Demographic parity
Same rate of positive decisions in each protected group — ignoring whether those decisions were correct.
$$P(\hat Y=1\mid G=a)=P(\hat Y=1\mid G=b)$$
University admissions numbers
Group $a$: 450 accepted of 900 (50%). Group $b$: 50 of 200 (25%). Demographic parity fails.
To accept 500 students with parity given the applicant mix (~82% / 18%), take about 410 from $a$ and 90 from $b$ — possibly different score cutoffs, and some lower-scoring $b$ applicants above higher-scoring $a$ rejects.
Drawbacks
Ignores correctness. Awkward when base rates of true $Y$ differ across groups, or when the model is unequally accurate.
Key takeaways
- Equal selection rates across $G$.
- Simple but blunt.
- Can conflict with accuracy and with other fairness notions.