Efficient Inference for Noisy LLM-as-a-Judge Evaluation

Large language models (LLMs) are increasingly used as automatic evaluators of generative AI outputs, a paradigm often referred to as "LLM-as-a-judge." In practice, LLM judges are imperfect predictions for the underlying truth and can exhibit systematic, non-random errors. Two main approaches have recently been proposed to address this issue: (i) direct measurement-error correction based on misclassification models such as Rogan--Gladen-style estimators, and (ii) surrogate-outcome approaches such as prediction-powered inference (PPI), which correct bias by calibrating prediction residuals on a small set of gold-standard human labels. In this paper, we systematically study the performance of these two approaches for estimating mean parameters (e.g., average benchmark scores or pairwise win rates). Leveraging tools from semiparametric efficiency theory, we unify the two classes of estimators by deriving explicit forms of efficient influence function-based efficient estimators and characterize conditions under which PPI-style estimators attain strictly smaller asymptotic variance than measurement-error corrections. We verify our theoretical results through simulations and demonstrate the methods on a real-data example using our open-source software package for performing the calibration.