address the more major concerns

We take your comments to heart and will make all of the small changes suggested. The purpose of the experiments is modest: to support the theory. Reviewer 3 is correct that prior work -- in particular, [Kearns et al.] -- In short, because the framework of "oracle efficiency" leaves a gap between theory and practice, we think of it as The group-fairness proposal of [Kearns et al.] indeed mitigates the "gerrymandering" concern we cite