Modeling and Mitigating Gender Bias in Matching Problems: A Simulation-Based Approach with Quota Constraints

In high-stakes matching scenarios, such as hiring or resource distribution, biases tied to protected attributes, such as gender, can compromise fairness and efficiency. We propose a simulation-based framework to study the interplay between gender bias and quota policies in many-to-one matching problems, where individuals have preferences over positions with fixed capacities. Individuals' preferences are sampled from gender-specific Dirichlet priors, and we introduce a bias term to favor males artificially. Quotas are incorporated as constraints that ensure a specified female representation. We systematically analyze how bias levels and preference divergence, measured by Total Variation Distance, interact with different quota rules to affect gender-specific and overall efficiency. Our results highlight trade-offs between fairness and total efficiency, demonstrating that carefully calibrated quotas can mitigate disparities while maintaining acceptable efficiency levels.