[FreakLegion]

When looking at admissions rates across the entire university, women are less likely to be accepted than men. But when (in this example) you break that down into departments, every department favors women over men.

If every department favored women then the entire university would also favor women. Parity is guaranteed in that scenario. What happened in the Berkeley case is that not every department favored women, and women applied disproportionately to the departments with lower admissions rates (including some that didn't favor them), while men did the opposite.

[jldugger]

Yes, apologies, what I meant by "favored" was that in every department, women applicants were more likely to get an admission than men. But I'm pretty sure the admission rate can still be lower for women overall than men overall, using exactly the same scenario you described. If the sociology department admits 10 percent of applicants and the physics department admits 90, it seems very easy for gender bias in applications to shift women towards 10 and men towards 90, even if the rate is a few percent higher for women.

[FreakLegion]

I get your point now. You're quite right that you can construct scenarios that arbitrarily favor men in the aggregate but women in specific departments, given the right ratio of applicants.