Paper:
From Parity to Preference-based Notions of Fairness in Classification
The adoption of automated, data-driven decision making in an ever expanding range of applications has raised concerns about its potential unfairness towards certain social groups. In this context, a number of recent studies have focused on defining, detecting, and removing unfairness from data-driven decision systems. However, the existing notions of fairness, based on parity (equality) in treatment or outcomes for different social groups, tend to be quite stringent, limiting the overall decision making accuracy. In this paper, we draw inspiration from the fairdivision and envy-freeness literature in economics and game theory and propose preference-based notions of fairness-given the choice between various sets of decision treatments or outcomes, any group of users would collectively prefer its treatment or outcomes, regardless of the (dis)parity as compared to the other groups. Then, we introduce tractable proxies to design margin-based classifiers that satisfy these preference-based notions of fairness. Finally, we experiment with a variety of synthetic and real-world datasets and show that preference-based fairness allows for greater decision accuracy than parity-based fairness.

Review:
ML models control many aspects of our life such as our bank decision on approving a loan or a medical centers that use ML to make treatment decision. Therefore, it is paramount that these models are fair, even in cases where the data contains biases. This study follows previous studies in the field but argues that the definition of fairness provided in previous studies might pose a too high bar which results in unnecessary cost in terms of accuracy. Instead they present an alternative fairness definition, presenting an algorithm to apply it for linear classifiers together with some empirical results.
I find this paper very interesting and relevant but lacking in several aspects. I think that it will benefit from some additional depth which will make it a significant contribution. Here are some issues that I find with this paper:
1.	I am not sure that the treatment of the bias is comprehensive enough. For example, if z is a gender feature. A classifier may ignore this feature altogether but still introduce bias by inferring gender from other features such that height, weight, facial image, or even the existence of male/female reproducing organs. I could not figure out from the text how this issue is treated. This is important that in the current definition, if a model never treats a person with male reproducing organs for cancer, this model may be gender-fair. The paragraph at lines 94-100 gives a short discussion that relates to this issue but it should be made more explicit and clear.
2.	There is a sense of over-selling in this paper. The abstract suggests that there is an algorithmic solution but only in section 3 an assumption is added that the classification model is linear. This is a non-trivial constraint but there is no discussion on scenarios in which linear models are to be used.
Some additional comments that the authors may wish to consider:
3.	The introduction can benefit from concrete examples. For example, you can take the case of treating cancer: while male and female should receive equally good treatment, it does not mean that female should be treated for prostate cancer or male should be treated for breast cancer in the same rates.
4.	Lines 66-74 are repetition of previous paragraphs
5.	Line 79: “may” should be “many”
6.	When making the approximations (lines 171-175) you should show that these are good approximation in a sense that a solution to the approximated problem will be a good solution to the original problem. It may be easier to state the original problem as (9) and avoid the approximation discussion.