OSCAR: Order-aware Sensitivity Correction for AI Rankings

LLM judges evaluate candidate language models through pairwise comparisons of their responses. Judge-aware Bradley--Terry models aggregate pairwise comparisons by jointly estimating candidate scores and judge-specific sensitivities (how strongly each judge responds to quality differences), often interpreted as reliability. We show that this reading fails when judges prefer a display position. Even under balanced display orders or swap-and-average, omitting position attenuates fitted judge sensitivity by approximately the factor 1-D2 near equal quality, where D is the judge's net first-slot preference between equally good responses. We propose OSCAR, which jointly estimates candidate scores, judge sensitivities and judge-specific position, length and family effects, and provides confidence intervals for pairwise win probabilities that account for dependence within prompts. On held-out data, observed attenuation closely matches the prediction 1-D2 (correlation of log ratios 0.99). Across four datasets, position adjustment lowers held-out log loss by 14-23% and changes which judges would be dropped for low sensitivity on three datasets. On MT-Bench, it ranks GPT-4 first instead of claude-v1, matching human votes. Simulations with known parameters show improved recovery of judge sensitivities and candidate rankings, with 94.4-95.2% confidence interval coverage. Low estimated sensitivity alone is therefore not evidence of an unreliable judge.