# Bias and Volatility: A Statistical Framework for Evaluating Large Language Model's Stereotypes and the Associated Generation Inconsistency

arXiv: https://arxiv.org/abs/2402.15481 · HTML: https://mlsanity.com/paper/2402.15481/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 61 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 30 of 36)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [Red Teaming Language Models with Language Models](https://mlsanity.com/paper/2202.03286/) (2022)
- [StereoSet: Measuring stereotypical bias in pretrained language models](https://mlsanity.com/paper/2004.09456/) (2020)
- [Semantics derived automatically from language corpora contain human-like biases](https://mlsanity.com/paper/1608.07187/) (2016)
- [GLM-130B: An Open Bilingual Pre-trained Model](https://mlsanity.com/paper/2210.02414/) (2022)
- [Automated Hate Speech Detection and the Problem of Offensive Language](https://mlsanity.com/paper/1703.04009/) (2017)
- [CrowS-Pairs: A Challenge Dataset for Measuring Social Biases in Masked Language Models](https://mlsanity.com/paper/2010.00133/) (2020)
- [Gender Bias in Coreference Resolution: Evaluation and Debiasing Methods](https://mlsanity.com/paper/1804.06876/) (2018)
- [Bias and Fairness in Large Language Models: A Survey](https://mlsanity.com/paper/2309.00770/) (2023)
- [On Measuring Social Biases in Sentence Encoders](https://mlsanity.com/paper/1903.10561/) (2019)
- [Bias in Bios: A Case Study of Semantic Representation Bias in a High-Stakes Setting](https://mlsanity.com/paper/1901.09451/) (2019)
- [Evaluating Gender Bias in Machine Translation](https://mlsanity.com/paper/1906.00591/) (2019)
- [Identifying and Reducing Gender Bias in Word-Level Language Models](https://mlsanity.com/paper/1904.03035/) (2019)
- [Gender Bias in Neural Natural Language Processing](https://mlsanity.com/paper/1807.11714/) (2018)
- [Social Biases in NLP Models as Barriers for Persons with Disabilities](https://mlsanity.com/paper/2005.00813/) (2020)
- [Intrinsic Bias Metrics Do Not Correlate with Application Bias](https://mlsanity.com/paper/2012.15859/) (2020)
- [UnQovering Stereotyping Biases via Underspecified Questions](https://mlsanity.com/paper/2010.02428/) (2020)
- [Ethical-Advice Taker: Do Language Models Understand Natural Language Interventions?](https://mlsanity.com/paper/2106.01465/) (2021)
- [OSCaR: Orthogonal Subspace Correction and Rectification of Biases in Word Embeddings](https://mlsanity.com/paper/2007.00049/) (2020)

## Built on by (most cited first, 15 of 15)

- [More of the Same: Persistent Representational Harms Under Increased Representation](https://mlsanity.com/paper/2503.00333/) (2025)
- [Variance reduction in output from generative AI](https://mlsanity.com/paper/2503.01033/) (2025)
- [Evaluate Bias without Manual Test Sets: A Concept Representation Perspective for LLMs](https://mlsanity.com/paper/2505.15524/) (2025)
- [Do Large Language Models (Really) Need Statistical Foundations?](https://mlsanity.com/paper/2505.19145/) (2025)
- [InfiCoEvalChain: A Blockchain-Based Decentralized Framework for Collaborative LLM Evaluation](https://mlsanity.com/paper/2602.08229/) (2026)
- [Structured Reasoning for Fairness: A Multi-Agent Approach to Bias Detection in Textual Data](https://mlsanity.com/paper/2503.00355/) (2025)
- [Designing Synthetic Discussion Generation Systems: A Case Study for Online Facilitation](https://mlsanity.com/paper/2503.16505/) (2025)
- [DIF: A Framework for Benchmarking and Verifying Implicit Bias in LLMs](https://mlsanity.com/paper/2505.10013/) (2025)
- [P2VA: Converting Persona Descriptions into Voice Attributes for Fair and Controllable Text-to-Speech](https://mlsanity.com/paper/2505.17093/) (2025)
- [DeFrame: Debiasing Large Language Models Against Framing Effects](https://mlsanity.com/paper/2602.04306/) (2026)
- [Bias in the Tails: How Name-conditioned Evaluative Framing in Resume Summaries Destabilizes LLM-based Hiring](https://mlsanity.com/paper/2604.19984/) (2026)
- [BiAxisBias: Evaluating LLM Bias Beyond a Single Prompt and a Single Explanation](https://mlsanity.com/paper/2605.09041/) (2026)
- [BiasGRPO: Stabilizing Bias Mitigation in High-Variance Reward Landscapes via Group-Relative Policy Optimization](https://mlsanity.com/paper/2606.04807/) (2026)
- [Adversarial Alignment: Ensuring Value Consistency in Large Language Models for Sensitive Domains](https://mlsanity.com/paper/2601.13137/) (2026)
- [LLM Nepotism in Organizational Governance](https://mlsanity.com/paper/2604.09620/) (2026)

## Abstract (arXiv)

We present a novel statistical framework for analyzing stereotypes in large language models (LLMs) by systematically estimating the bias and variation in their generation. Current alignment evaluation metrics often overlook stereotypes' randomness caused by LLMs' inconsistent generative behavior. For instance, LLMs may display contradictory stereotypes, such as those related to gender or race, for identical professions in different contexts. Ignoring this inconsistency risks misleading conclusions in alignment assessments and undermines efforts to evaluate the potential of LLMs to perpetuate or amplify social biases and unfairness. To address this, we propose the Bias-Volatility Framework (BVF), which estimates the probability distribution of stereotypes in LLM outputs. By capturing the variation in generative behavior, BVF assesses both the likelihood and degree to which LLM outputs negatively impact vulnerable groups, enabling a quantification of aggregated discrimination risk. Additionally, we introduce a mathematical framework to decompose this risk into bias risk (from the mean of the stereotype distribution) and volatility risk (from its variation). Applying BVF to 12 widely used LLMs, we find: i) Bias risk is the dominant contributor to discrimination; ii) Most LLMs exhibit substantial pro-male stereotypes across nearly all professions; iii) Reinforcement learning from human feedback reduces bias but increases volatility; iv) Discrimination risk correlates with socio-economic factors, such as professional salaries. Finally, we highlight BVF's broader applicability for assessing how generation inconsistencies in LLMs impact behavior beyond stereotypes.