Two Ways to De-Bias an LLM-as-a-Judge: A Continuous-Score Comparison of Hierarchical Bayesian Calibration and Neural-ODE Score Transport

Andrea Morandi

cs.CLMay 9, 2026

Two Ways to De-Bias an LLM-as-a-Judge: A Continuous-Score Comparison of Hierarchical Bayesian Calibration and Neural-ODE Score Transport

Authors: Andrea Morandi

Organizations: Cisco Systems, Inc.

Abstract

[Abridged] Using a Large Language Model (LLM) as an automatic rater (LLM-as-a-judge) is cheap but potentially biased: some judges run lenient, others strict, the middle of the scale gets compressed, and verbose answers may be over-rewarded. A common remedy is post-hoc calibration: leave the cheap judge in place and, on a modest set of paired anchors, fit a transformation from raw judge scores to an estimate of the human rating. We compare two correctors that take opposing views on how this mapping should be modeled: a parametric, small-anchor hierarchical Bayesian linear correction with per-score uncertainty, and a non-parametric Neural-ODE (FFJORD) score-transport flow. Both are run head-to-head on UltraFeedback fine-grained_score (1700 paired examples, 200 held out), with calibration split into three operational sub-questions: population-mean recovery, per-item accuracy, and distributional-shape match. The headline result is that the choice between methods is primarily a data-budget question. Both correctors close the raw $+0.71$ -point mean offset to within $\pm 0.08$ of the GPT-4 reference, at 100 and at 1500 anchors. Past that, the methods swap roles. With 100 anchors, the linear corrector reconstructs the human-score distribution roughly twice as well by KL divergence (0.031 vs. 0.058) and ties the flow on MAE. With 1500 anchors the flow wins on every metric (MAE 0.320 vs. 0.359, Pearson 0.922 vs. 0.896, KL 0.026 vs. 0.037). The Bayesian linear corrector saturates well below 1500 anchors: residual $\tanh$ -shaped non-linearity is, by construction, structure a linear correction cannot fit. The flow keeps improving as labels grow. We translate these findings into an explicit decision rule for production deployments.

Explore similar work

May 7, 2026cs.LG

Bias and Uncertainty in LLM-as-a-Judge Estimation

LLM-as-a-Judge evaluation has become a standard tool for assessing base model performance. However, characterizing performance via the naive estimator, i.e., raw judge outputs, is systematically biased. Recent work has proposed estimators to correct this bias, but their reliability depends critically on judge quality and, for model comparisons, on calibration stability. Sharing calibration across compared models is practically attractive but can introduce severe bias, including cases where the comparison estimate points in the wrong direction with high apparent confidence. We study these failure modes through analytical results, simulations over judge quality (

J

) and cross-model calibration instability (

ΔJ

), and a real-data MMLU-Pro case study with sign reversal. We propose

J

and

ΔJ

as diagnostics for when corrected estimates, especially shared-calibration comparisons, are likely unreliable, and provide reporting guidance for LaaJ evaluation.

James Fiedler

Llm-As-A-Judge Raw Judge Outputs Mmlu-Pro

Ask PDF

Sep 14, 2026cs.LG

Can We Trust LLM Judges: A Study of Capability-Dependent Biases and Multi-Judge Ensemble for Bias Calibration

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.

Gemma Zhang, Prachi Badarayani, Asmi Kumar +2

Large Language Model Judges Llm-As-A-Judge Implicit Bias Ensemble

Ask PDF

Apr 25, 2026cs.AI

Judging the Judges: A Systematic Evaluation of Bias Mitigation Strategies in LLM-as-a-Judge Pipelines

LLM-as-a-Judge has become the dominant paradigm for evaluating language model outputs, yet LLM judges exhibit systematic biases that compromise evaluation reliability. We present a comprehensive empirical study comparing nine debiasing strategies across five judge models from four provider families (Google, Anthropic, OpenAI, Meta), three benchmarks (MT-Bench n=400, LLMBar n=200, custom n=375), and four bias types. Our headline practical finding is that a mid-tier model with the right debiasing can outperform frontier judges at a fraction of the cost: Gemini 2.5 Flash with the Combined Budget strategy reaches the highest agreement of any configuration we tested (71.0%, kappa=0.549) at ~

0.001 per evaluation, about 15x cheaper than the best frontier setup (Claude Sonnet 4, 69.5%, ~

0.015). Other key findings: (1) Style bias is the dominant bias (0.10-0.76 across models, favoring markdown over plain prose), far exceeding position bias (<=0.04), yet is rarely studied. (2) Verbosity bias is heterogeneous when measured length-aware: Pro, Flash, and Llama prefer longer answers (+0.24 to +0.44), Claude prefers concise (-0.12), and GPT-4o is neutral (-0.04); on truncation controls all models correctly prefer the complete response (0.88-1.00 accuracy). (3) Debiasing helps multiple models: Claude S8 (+11.5 pp), Flash S8 (+7.5 pp), and Claude S5 (+7.3 pp) survive Holm-Bonferroni correction, with Flash S1 (+4.7 pp) and Llama S8 (+4.5 pp) also significant. We release our evaluation framework, the 375-pair controlled dataset, and per-instance cached results for all nine strategies.

Sadman Kabir Soumik

Llm-As-A-Judge Judges Bias Mitigation

Ask PDF