disparate impact ratio concept
| Definition | The rate of a favourable decision in one group divided by the rate in another. Equation 0.37. Also disparate impact, four-fifths, per group. |
|---|---|
| Example | Positive rates of 0.48 for one group and 0.60 for another give a ratio of 0.8. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id disparate-impact-ratio, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 0.37. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/DisparateImpact.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 0.37.
\[\mathrm{DI}=\frac{\Pr[\hat y=1\mid g=a]}{\Pr[\hat y=1\mid g=b]},\qquad \text{equalized odds}:\ \mathrm{TPR}_a=\mathrm{TPR}_b,\ \mathrm{FPR}_a=\mathrm{FPR}_b.\]
Book equation 14.5.
\[\mathrm{FC}_g=\Pr\big[y=\text{violation}\ \big|\ \hat y=\text{clear},\ g\big],\qquad \text{verdict}=\max_{g:\ n_g\ge n_{\min}}\mathrm{FC}_g,\qquad \text{ABSTAIN otherwise}.\]
Conditions
- The ratio of the favourable-decision rate in one group to the rate in another. It is one exactly when the rates agree, it inverts when the groups are swapped, and the four-fifths rule is a statement about the rate gap.
- The book’s verdict is per group with a null, the worst group’s false-clear rate over the groups large enough to score, which clears a bar exactly when every scored group does and is never below the pooled rate.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 0 section 0.18 and chapter 14 section 14.6 of Data Mining as Observation, with the per-group verdict of equation 14.5.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/DisparateImpact.lean,
theorems ratio_eq_one_iff, ratio_swap,
four_fifths_iff, verdict_le_iff,
weighted_le_verdict, at observation-data-mining f3914f0;
what the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation primer S, chapters 0, 14.
Related
equalized odds; min-over-strata; false-clear rate; abstention.
See also
Sources-table rows that share a record with the entry without naming it: chapter 14 section 14.1.
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.