response vector, and both a response matrix. Cast as a two-component finite mixture, the problem makes the identification failure transparent: absent restrictions that separate the latent components, the prevalence $θ$ is completely unidentified, and weak stochastic-ordering restrictions (first-order dominance, monotone likelihood ratio, mean ordering) leave the identified set at $[0,1]$. Identifying power comes instead from externally calibrated scores and events, which discipline the mixture in the spirit of the misclassification and corrupted-data literature. We characterize the resulting bounds, establishing validity and sharpness, and give an exact account of the identifying information in the full score distribution beyond its mean. When named models are asked repeated versions of the same question, what identifies $θ$ is not the number of positive answers but which models agree across prompts -- a feature a vote count discards. An extension derives implied bounds on regression coefficients when $X^*$ is a regressor of interest that is not directly observed.

Problem

• partial identification
• large language models
• latent prevalence
• misclassification
• binary classification

Innovation

• partial identification
• large language models
• latent prevalence
• finite mixture models
• calibrated scores