Fairness Criteria

Definition

• Demographic parity (independence): $\hat{Y}\perp A$, i.e. $P(\hat{Y}=1\mid A=0)=P(\hat{Y}=1\mid A=1)$.
• Equalized odds (separation): $\hat{Y}\perp A\mid Y$, equal TPR and FPR; equal TPR alone is equal opportunity.
• Predictive parity (sufficiency): $Y\perp A\mid \hat{Y}$, equal $P(Y=1\mid \hat{Y}=y,A)$; calibration $P(Y=1\mid \hat{Y}=y,A=a)=y$.

Formula

From a group table: $P(\hat{Y}=1\mid A)=\frac{TP+FP}{n}$, TPR $=\frac{TP}{TP+FN}$ (column $Y=1$), FPR $=\frac{FP}{FP+TN}$ (column $Y=0$), PPV $=\frac{TP}{TP+FP}$ (row $\hat{Y}=1$).

If $A/\perp Y$ (different base rates), demographic parity and predictive parity cannot both hold, and neither can equalized odds and predictive parity. The constant classifier satisfies demographic parity and equalized odds, the perfect classifier equalized odds and predictive parity. Individual fairness (similar people, similar treatment) and counterfactual fairness are alternatives beyond groups.

Appears in

• Lecture 9.1, the COMPAS debate
• Lecture 9.1, demographic parity, equalized odds, predictive parity
• Lecture 9.1, exam-style task with two tables
• Lecture 9.1, impossibility results

Related concepts

• Fair Post-Processing
• Measurement and Construct
• Counterfactual Explanation