Four-Fifths Rule

The four-fifths rule — the 80% rule — is a screening guideline from the US Uniform Guidelines on Employee Selection Procedures. Compute each group’s selection rate, divide by the highest group’s rate, and a ratio below 0.80 will generally be regarded by the federal enforcement agencies as evidence of adverse impact.

\[ \text{Impact Ratio}_g = \frac{\text{Selection Rate}_g}{\text{Highest Group Selection Rate}} \]

The denominator is the group with the highest rate — not the largest group, not a permanent reference group. If 60 of 100 male applicants and 20 of 50 female applicants are hired, the rates are 0.60 and 0.40 and the ratio is 0.667, below the threshold.

It applies to hiring, promotion, transfer and retention, and it transfers directly to algorithmic selection tools whose outputs drive those decisions. It is a screening guideline, not a legal definition: falling below 0.80 does not establish discrimination, and clearing it is not a safe harbor.

Small pools can produce low ratios under equal selection probabilities

import numpy as np

rng = np.random.default_rng(0)
trials, rate = 5_000, 0.30
"""Two groups drawn from exactly the same process: every candidate is selected
   with probability 0.30, whatever group they are in. There is no disparity here."""

print(f"{'applicants per group':>22}  {'ratio below 0.80':>17}  {'median ratio':>13}  {'5th percentile':>15}")
for size in (20, 50, 100, 200, 500, 2000):
    picked = (rng.random((2, trials, size)) < rate).sum(axis=2) / size
    lower, higher = picked.min(axis=0), picked.max(axis=0)
    ratio = np.divide(lower, higher, out=np.zeros(trials), where=higher > 0)
    print(f"{size:>22}  {np.mean(ratio < 0.80):>16.1%}  {np.median(ratio):>13.4f}  {np.percentile(ratio, 5):>15.4f}")
#   applicants per group   ratio below 0.80   median ratio   5th percentile
#                     20             61.7%         0.7143           0.3333
#                     50             47.1%         0.8125           0.5294
#                    100             29.8%         0.8621           0.6512
#                    200             14.5%         0.9032           0.7344
#                    500              2.2%         0.9379           0.8248
#                   2000              0.0%         0.9678           0.9083

Both groups here are drawn from the identical process. Every candidate has the same 0.30 chance of selection and group membership does nothing. There is no disparity to detect.

With twenty applicants per group, the rule indicates adverse impact in 61.7% of runs. With fifty, 47.1%. With a hundred, 29.8%. It takes five hundred per group before the false alarm rate drops to 2.2%.

The median column says the same thing from another angle. Two identical processes produce a median impact ratio of 0.7143 at twenty applicants and 0.8621 at a hundred. The ratio is a quotient of two noisy estimates, and dividing the smaller by the larger biases it downward — at small counts it will sit below 1.0 even when the processes are the same, systematically.

This is exactly what the Uniform Guidelines anticipate. The same paragraph that states the rule adds that greater differences “may not constitute adverse impact where the differences are based on small numbers and are not statistically significant.” That sentence is usually dropped when the rule is quoted as an 80% test, and the table above is what it is protecting against.

It is not a safe harbor either

The symmetric failure is less visible and more consequential. At large sample sizes the rule almost never fires, and a real disparity that keeps the ratio at 0.85 will pass every quarter while affecting thousands of people.

The Guidelines say this too: smaller differences “may nevertheless constitute adverse impact, where they are significant in both statistical and practical terms.” A ratio of 0.85 across fifty thousand applicants is a large, reliably measured gap. A threshold designed for a rule of thumb is the wrong instrument for it.

Reporting one properly

• Publish the counts, not just the ratio. Applicants and selections per group, so a reader can judge whether the ratio means anything.
• Attach an interval or a test. The ratio alone cannot distinguish a real gap from the table above.
• Break it down by job, location, stage and period. Combining dissimilar roles can manufacture a disparity out of nothing, or hide one — the article on selection rate shows a case where both groups are hired at higher rates in every role and the combined ratio still reads 0.2629.
• Plan the comparisons in advance. Scanning many groups, jobs and stages produces sub-0.80 ratios by chance, at a rate the table makes obvious.
• Treat a result as a trigger, not a verdict. Whether a practice is job-related and consistent with business necessity is a legal question, and the Guidelines were adopted jointly by the EEOC, the Department of Labor, the Department of Justice and the former Civil Service Commission to frame it.

Where it sits among fairness criteria

The impact ratio is demographic parity in legal dress: a comparison of selection rates that never looks at the outcome. That is a deliberate feature in the employment context, where the recorded outcome is often the thing under suspicion.

The rule compares selection rates without assessing which selected candidates meet an outcome criterion. It does not automatically conflict with precision parity or error-rate constraints whenever base rates differ. Exact parity, an impact-ratio bound and approximate error-rate guardrails are different requirements. Check the particular combination and its feasible operating range, as discussed in fairness guardrails.

The broader fairness parity criteria answer different questions; passing this selection-rate screen does not establish them.

References

• 29 CFR 1607.4, Uniform Guidelines on Employee Selection Procedures — Information on impact
• 29 CFR Part 1607, Uniform Guidelines on Employee Selection Procedures