equalized odds concept
| Definition | The requirement that the true-positive rate and the false-positive rate be the same across groups. Equation 0.37. Also three ways. |
|---|---|
| Example | True positive rates of 0.90 and 0.88 with false positive rates of 0.10 and 0.11 across two groups are nearly equalized odds. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id equalized-odds, 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/EqualizedOdds.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 0.37.
\[\mathrm{DI}=\frac{\Pr[\hat y=1\mid g=a]}{\Pr[\hat y=1\mid g=b]},\qquad \text{equalized odds}:\ \mathrm{TPR}_a=\mathrm{TPR}_b,\ \mathrm{FPR}_a=\mathrm{FPR}_b.\]
Conditions
- Equal true-positive and false-positive rates across groups. A group’s favourable rate is its true-positive rate times its base rate plus its false-positive rate times the rest, so under equalized odds the favourable rates agree exactly when the base rates do, given that the classifier separates at all.
- Equalized odds and parity of outcomes therefore conflict whenever the base rates differ. With rates 0.8 and 0.2 and base rates one half and one tenth the favourable rates are 0.5 and 0.26, a ratio below four fifths.
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, where fairness cannot be had three ways.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/EqualizedOdds.lean,
theorems parity_of_equal_base, favourable_sub,
parity_iff_equal_base, example_conflict, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation chapters 0, 3, 10, 12, 14.
Related
disparate impact ratio; calibration; min-over-strata; certificate.
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.