Ask the Right Comparison:Bias-Aware Bayesian Active Top-$k$ Ranking with LLM Judges

Jian Xu; Delu Zeng; John Paisley; Qibin Zhao

cs.LGJul 2, 2026

Ask the Right Comparison:Bias-Aware Bayesian Active Top- $k$ Ranking with LLM Judges

Authors: Jian Xu, Delu Zeng, John Paisley, Qibin Zhao

Organizations: RIKEN iTHEMS · RIKEN AIP · South China University of Technology · Columbia University

Abstract

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.

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