Localize-Then-Decide Guarantees for LLM Judgments

Jung et al. (2025) introduce a hypothesis testing framework for guaranteeing agreement between large language models (LLMs) and human judgments, relying on the assumption that the model's estimated confidence is monotonic with respect to human-disagreement risk. In practice, however, this assumption may be violated, and the generalization behavior of the confidence estimator is not explicitly analyzed. We mitigate these issues by learning a dedicated confidence estimator instead of relying on heuristic confidence signals. Our approach leverages simulated annotator diversity and a margin-based ranking formulation to explicitly model how confidently an LLM distinguishes between human-agreement and human-disagreement cases. We further derive generalization guarantees for this estimator, revealing a margin-dependent trade-off that informs the design of an adaptive estimator training procedure. When integrated into fixed-sequence testing, the learned confidence estimator yields improved ranking accuracy and empirically strengthens the monotonic relationship between confidence and disagreement risk, leading to higher success rates in satisfying target agreement levels across multiple datasets and judge models.

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.

Large language models (LLMs) are increasingly used to evaluate the responses of other language models. This approach, known as LLM-as-a-Judge, is faster and cheaper than human evaluation. However, a judge may produce consistent scores without necessarily agreeing with human evaluators. In this work, we study this issue using two local open-weight LLM judges, LLaMA-3-8B and Qwen2.5-7B. We evaluate 300 responses generated by an instruction-tuned GPT-2 (124M) model for 100 questions covering five categories: factual knowledge, instruction following, mathematics, reasoning, and writing. Each response is scored by nine human annotators and is evaluated three times by each LLM judge using the same rubric. We compare the judge scores with the average human scores using Pearson correlation, Spearman correlation, mean absolute error (MAE), signed bias, and self-consistency. LLaMA-3-8B shows a Pearson correlation of 0.275 with human scores, while Qwen2.5-7B achieves 0.340. Their MAEs are 27.71 and 18.64, respectively. Despite this limited agreement, both judges show high self-consistency, with exact consistency rates of 97.3% for LLaMA-3-8B and 92.3% for Qwen2.5-7B. These results show that high self-consistency does not necessarily indicate high agreement with human judgments. Our findings highlight the need to evaluate both consistency and human alignment when using local LLMs as automatic judges.