OSCAR: Order-aware Scoring and Calibration for AI Rankings

Large language models are widely employed as evaluators, a paradigm commonly referred to as LLM-as-a-judge. Prior research has predominantly examined point-wise or pair-wise evaluation protocols; in contrast, our focus is on rubric-based evaluation, which has been attracting increasing attention owing to its utility for training models in domains where verification is otherwise difficult. In this work, we show that rubric-based evaluation implicitly resembles a multiple-choice setting and therefore exhibits position bias: LLMs tend to prefer score options that appear at specific positions within the rubric list. Through controlled experiments across multiple models and datasets, we demonstrate that this position bias is consistent. Its direction, however, is model-specific: some judges favor the first option, while others favor the last. We further identify a second, orthogonal axis of bias: when a prompt scores several criteria simultaneously, the ordering of the criteria itself shifts the resulting scores. We additionally explore permuting the order of the rubric options as a means of mitigating position bias, and find that although the bias can be attenuated, improvements in the correlation between model judgments and human annotations are obtained primarily for models that exhibit strong bias. Our results recast rubric-based LLM-as-a-judge as a multiple-choice problem with measurable, model-specific position bias, and we further confirm that only a small number of random order permutations are sufficient to reduce the error introduced by this bias for the majority of models.

Large language models (LLMs) are increasingly used as cheap, scalable judges that compare candidate outputs pairwise -- to rank responses, select models, or triage papers. Yet LLM judges are both noisy and systematically biased: they favor verbose or well-formatted answers and exhibit position effects, so simply aggregating their votes recovers a ranking of presentation, not of true quality. We study the practical goal of identifying the \topk{} items under a fixed comparison budget, and make two contributions. First, we cast judging as Bayesian inference over latent quality with explicit, judge-specific bias covariates (verbosity, position), regularized by a shrinkage prior so that the data decide which biases a given judge actually exhibits. Second, we introduce a \topk-aware active acquisition rule that chooses the next comparison to maximally reduce uncertainty about \topk{} \emph{membership}, rather than about the full ranking. On a controlled benchmark with known ground-truth quality, judged by sixteen real LLMs spanning open and proprietary families (Llama, Qwen, Phi-4, GPT-4o-mini/5.1/5.5, Gemini, DeepSeek, and Claude Haiku/Sonnet/Opus), naive aggregation plateaus at a wrong \topk{} on biased judges regardless of budget, while our bias-aware model recovers it; \topk-aware acquisition reaches this ceiling with far fewer comparisons than round-robin or a global-uncertainty (D-optimal) rule. Bias is real but heterogeneous and capability-dependent: cheap and mid-tier judges carry a strong verbosity bias that our model corrects (lifting recall from \sim$$0.5--$0.6$ to $0.84$--$1.0$), whereas the frontier judges we tested show little bias and already rank accurately, so bias-aware modeling changes little there.

Large Language Model judges are widely used to rank texts and text-generating systems through pairwise comparison, and their reliability is typically assessed via three proxies: position bias, transitivity, and pairwise agreement (self- or human-labeled). Because these proxies drive judge selection and benchmarking, a substantial literature reporting that judges perform poorly on them risks steering practitioners away from otherwise capable evaluators. We argue this assessment is misleading. Under the Bradley--Terry geometry underlying pairwise aggregation, each proxy is dominated by close-rank-gap pairs, where inconsistency is information-theoretically expected and individual verdicts contribute little to the aggregate ranking; far-gap pairs carry the ranking signal but barely move the proxies. We formalize this argument and validate it in a controlled simulation and on two human-rated corpora: the proxies correlate only weakly with ranking accuracy against gold, and their predictive component concentrates in the far-gap regime. Judges should therefore be assessed on rank-gap-conditional metrics, ideally against human rankings. Code at https://github.com/brunobrocai/PairDifficulty.