weakness that there is much tuning and other specifics of the implementation that need to be determined on a case by case basis. It could be improved by giving some discussion of guidelines, principles, or references to other work explaining how tuning can be done, and some acknowledgement that the meaning of fairness may change dramatically depending on that tuning.
* Clarity
The paper is well organized and explained. It could be improved by some acknowledgement that there are a number of other (competing, often contradictory) definitions of fairness, and that the two appearing as constraints in the present work can in fact be contradictory in such a way that the optimization problem may be infeasible for some values of the tuning parameters.
* Originality
The most closely related work of Zemel et al. (2013) is referenced, the present paper explains how it is different, and gives comparisons in simulations. It could be improved by making these comparisons more systematic with respect to the tuning of each method--i.e. compare the best performance of each.
* Significance
The broad problem addressed here is of the utmost importance. I believe the popularity of (IF) and modularity of using preprocessing to address fairness means the present paper is likely to be used or built upon.
* Significance The broad problem addressed here is of the utmost importance. I believe the popularity of (IF) and modularity of using preprocessing to address fairness means the present paper is likely to be used or built upon.