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.
LLM-as-judge (Zheng et al., 2023) is increasingly the default for evaluating AI systems in enterprise pipelines, often scaled to ensembles (Verga et al., 2024) or "mixture-of-experts" (Shazeer et al., 2017) panels of judges. These systems share a key assumption: that consistency -- agreement among judges, or among a model's own samples -- indicates correctness. We show this assumption is unreliable. Agreement is not accuracy: a model can agree with itself, and different models can agree with each other, out of shared bias, a memorized heuristic, or an option-position prior rather than truth. We ask when agreement is nonetheless a usable proxy, in a large-scale cross-runner study: 53 runners drew K=50 samples for assigned overlapping cases across comparisons of model tier, prompting, and scale on GPQA Diamond and AIME -- 265,000 samples. Using majority-correctness as the deployment label and a hierarchical runner-clustered bootstrap, agreement is a positive but weak predictor (rho 0.20-0.59, all positive under item-clustered resampling) whose usefulness is regime-dependent: best for unsaturated mid-tier models and for allocating compute, and worst -- over-confident yet no more accurate -- for the most consistent frontier model (agreement >=0.8 on 77% of GPQA case-result entries, 48% of those wrong). An exploratory cross-family check on three Claude tiers shows the same frontier over-confidence, with confident errors recurring across providers above a marginal-preserving null. Self-consistency is thus a conditional proxy for correctness, not a standalone confidence score. We publicly release the de-identified per-run rows and answer distributions.
Evaluating new large language models typically requires costly human annotation campaigns at scale. LLM-as-a-judge offers a cheaper alternative, but judge scores carry systematic errors - such as position bias, self-preference, or intransitivity - that can strongly miscalibrate the resulting rankings. We quantify the resulting judge-human disagreement at two complementary levels. At the local level, we estimate per-battle uncertainty from the judge's own score differences by propagating calibrated win probabilities rather than hard labels into the Bradley-Terry procedure. This alone provides a drastic improvement to Elo estimation accuracy, bringing LLM-derived ratings within 17.9 Elo MAE of human-derived ones when averaged over 55 held-out models on LMArena. At the global level, we apply split conformal prediction to the residual gap between LLM-derived and human-derived Elo ratings across held-out models, producing prediction intervals with distribution-free marginal coverage guarantees that account for irreducible LLM-human disagreement. Together, these two layers yield a low-cost evaluation tool that provides developers with calibrated Elo estimates and honest uncertainty bounds, without access to large-scale human annotations. To facilitate reproducibility, we release our code at https://github.com/kargibora/SoftElo .
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}.