Group Fairness

Also known as statistical parity, this independence-based metric requires the probability of a positive prediction to be identical across all groups.

• Formula: P(Ŷ=1 | A=a) = P(Ŷ=1 | A=b)
• Key weakness: Can lead to 'levelling down' where qualified candidates in one group are rejected to match a lower-performing group's rate
• Use case: College admissions and hiring where proportional representation is the explicit goal
• Violation example: A lending model approving 80% of Group A but only 60% of Group B

A separation-based metric requiring both the true positive rate and false positive rate to be equal across groups. This ensures the classifier is equally accurate for all populations.

• Formula: P(Ŷ=1 | Y=1, A=a) = P(Ŷ=1 | Y=1, A=b) AND P(Ŷ=1 | Y=0, A=a) = P(Ŷ=1 | Y=0, A=b)
• Key insight: Satisfies both the 'equal opportunity' and 'equal mistreatment' criteria simultaneously
• Limitation: Impossible to satisfy simultaneously with demographic parity when base rates differ across groups, except in trivial cases
• Origin: Formalized by Hardt, Price, and Srebro in their 2016 NeurIPS paper

A relaxed subset of equalized odds that only constrains the true positive rate across groups. It ensures equally qualified individuals have the same chance of receiving a positive outcome.

• Formula: P(Ŷ=1 | Y=1, A=a) = P(Ŷ=1 | Y=1, A=b)
• What it ignores: Does not constrain false positive rates, meaning one group could still experience higher rates of erroneous positive classifications
• Practical advantage: Less restrictive than full equalized odds, allowing for better accuracy-fairness trade-offs
• Example: A recidivism prediction tool where the true re-offense rate is captured equally across racial groups

A sufficiency-based metric requiring that the positive predictive value (precision) be equal across groups. A positive prediction must imply the same probability of success regardless of group membership.

• Formula: P(Y=1 | Ŷ=1, A=a) = P(Y=1 | Ŷ=1, A=b)
• Also called: 'Outcome test' in economics and legal scholarship
• Key property: When satisfied, a decision-maker can treat the model's score as meaning the same thing for all individuals
• Trade-off: Cannot be simultaneously satisfied with equalized odds when base rates differ, a result known as the impossibility theorem of fairness

A legal doctrine operationalized as the 80% rule (or four-fifths rule) from the Uniform Guidelines on Employee Selection Procedures.

• Formula: DI = P(Ŷ=1 | A=disadvantaged) / P(Ŷ=1 | A=advantaged)
• Threshold: A ratio below 0.8 indicates prima facie disparate impact
• Origin: Rooted in US employment discrimination law (Griggs v. Duke Power Co., 1971)
• Limitation: A purely statistical threshold that does not account for business necessity or job-relatedness defenses
• Modern use: Frequently reported in algorithmic bias audits alongside other metrics

A foundational result in algorithmic fairness proving that no classifier can simultaneously satisfy three common fairness criteria except in degenerate cases.

• The three incompatible criteria: Demographic Parity, Equalized Odds, and Predictive Parity
• When they align: Only when base rates Y are identical across groups or the classifier achieves perfect accuracy
• Practical implication: Organizations must explicitly choose which fairness definition aligns with their ethical and legal obligations—there is no one-size-fits-all solution
• Source: Proved independently by Kleinberg et al. (2016) and Chouldechova (2017)