Four-Fifths Rule

The rule defines a selection rate for a protected group that is less than 80% of the rate for the group with the highest selection rate as evidence of adverse impact.

• Formula: (Selection Rate of Protected Group) / (Selection Rate of Highest Group)
• Example: If 60% of men pass a screening test but only 30% of women pass, the ratio is 30/60 = 50%. This violates the rule.
• Origin: Codified in the Uniform Guidelines on Employee Selection Procedures (1978).

The Four-Fifths Rule is a practical significance test, not a formal test of statistical significance. It acts as a preliminary diagnostic trigger.

• Small Sample Problem: The rule can be unreliable with very small applicant pools, flagging random variance as bias.
• Complementary Tests: Courts and auditors often pair it with Fisher's Exact Test or chi-squared tests to confirm that the disparity is not due to chance.
• Not a Legal Conclusion: A violation is evidence of adverse impact, not an automatic finding of illegal discrimination.

In bias detection, the rule is applied to the output of machine learning models to compare approval rates across demographic groups.

• Model Evaluation: Applied to the confusion matrix to compare the selection rate (positive predictions) for different groups.
• Proxy Variables: The rule can detect bias even when protected attributes are not explicitly used, by testing outcomes against known demographic segments.
• Monitoring: It serves as a continuous fairness metric in production ML pipelines to trigger alerts for model drift.

An employer cannot use overall workforce parity to mask internal selection disparities. The rule applies to each step of a multi-stage selection process.

• Hurdle Analysis: If a cognitive test and a physical test are used sequentially, the pass rate must be analyzed for each hurdle independently.
• Compensation Logic: A high hiring rate for a minority group in the final round does not excuse a discriminatory filter in the initial screening round.

If a selection procedure violates the rule, the employer bears the burden of proving job-relatedness and business necessity.

• Validation: The tool must be shown to be predictive of or significantly correlated with important elements of work behavior.
• Alternative Practices: The plaintiff can still win by showing that a less discriminatory alternative selection procedure exists that serves the employer's legitimate interest, but the employer refuses to adopt it.

The rule focuses solely on demographic parity and ignores the underlying ground truth of qualifications.

• Anti-Classification Blind Spot: It only looks at outcomes, not whether the model used protected attributes directly.
• Tension with Calibration: A perfectly calibrated model (equal predictive accuracy across groups) can still violate the Four-Fifths Rule if base rates differ.
• Intersectional Gaps: The rule must be applied to intersectional subgroups (e.g., Black women) to avoid masking compounded discrimination.

A fairness criterion requiring equal true positive rates and false positive rates across protected groups. Unlike statistical parity, equalized odds conditions on the true outcome, making it compatible with accuracy optimization.

• Matches error rates across groups
• More nuanced than the Four-Fifths Rule alone
• Harder to satisfy than demographic parity in practice

A framework evaluating bias across overlapping social identities—such as race and gender combined—rather than single-axis demographic categories. Standard Four-Fifths Rule analysis can mask compounded discrimination when examining only one protected attribute at a time.

• Reveals subgroup-level adverse impact
• Builds on Kimberlé Crenshaw's legal theory
• Requires sufficient sample sizes for compound groups

The quantitative metric directly derived from the Four-Fifths Rule. Calculated as the selection rate of the disadvantaged group divided by the selection rate of the advantaged group. A ratio below 0.80 (or 80%) constitutes evidence of adverse impact.

• Formula: AIR = SR_disadvantaged / SR_advantaged
• Values below 0.80 trigger further investigation
• Often supplemented with statistical significance tests like Fisher's Exact Test