Relative Bias: A Comparative Framework for Quantifying Bias in LLMs
Bibliographic record
Abstract
The growing deployment of large language models (LLMs) has amplified concerns regarding their inherent biases, raising critical questions about their fairness, safety, and societal impact. However, quantifying LLM bias remains a fundamental challenge, complicated by the ambiguity of what "bias" entails. This challenge grows as new models emerge rapidly and gain widespread use, while introducing potential biases that have not been systematically assessed. In this paper, we propose the Relative Bias framework, a method designed to assess how an LLM's behavior deviates from other LLMs within a specified target domain. We introduce two complementary methodologies: (1) Embedding Transformation analysis, which captures relative bias patterns through sentence representations over the embedding space, and (2) LLM-as-a-Judge, which employs a language model to evaluate outputs comparatively. Applying our framework to several case studies on bias and alignment scenarios following by statistical tests for validation, we find strong alignment between the two scoring methods, offering a systematic, scalable, and statistically grounded approach for comparative bias analysis in LLMs.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.076 | 0.340 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.010 | 0.006 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.007 | 0.013 |
| Open science | 0.003 | 0.008 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".