Gender (or other) quotas for entering PhD classes: what do we really know about their effects?

A reader writes:

In my department's recent annual graduate student meeting, one colleague brought up the idea that our department should strive to achieve gender balance for each incoming class. There were a lot of armchair speculations about the positive and negative effects of imposing such an 'affirmative action' policy, but very little empirical evidence presented. I am wondering if it would be possible for you to put the question to your blog's readers. I would especially be interested to hear from departments who have implemented some version of the policy and what they perceive the effects to be.

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