Fairness Metric

Requires the selection rate (probability of a positive prediction) to be equal across all protected groups.

• Formula: P(ŷ=1 | A=a) = P(ŷ=1 | A=b)
• Strength: Intuitive and legally aligned with the Four-Fifths Rule.
• Weakness: Ignores ground truth labels, potentially forcing the model to select unqualified individuals to meet quotas.
• Use Case: Hiring pipelines where legal compliance demands equal selection proportions.

A stricter metric requiring equal True Positive Rates (TPR) and False Positive Rates (FPR) across groups.

• Formula: TPR_a = TPR_b AND FPR_a = FPR_b
• Strength: Aligns fairness with accuracy by conditioning on the true outcome.
• Weakness: Impossible to satisfy simultaneously with Demographic Parity when base rates differ.
• Use Case: Medical diagnosis where missing a disease (false negative) has severe consequences.

A relaxation of Equalized Odds that only requires equality of True Positive Rates across groups.

• Formula: TPR_a = TPR_b
• Strength: Focuses solely on ensuring qualified individuals have equal chances of a positive outcome.
• Weakness: Does not constrain false positives, potentially exposing one group to higher rates of erroneous positive predictions.
• Use Case: Loan approval where the primary concern is ensuring creditworthy applicants are not denied.

Requires equal Positive Predictive Value (precision) across groups, meaning a positive prediction carries the same probability of being correct regardless of group membership.

• Formula: P(Y=1 | ŷ=1, A=a) = P(Y=1 | ŷ=1, A=b)
• Strength: Calibrates the meaning of a positive score across populations.
• Weakness: Can conflict with Equalized Odds when prevalence differs.
• Use Case: Predictive policing where the cost of a false positive (unnecessary stop) must be evenly distributed.

A causal metric defining a decision as fair if it remains the same in a counterfactual world where the individual belonged to a different demographic group.

• Mechanism: Uses Structural Causal Models (SCMs) to distinguish discriminatory path-specific effects from legitimate explanatory variables.
• Strength: Captures nuanced causal discrimination that statistical parity misses.
• Weakness: Requires a fully specified causal graph, which is difficult to construct and verify.
• Use Case: University admissions where legacy status may be a proxy for race.

Formalizes the principle that similar individuals should be treated similarly, regardless of group membership.

• Mechanism: Requires a task-specific distance metric d(x_i, x_j) and a Lipschitz constraint: D(f(x_i), f(x_j)) ≤ d(x_i, x_j).
• Strength: Avoids the statistical paradoxes of group metrics by operating at the instance level.
• Weakness: Defining the "right" similarity metric is a profound ethical and technical challenge.
• Use Case: Personalized content recommendation where individual user profiles should drive outcomes.