Trustworthy Method Comparison with AI Judges: Estimation and Design under Order, Batch, and Aggregation Effects

Abstract:Large language models (LLMs) are increasingly used as judges for automated AI evaluation. A common practice is to randomize prompt sequences and average the resulting scores, but its statistical validity remains unclear. We show that LLM evaluation mechanisms can be approximated by a class of Markov generalized linear mixed models (GLMMs), supported by out-of-sample predictions across three major commercial LLMs. Using a first-order Markov GLMM, we study leaderboard ranking and group comparison. For leaderboard ranking, randomize-and-average selection is consistent under a mild separation condition, and a Williams square design can improve efficiency when item qualities are close. For group comparison, naive averaging can yield inconsistent conclusions about differences in group-level quality because of the response model's nonlinearity. Empirical results further support the validity of the proposed model-based inference beyond the first-order theory, including settings with higher-order sequence memory. We illustrate the approach in an application where AI judges compare two graphical model estimation methods.

Machine Learning (stat.ML); Machine Learning (cs.LG); Applications (stat.AP); Methodology (stat.ME)

arXiv:2610.07755 [stat.ML]

(or arXiv:2610.07755v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.07755 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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