Predicting Disagreement with Human Raters in LLM-as-a-Judge Difficulty Assessment without Using Generation-Time Probability Signals

Accurate estimates of item difficulty are essential for valid assessment and effective adaptive learning. However, for newly created tasks, response data are typically unavailable. Pretesting and expert judgement can be costly and slow, while machine learning methods often require large labelled training datasets. Recent work suggests that large language models (LLMs) may help. However, there is limited evidence on the elicitation procedures and prompt configurations used to emulate experts for difficulty estimation. This study addresses this gap by evaluating three off-the-shelf LLMs as difficulty raters for newly created items without access to response data. Using an item bank from an online learning system, the study examined 6 domains of primary-school mathematics, with empirical difficulty estimates treated as empirical reference. The study used a full factorial design crossing three factors: judgement format (absolute vs pairwise), decision type (hard decisions vs token-probability-based estimates), and prompting strategy (zero-shot vs few-shot). LLM-derived difficulty estimates were compared with empirical difficulties using Spearman rank correlations. Across domains, LLM-based estimates exhibited moderate to strong positive correlations with empirical item difficulties. For simpler arithmetic tasks, some configurations approached the upper end of the accuracy range reported for human experts in previous research. Pairwise comparison consistently outperformed absolute judgement in the absence of additional refinements. However, when token-level probabilities were incorporated and examples of items with known empirical difficulty were provided, the absolute judgement configuration likewise demonstrated moderate-to-high alignment. The study positions LLMs as a promising tool for initial item calibration and offers insights into effective workflow configuration.

LLMs now sit on every side of evaluation: as examinees scored on benchmarks, judges of other models' outputs, and raters of human-generated content. Each paradigm can be viewed as a measurement problem, where a latent property of an object is probed with items from an instrument (e.g., benchmark) by judges or raters. Standard evaluation practices often neglect the contributions of each core component to the end result, limiting our understanding of what is being measured. Rasch measurement theory (RMT) is well-suited to this problem. RMT decomposes ordinal ratings into separable facets on a common scale. It further provides a battery of diagnostics that can identify miscalibrated measurements and rater biases. We present a case study of RMT applied to the LLM-as-rater paradigm using the Measuring Hate Speech corpus, whose construct was itself built under RMT. We fit a series of many-facet Rasch models to annotations from nine LLMs spanning families and capability levels. Our analyses show that LLMs systematically differ from human raters in severity, item-level calibration, question-order robustness, target-identity sensitivity, and rating scale use, all of which standard evaluation practice would largely obscure. Overall, we argue that RMT belongs in the toolkit for evaluating LLM-as-examinee, -judge, and -rater paradigms.

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 .