Structured Multi-Criteria Evaluation of Large Language Models with Fuzzy Analytic Hierarchy Process and DualJudge

Large language models (LLMs) are increasingly used as judges for open-ended generation, as large-scale human evaluation is often expensive and difficult to scale, yet their preferences remain imperfect proxies for human judgment. Existing auditing pipelines often assume that a reliable subset of examples or clean supervision signals are available beforehand, for example from human annotation, heuristic filtering, or the outputs of strong judges. In LLM evaluation, this assumption is fragile: the initial split may inherit judge bias, while human verification is typically too scarce to define stable groups at scale. We propose AURA, an adaptive uncertainty--aware refinement framework for auditing pairwise LLM--as--a--judge decisions under selected human verification. AURA iteratively learns a human-consistency signal, propagates reliable evidence, and prioritizes uncertain comparisons for human review. The key idea is to treat trust in a judge as a latent quantity that is progressively refined as evidence accumulates. We provide a compact formulation, a stable refinement procedure, and a comprehensive evaluation on both synthetic and real pairwise LLM-answer data.

Using LLMs as judges has become standard practice for evaluating model outputs at scale. This is particularly common for subjective, open-ended tasks such as assessing helpfulness or alignment, where no single reference answer exists. However, objective tasks introduce a distinct reliability challenge for reference-free LLM judging. In the absence of a reference answer, the judge evaluates factual correctness either through its parametric knowledge or through tool augmentation. Although the former enables efficient evaluation, the judge may hallucinate or lack sufficient evidence for its verdict. Conversely, tool augmentation can provide additional evidence but introduces extra computational cost and requires an appropriate mechanism to determine when and how that evidence should be used reliably. More importantly, neither approach alone provides formal control over the risk of accepted verdicts or guarantees their reliability at a specified level. We propose a risk-controlled framework that calibrates uncertainty thresholds on a held-out set so that the false discovery rate among accepted verdicts remains below a user-specified level~$α$ with high probability, using finite-sample Clopper--Pearson intervals. When the parametric mode is not sufficiently confident, the instance is routed to a retrieval-augmented mode, where the judge gathers web evidence and re-evaluates the instance under a second calibrated threshold. The finite-sample guarantee carries over to this two-threshold routing without additional assumptions. Across open-domain QA benchmarks and judges of varying scales, the framework maintains the target error rate while achieving substantially higher coverage than single-mode baselines.

Rubric-based evaluation is widely used to assess large language model (LLM) outputs by decomposing quality into multiple criteria and assigning each a binary judgment from an LLM verifier. However, judgment certainty varies substantially across criteria. Existing methods uniformly aggregate these judgments into a final score, implicitly treating every criterion as equally certain and overlooking this heterogeneity. As a result, uncertain judgments remain incorporated into reward estimation without distinction, potentially yielding misleading training signals for downstream reinforcement learning (RL). To address this limitation, we propose Uncertainty-aware Rubric Weighting (URW), a training-free framework that quantifies criterion-level judgment uncertainty via conformal calibration. Specifically, URW elicits a soft uncertainty signal from a fixed pool of paraphrased judgment templates and converts it into a per-criterion weight using split-conformal $p$-values with provable coverage guarantees. Extensive experiments demonstrate that URW consistently improves pairwise preference accuracy and delivers stronger downstream RL alignment.