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:

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.