Home / 13. Fairness / Equalized odds

Equalized odds

Match true-positive and true-negative rates across groups — fairness conditional on the true label $Y$.

Equalized odds

Require the same true-negative rate and true-positive rate across groups: $$P(\\hat Y=0\\mid Y=0,G=a)=P(\\hat Y=0\\mid Y=0,G=b)$$ $$P(\\hat Y=1\\mid Y=1,G=a)=P(\\hat Y=1\\mid Y=1,G=b)$$

Equalized odds ≈ matched TPR & TNR TPR a / b TNR a / b Bars nearly equal across groups ⇒ EO holds
TPR and TNR bars matched across groups — the equalized-odds idea.
Tiredness detector (toy table)

Group $a$: among not-tired ($Y=0$), 70/85 ≈ 82% correctly called not-tired; among tired, 130/150 ≈ 87% caught.

Group $b$: similar TNR/TPR (e.g. ~75% and ~86% in the course-style table) can approximately satisfy equalized odds even if overall positive rates differ.

Contrast with demographic parity

DP equalizes $P(\hat{{Y}}=1\mid G)$ and ignores $Y$. Equalized odds conditions on $Y$ and equalizes error behaviour.

Key takeaways

  • Conditions on true $Y$.
  • Equalizes TPR and TNR across $G$.
  • Still forces tradeoffs — may hurt some group’s raw accuracy.