1. Definition

  • Equal Opportunity requires that true positive rates (TPR) are the same across demographic groups.
  • In other words, among people who should receive a positive outcome ($Y=1$), each group should have an equal chance of being correctly predicted positive.

Formally:

$P(\hat{Y}=1 \mid Y=1, A=a) = P(\hat{Y}=1 \mid Y=1, A=b) \quad \forall \, a,b$

Where:

  • $\hat{Y}$ = model prediction
  • $Y$ = ground truth (actual label)
  • $A$ = protected attribute (e.g., gender, race)

It focuses on avoiding false negatives disproportionately in disadvantaged groups.

2. Example

Loan approval model:

  • Group A (men) — among actual qualified applicants ($Y=1$), 80% were approved ($\hat{Y}=1$).
  • Group B (women) — among actual qualified applicants, only 60% were approved.

This violates Equal Opportunity, since qualified women are less likely to be correctly recognized compared to men.

3. Why It’s Important

  • More practical than Demographic Parity because it considers ground truth labels.
  • Ensures qualified individuals are treated fairly, regardless of demographic group.
  • Common in high-stakes settings: hiring, college admissions, healthcare, lending.

4. Relation to Other Fairness Metrics

  • Demographic Parity → outcome rates equal across groups (ignores true labels).
  • Equal Opportunity → true positive rates equal across groups.
  • Equalized Odds → both true positive rates and false positive rates equal across groups.

5. Limitations

  • Does not enforce fairness in false positives.
  • If base rates ($P(Y=1 \mid A)$) differ across groups, achieving Equal Opportunity may reduce overall accuracy.

Summary:
Equal Opportunity = true positive rates are equal across groups.
It means qualified individuals from all demographics should have the same chance of being correctly recognized.