Disparate-impact math and the bias-audit machine

Lesson 3 of 6 in Testing and Evaluation: Fairness Math, Red-Teaming, and Explainability.

US employment law gave the world the oldest operational fairness test, and it is pure demographic parity: the four-fifths rule from the EEOC’s 1978 Uniform Guidelines. Compute each group’s selection rate (selected ÷ applied). Divide the lower rate by the highest. If the ratio falls below 0.80, the selection procedure is presumptively evidence of adverse impact.

Worked example: 120 of 200 male applicants pass a screening model (60%); 45 of 100 female applicants pass (45%). Impact ratio = 45 ÷ 60 = 0.75. Below 0.80 — flagged. The employer must now justify the procedure as job-related and consistent with business necessity, and show no less-discriminatory alternative exists.

Two technical caveats every auditor recites. Small samples lie: with 10 applicants per group, one person flips the ratio across the line, so practitioners supplement with statistical significance tests (the classic threshold: a difference greater than two or three standard deviations). And the rule is a screening heuristic, not a safe harbour — courts have found impact above 0.80 unlawful and below 0.80 defensible on the full evidence.

The measurement paradox. To compute any of this you need protected-attribute data — which privacy law and company policy often prevent collecting. US financial regulators square the circle with inference: BISG (Bayesian Improved Surname Geocoding) estimates race probabilities from surname and address, and the CFPB has used it in fair-lending enforcement. It works acceptably at portfolio level and poorly at individual level, and its error is itself unevenly distributed — so governance treats inferred attributes as an auditing instrument, never as an input to decisions about individuals.

Once bias is found, the mitigation families:

• Pre-processing — repair the data: reweighting, resampling, relabeling, removing proxies.
• In-processing — constrain the training: add a fairness term to the loss, adversarial debiasing.
• Post-processing — adjust the outputs: group-specific thresholds, score recalibration.

Post-processing is the cheapest and most transparent — and the most legally exposed, because explicitly group-conditional thresholds can constitute disparate treatment (intentional differential treatment) even when deployed to cure disparate impact. After the US Supreme Court’s SFFA decision sharpened scrutiny of race-conscious decision-making, most US counsel steer teams toward pre-processing and label/feature redesign. The legal tension is unresolved; document the reasoning either way.

Key terms: four-fifths rule, disparate impact, disparate treatment, bias audit (NYC LL144), bisg, automated employment decision tool

Tool: Bias Audit Lab — Run a full LL144-style audit: compute selection rates and impact ratios on a synthetic applicant pool, hit the small-sample trap, and write the published summary.

Interactive checkpoint quiz (2 questions) — open this page in a browser to take it.