  Machine learning models are increasingly used in critical decision-making
applications. However, these models are susceptible to replicating or even
amplifying bias present in real-world data. While there are various bias
mitigation methods and base estimators in the literature, selecting the optimal
model for a specific application remains challenging.
  This paper focuses on binary classification and proposes FairGridSearch, a
novel framework for comparing fairness-enhancing models. FairGridSearch enables
experimentation with different model parameter combinations and recommends the
best one. The study applies FairGridSearch to three popular datasets (Adult,
COMPAS, and German Credit) and analyzes the impacts of metric selection, base
estimator choice, and classification threshold on model fairness.
  The results highlight the significance of selecting appropriate accuracy and
fairness metrics for model evaluation. Additionally, different base estimators
and classification threshold values affect the effectiveness of bias mitigation
methods and fairness stability respectively, but the effects are not consistent
across all datasets. Based on these findings, future research on fairness in
machine learning should consider a broader range of factors when building fair
models, going beyond bias mitigation methods alone.
