equalized odds

**Equalized odds** is a **fairness criterion** in machine learning that requires a classifier to have the **same true positive rate** and **same false positive rate** across all demographic groups. It ensures that the model's **accuracy and errors** are distributed equally, regardless of group membership. **Formal Definition** A classifier satisfies equalized odds with respect to a protected attribute A (e.g., race, gender) and true label Y if: $$P(\hat{Y}=1|A=a, Y=y) = P(\hat{Y}=1|A=b, Y=y) \quad \forall y \in \{0,1\}$$ This means: - **Equal True Positive Rates**: Among people who actually qualify (Y=1), the model approves them at the same rate regardless of group. - **Equal False Positive Rates**: Among people who don't qualify (Y=0), the model incorrectly approves them at the same rate regardless of group. **Why It Matters** - **Lending Example**: If a loan approval model has a **90% true positive rate** for one racial group but **70%** for another, equally qualified applicants from the second group are unfairly rejected more often. - **Hiring**: A resume screening tool must have similar error rates across gender, race, and age groups. - **Criminal Justice**: Risk assessment tools must not have systematically different error rates across racial groups. **Relationship to Other Fairness Metrics** - **Demographic Parity**: Requires equal prediction rates regardless of outcome — weaker than equalized odds. - **Equal Opportunity**: Requires only equal true positive rates — a relaxation of equalized odds. - **Predictive Parity**: Requires equal precision across groups — a different perspective on fairness. **Achieving Equalized Odds** - **Post-Processing**: Adjust prediction thresholds per group to equalize error rates (Hardt et al., 2016). - **In-Processing**: Add fairness constraints during model training. - **Trade-Offs**: Enforcing equalized odds typically requires sacrificing some **overall accuracy** — the accuracy-fairness trade-off. Equalized odds is one of the most widely studied fairness criteria and is referenced in **AI regulations** and **fairness auditing** frameworks.