A CaLLM Judge is a Better Judge: Mitigating Bias in LLM-as-a-judge

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.