Noise-Response Calibration: A Causal Intervention Protocol for LLM-Judges

Large language models (LLMs) are increasingly used as judges to predict which of two candidate answers a human evaluator would prefer, providing a scalable alternative when human evaluation is too costly. Unfortunately, LLM judgments can exhibit systematic biases. Prior work has documented position, verbosity or model family of the candidate answers influencing the judge decision rather than their quality, while additional biases may remain undocumented. $\textit{Multicalibration}$ provides a natural framework to address this problem: each bias corresponds to miscalibration on an identifiable group, $\textit{e.g.}$, family bias manifests as overconfidence in answers generated by models belonging to the same family of the judge. The challenge is to fix miscalibration simultaneously across many, potentially unknown groups. To this end, we introduce $\mathrm{CaLLM}$, a post hoc framework that multicalibrates an LLM judge, thereby bounding all such biases simultaneously. We prove that $\mathrm{CaLLM}$ bounds the bias of every group whose error structure is captured by an available representation, and that augmenting it with explicit bias groups further reduces the residual bias. We then derive theoretical conditions under which $\mathrm{CaLLM}$ improves the judge's accuracy, rather than trading it for calibration. Finally, we evaluate $\mathrm{CaLLM}$ across pairwise preference benchmarks, showing that it reduces the multicalibration error on both specified and unspecified bias groups, while improving predictive performance of the judge.

Large language models are increasingly used as judges to measure social bias in text, yet the passages they judge are often noisy, containing typos, informal spelling, and broken punctuation. The consequences of such surface noise for social bias measurement remain unclear. To investigate this question, we apply five realistic noise conditions at multiple intensity levels to 3,822 stereotype-related responses and compare the resulting bias judgments with those on the original text. We find that such surface noise does not degrade bias measurement symmetrically: it is far more likely to turn neutral judgments into biased ones than biased judgments into neutral ones, by up to a 120x margin. We further observe two non-obvious effects across four LLM judges: in the most fragile judge the distortion is at its purest at mild, realistic noise levels, where erasure is scarcest, and as judges grow robust it attenuates toward parity rather than reversing. Bias measured on noisy text is therefore systematically overestimated, most in the categories that matter most for fairness.

LLMs are increasingly used as automated judges for model training and evaluation, yet individual judges exhibit systematic biases that undermine reliability. Much of prior work has studied biases in pairwise LLM-as-a-judge settings; in this paper, we focus on absolute scoring tasks, which mirror more realistic use cases. Across four benchmarks and six models (36 judge-examinee pairs), we show that a model's task accuracy strongly predicts its judging accuracy (Pearson $r \geq 0.90$ on most models) and inversely predicts its directional bias ($r \leq -0.83$), but that accuracy alone does not ensure fair evaluation: more capable examinee models consistently receive more lenient judgments from all judges ($r \geq 0.83$). To address this, we propose calibrated weighted majority voting (WMV), an ensemble evaluation method that aggregates multiple LLM judges weighted by online estimates of their false-positive and false-negative rates. We introduce a disagreement-based estimator that derives these error rates purely from inter-judge agreement patterns, requiring no ground-truth labels or task metadata. In a simulated experiment with shifting task distributions, our label-free WMV tracks an oracle with perfect error-rate knowledge to within 0.5 percentage points on average, outperforming both individual judges and unweighted majority voting. These results demonstrate that principled multi-judge calibration can simultaneously improve accuracy and correct for systematic leniency without requiring labeled data, offering a scalable path to reliable automated evaluation as model capabilities increase.