CAIN-42 CAIN StudioFairGate: the four-fifths rule, done exactly
Compare favorable-outcome rates between two groups. If the lower group's rate is below four fifths of the higher group's, it is flagged (the EEOC rule of thumb used in hiring audits such as NYC Local Law 144).
Today's changes
- Exact arithmetic. With floats, 1 of 3 vs 5 of 12 (exactly 0.8) computed as 0.7999… and was flagged. Across every count pair up to 59 per group, 1,053 were wrongly flagged. The decision now uses exact fractions on the counts.
- Missing data is not "no". A record without an outcome used to count as unfavorable, and the string
"true"did not matchtrue. Both are now left out of the rates and reported. - Both directions. The rule compares each group with the highest one. A declared-privileged group at 30% vs 90%
was "not flagged"; it is now flagged and named in
impacted_group. - Small samples say so. Under 30 usable records per group, a warning says the ratio can flip on one record.
- Undefined is not clear. If the comparison group has no favorable outcomes, the verdict is UNDETERMINED and flagged for review.
| Group | Case | Want | Run 1 | After |
|---|---|---|---|---|
| FairGate | records missing the outcome field | refused or reported | failed | left out of the rates and reported (was counted as unfavorable) |
| FairGate | outcome 'true' string vs True | type mismatch reported | failed | left out and reported; a group with no usable records is a 400 |
| FairGate | privileged group has the lower rate | flagged or reported | failed | flagged, impacted_group named, four_fifths_ratio added |
| FairGate | 1 record per group | small-sample warning | failed | small-sample warning under 30 usable records per group |
| FairGate | ratio exactly 0.8 | not flagged | held | held on this pair; but exact-0.8 scan found 1,053 count pairs falsely flagged by float rounding: now exact fractions |
| FairGate | group value absent from data | 4xx | held | held |
FIRME AI CORPORATION · CAIN-42 is a Byzantine trust fabric. Numbers marked "our own check" were run by us, not by an independent party. Nothing on these pages is a certification.