I Never Thought of Quotas in Your Way

Women are less likely to compete for prestigious positions because they worry about backlash that could undermine their allies and alienate their husbands. You need to mitigate women's fear that competition will make them forfeit allies, et cetera. And you can do that in two ways: Either if they come from a matrilineal society where they've already got those strong allies or if they're very supportive of women. If you don't have a culture with that long history, if there is a risk of backlash, then the best way to mitigate it is boom! Quarters mandate it so that women who go for the top don't face that backlash that's been seen as up.