The reviewers were overall in agreement that the paper provides a useful unified treatment of different notions of group fairness. The analysis of the multi-class classification setting also seems novel. However, the reviewers were unified in their concern that the independent group fairness definition is not well-motivated aside from computational considerations. Given that intersectional fairness has received considerable treatment in prior work (e.g., the fairness gerrymandering work), the authors should provide stronger practical motivation for the intermediate fairness definitions.