Three reviewers who are all good experts for this paper found the paper interesting, novel, compelling, and well-written. With such a difficult topic as fairness, it was particularly helpful that the authors were able to discuss their assumptions, results, and proofs so clearly, and that definitely adds value to the work. The authors' response was appreciated and was found to be helpful, but reviewers expressed some concern in discussion about adding too many new results they didn't have a chance to review, so while we hope the authors can address some of the reviewers suggestions in the final paper, they are encouraged not to add too much stuff that wasn't reviewed, but instead to consider expanding on some of that for a follow-on submission.