  Clustering is a fundamental problem in machine learning and operations
research. Therefore, given the fact that fairness considerations have become of
paramount importance in algorithm design, fairness in clustering has received
significant attention from the research community. The literature on fair
clustering has resulted in a collection of interesting fairness notions and
elaborate algorithms. In this paper, we take a critical view of fair
clustering, identifying a collection of ignored issues such as the lack of a
clear utility characterization and the difficulty in accounting for the
downstream effects of a fair clustering algorithm in machine learning settings.
In some cases, we demonstrate examples where the application of a fair
clustering algorithm can have significant negative impacts on social welfare.
We end by identifying a collection of steps that would lead towards more
impactful research in fair clustering.
