Beyond Parity: Fairness Objectives for Collaborative Filtering
We study fairness in collaborative-filtering recommender systems, which are sensitive to discrimination that exists in historical data. Biased data can lead collaborative-filtering methods to make unfair predictions for users from minority groups. We identify the insufficiency of existing fairness metrics and propose four new metrics that address different forms of unfairness. These fairness metrics can be optimized by adding fairness terms to the learning objective. Experiments on synthetic and real data show that our new metrics can better measure fairness than the baseline, and that the fairness objectives effectively help reduce unfairness.
In this paper the authors explore different metrics for measuring fairness in recommender systems.  In particular, they offer 4 different metrics that measure if a recommender system over-estimates or under-estimates how much a group of users will like a particular genre.  Further, they show that by regularizing the by the discrepancy across groups does not hurt the model accuracy while improving fairness on the metric used for the regularization (as well as undiscussed slight effects on the other fairness metrics).
In contrast to the work of Hardt et al, this paper focuses on a regression task (rating prediction) and explores the difference between absolute and relative errors.  This is an interesting point in recommender systems that could easily be overlooked by other metrics.  Further, the clear demonstration of bias on MovieLens data and the ability to improve it through regularization is a valuable contribution.  Additionally, the simplicity of the approach and clarity of the writing should be valued.
However, the metrics are also limited in my opinion.  In particular, all of the metrics focus on average ratings over different groups.  It is easy to imagine a model that has none of the biases discussed in this paper, but performs terribly for one group and great for the other.  A more direct extrapolation of equality of opportunity would seem to focus on model accuracy per-rating rather than aggregates.  I do not think this ruins the work here, as I mentioned above that the directionality of the errors is an important observation, but I do think it is a limitation that will need to be developed upon in the future.
In this vain, a significant amount of recommender systems research is not cited or compared against.  Data sparsity, missing not at random, learning across different subgroups, using side information, etc. have all been explored in the recommender systems literature.  At the least, comparing against other collaborative filtering models that attempt to improve the model accuracy by side information would provide better context (as well as reporting accuracy of the model by both gender and genre).  A few pieces of related work are included below.
"Collaborative Filtering and the Missing at Random Assumption" Marlin et al 
"Beyond Globally Optimal: Focused Learning for Improved Recommendations" Beutel al
"It takes two to tango: An exploration of domain pairs for cross-domain collaborative filtering" Sahebi et al