equalized odds

Equalized odds is a fairness definition that, unlike demographic parity, pays attention to whether the decision was correct. It asks: among the people who truly should get a yes, is the model just as likely to say yes regardless of their group? And among the people who truly should get a no, is it just as likely to wrongly say yes, again regardless of group? In plain terms: the model should make its mistakes — both kinds — at equal rates across groups.

Suppose a medical test flags patients for follow-up. Equalized odds says: of the patients who really are sick, the same fraction should be caught in every group (equal true-positive rates), and of the patients who are actually healthy, the same fraction should be falsely alarmed in every group (equal false-positive rates). It deliberately lets the overall rate of yeses differ between groups if their underlying need differs — what it forbids is a system that, say, catches 90% of sick people in one group but only 60% in another.

Why it matters: equalized odds targets a sharper harm than demographic parity. It directly fights the situation where a tool works well for one group and poorly for another — being more likely to falsely accuse, or more likely to miss real cases, depending on who you are. That is exactly the failure mode that has plagued real systems, from facial recognition that misidentifies darker-skinned faces more often, to risk scores that over-flag one community. The trade-off is honesty about its cost: enforcing it can force a model to be less accurate overall, and you usually can't have it together with equal calibration.