As the frontier of machine learning applications moves further into human interaction, multiple concerns arise regarding automated decision-making. Two of the most critical issues are fairness and data privacy. On the one hand, one must guarantee that automated decisions are not biased against certain groups, especially those unprotected or marginalized. On the other hand, one must ensure that the use of personal information fully abides by privacy regulations and that user identities are kept safe. The balance between privacy, fairness, and predictive performance is complex. However, despite their potential societal impact, we still demonstrate a poor understanding of the dynamics between these optimization vectors. In this paper, we study this three-way tension and how the optimization of each vector impacts others, aiming to inform the future development of safe applications. In light of claims that predictive performance and fairness can be jointly optimized, we find this is only possible at the expense of data privacy. Overall, experimental results show that one of the vectors will be penalized regardless of which of the three we optimize. Nonetheless, we find promising avenues for future work in joint optimization solutions, where smaller trade-offs are observed between the three vectors.

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