LLM ensembles are widely used for LLM judges. However, how to estimate their accuracy, especially in an efficient way, is unknown. In this paper, we present a principled maximum a posteriori (MAP) framework for an economical and precise estimation of the performance of LLM ensemble judgment. We first propose a mixture of Beta-Binomial distributions to model the judgment distribution, revising from the vanilla Binomial distribution. Next, we introduce a conformal prediction-driven approach that enables adaptive stopping during iterative sampling to balance accuracy with efficiency. Furthermore, we design a prior transfer mechanism that utilizes learned distributions on open-source datasets to improve estimation on a target dataset when only scarce annotations are available. Finally, we present BetaConform, a framework that integrates our distribution assumption, adaptive stopping, and the prior transfer mechanism to deliver a theoretically guaranteed distribution estimation of LLM ensemble judgment with minimum labeled samples. BetaConform is also validated empirically. For instance, with only 10 samples from the TruthfulQA dataset, for a Llama ensembled judge, BetaConform gauges its performance with error margin as small as 3.37%.
View on arXiv@article{qu2025_2504.12589,
title={ Efficient MAP Estimation of LLM Judgment Performance with Prior Transfer },
author={ Huaizhi Qu and Inyoung Choi and Zhen Tan and Song Wang and Sukwon Yun and Qi Long and Faizan Siddiqui and Kwonjoon Lee and Tianlong Chen },
journal={arXiv preprint arXiv:2504.12589},
year={ 2025 }
}