Quantifying Gender Bias in Large Language Models Using Information-Theoretic and Statistical Analysis
Abstract
:1. Introduction
2. Related Work
3. The Proposed Method
- ensure robust experimental control,
- account for random variation in persona generation, and
- apply rigorous quantitative and qualitative analyses.
3.1. Large Language Models
3.1.1. OpenAI’s GPT-4o
- Temperature (): A scalar in the range (default: 0.8) that controls randomness in generation. A higher value of increases the entropy of the probability distribution, leading to more creative but less reproducible outputs, while a lower results in more deterministic responses.
- Max tokens (M): This parameter determines the maximum length of the output sequence in tokens. It constrains the sequence generation process such that the total number of tokens .
- System prompt: A mechanism to condition the behavior of the model by providing an initial context or directive.
3.1.2. Quantitative Modeling of Bias
3.1.3. Experimental Control and Random Variation
- Standardized Prompts: Every persona-generation task employs an identical prompt template to eliminate variability arising from prompt design.
- Randomization: Job titles are presented in a randomized order across trials. Let denote a random permutation of the set of job titles, ensuring that the sequence of prompts is uniformly randomized, thereby mitigating any potential order effects.
- Repetition: Each job title is subjected to N independent runs. This repetition permits modeling the inherent stochasticity of the generation process. For instance, if the generation of a particular gender label is treated as a Bernoulli trial with success probability p, then the count follows a Binomial distribution:This statistical model enables us to compute confidence intervals for and perform hypothesis testing regarding the presence of bias.
3.1.4. Anthropic’s Sonnet 3.5
3.1.5. Google’s Gemini 1.5 Pro
3.1.6. Meta’s Llama 3.1 8b
3.2. Experimental Design
- GPT-4o
- Gemini 1.5 Pro
- Sonnet 3.5
- LLaMA 3.1:8b
- Healthcare (e.g., “nurse”, “radiologist”, “doctor”, “surgeon”, “anesthesiologist”, “pharmacist”, etc.)
- Information Technology (e.g., “python developer”, “machine learning engineer”, “project manager”, “product manager”, “data scientist”, “data analyst”, etc.)
- Professional Services (e.g., “lawyer”, “accountant”, “office assistant”, “secretary”, “police officer”, “detective”, “sheriff”, “deputy”, etc.)
Create a perfect persona for a {{job}}. Make sure you will also assign gender to this persona.
3.3. Data Collection
3.4. Data Analysis
3.5. Rigor and Validity Measures
3.5.1. Control of Confounding Variables
3.5.2. Sample Size Justification
3.5.3. Ethical and Conceptual Trade-Offs in the “Perfect Persona” Framework
4. Experimental Results and Discussion
4.1. Overview of Gender Assignments
- Dominance of the “Female” Category: Across all models, female assignments were predominant. For example, Gemini 1.5 Pro produced 3716 female designations, while Clause 3.5 Sonnet recorded 3060 female designations. These high frequencies indicate that, for these models, the probability far exceeds the expected ideal of (assuming an unbiased distribution).
- Secondary Prevalence of the “Male” Category: Although male designations were the second most common, their occurrence was notably lower. GPT-4o, for instance, generated 1262 male assignments compared to 1514 female assignments in a comparable evaluation window.
- Marginal Representation of “Non-Binary” and “Other”: The frequencies for non-binary and other categories were extremely low. LLaMA 3.1:8b assigned the “non-binary” label only 19 times, and Clause 3.5 Sonnet did not generate any non-binary or other designations. These results suggest that the internal representations for non-binary identities are severely underdeveloped in these models.
4.2. Model-Specific Gender Distribution Patterns
4.2.1. Gemini 1.5 Pro
4.2.2. GPT-4o
4.2.3. LLaMA 3.1:8b
4.2.4. Clause 3.5 Sonnet
4.3. Cross-Model Comparative Analysis
4.3.1. Binary-Centric Bias
4.3.2. Magnitude of Skew
4.3.3. Inclusivity and Representation Challenges
4.4. Implications and Future Directions
- Dataset Augmentation: Incorporate more balanced and inclusive datasets that ensure adequate representation of non-binary and other gender identities. Synthetic datasets with controlled distributions could be employed for this purpose.
- Fairness-Constrained Training: Integrate fairness-aware regularization terms into the training loss, as exemplified by the augmented loss function above. This would mathematically enforce a penalty on biased gender distributions.
- Architectural Modifications: Adapt model architectures to include specialized classification heads or embedding layers that explicitly model a broader spectrum of gender identities. Techniques such as multi-task learning or the use of adversarial networks to debias representations could be explored.
- Interpretability and Attribution: Utilize attention-based analyses, gradient-based attribution methods, and contrastive prompting to dissect the internal representations of the models. Such techniques can reveal the contextual triggers behind biased outputs and guide targeted interventions.
4.5. Analysis of Bias Origins
4.6. Bias Mitigation Experiment
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Job Titles | |||||
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Mirza, I.; Jafari, A.A.; Ozcinar, C.; Anbarjafari, G. Quantifying Gender Bias in Large Language Models Using Information-Theoretic and Statistical Analysis. Information 2025, 16, 358. https://doi.org/10.3390/info16050358
Mirza I, Jafari AA, Ozcinar C, Anbarjafari G. Quantifying Gender Bias in Large Language Models Using Information-Theoretic and Statistical Analysis. Information. 2025; 16(5):358. https://doi.org/10.3390/info16050358
Chicago/Turabian StyleMirza, Imran, Akbar Anbar Jafari, Cagri Ozcinar, and Gholamreza Anbarjafari. 2025. "Quantifying Gender Bias in Large Language Models Using Information-Theoretic and Statistical Analysis" Information 16, no. 5: 358. https://doi.org/10.3390/info16050358
APA StyleMirza, I., Jafari, A. A., Ozcinar, C., & Anbarjafari, G. (2025). Quantifying Gender Bias in Large Language Models Using Information-Theoretic and Statistical Analysis. Information, 16(5), 358. https://doi.org/10.3390/info16050358