MultiwayPAM: Multiway Partitioning Around Medoids for LLM-as-a-Judge Score Analysis

LLM-as-a-judge ensembles are the standard paradigm for scalable evaluation, but their aggregation mechanisms suffer from a fundamental flaw: they implicitly assume that judges provide independent estimates of true quality. However, in practice, LLM judges exhibit correlated errors caused by shared latent confounders -- such as verbosity, stylistic preferences, or training artifacts -- causing standard aggregation rules like majority vote or averaging to provide little gain or even amplify systematic mistakes. To address this, we introduce CARE, a confounder-aware aggregation framework that explicitly models LLM judge scores as arising from both a latent true-quality signal and shared confounding factors. Rather than heuristically re-weighting judges, CARE separates quality from confounders without access to ground-truth labels. We provide theoretical guarantees for identifiability and finite-sample recovery under shared confounders, and we quantify the systematic bias incurred when aggregation models omit confounding latent factors. Across 12 public benchmarks spanning continuous scoring, binary classification, and pairwise preference settings, CARE improves aggregation accuracy, reducing error by up to 26.8%. Code is released in \href{https://github.com/SprocketLab/CARE}{https://github.com/SprocketLab/CARE}.

Large Language Models (LLMs) are often used as evaluators of text quality, known as LLM-as-a-Judge, which can outperform conventional automatic evaluation metrics that rely on reference texts. However, LLM evaluators tend to generate particular scores regardless of the context of the evaluated text, which is known as scoring bias. This study proposes a novel method to mitigate this scoring bias. An LLM is instructed to randomly generate number tokens, and the latent numerical bias of the LLM is identified by measuring the deviation of the observed distribution of numbers from the uniform distribution. A definition of a downstream task, for which an LLM evaluator is used, is added to the prompts for random number generation to measure task-specific latent number bias. In the evaluation by an LLM, the token generation probabilities for a given input are rectified considering the LLM's latent number bias. Results of the experiment on four different tasks, evaluation of LLM alignment, evaluation of summarization, Semantic Textual Similarity, and Semantic Textual Relatedness, demonstrate that our proposed method outperforms the baselines, including an LLM without debiasing and previous calibration methods. In addition, it is confirmed that scoring bias varies across LLMs, tasks, and score ranges, indicating the importance of measuring latent number bias as the case may be.

Multimodal Large Language Models (MLLMs) have been increasingly used as automatic evaluators-a paradigm known as MLLM-as-a-Judge. However, their reliability and vulnerabilities to biases remain underexplored. We find that many MLLM judges fail to reliably integrate key visual or textual cues, yielding unreliable evaluations when evidence is missing or mismatched, and exhibiting instability under semantically irrelevant perturbations. To address this, we systematically define Compositional Bias in MLLM-as-a-Judge systems and introduce MM-JudgeBias, a benchmark for evaluating it. MM-JudgeBias introduces controlled perturbations across Query, Image, and Response, and evaluates model behavior via two complementary metrics: Bias-Deviation (BD) for sensitivity and Bias-Conformity (BC) for stability. Our dataset of over 1,800 curated and refined multimodal samples, drawn from 29 source benchmarks, enables a fine-grained diagnosis of nine bias types across diverse tasks and domains. Experiments on 26 state-of-the-art MLLMs reveal systematic modality neglect and asymmetric evaluation tendencies, underscoring the need for more reliable judges.