  To enable an ethical and legal use of machine learning algorithms, they must
both be fair and protect the privacy of those whose data are being used.
However, implementing privacy and fairness constraints might come at the cost
of utility (Jayaraman & Evans, 2019; Gong et al., 2020). This paper
investigates the privacy-utility-fairness trade-off in neural networks by
comparing a Simple (S-NN), a Fair (F-NN), a Differentially Private (DP-NN), and
a Differentially Private and Fair Neural Network (DPF-NN) to evaluate
differences in performance on metrics for privacy (epsilon, delta), fairness
(risk difference), and utility (accuracy). In the scenario with the highest
considered privacy guarantees (epsilon = 0.1, delta = 0.00001), the DPF-NN was
found to achieve better risk difference than all the other neural networks with
only a marginally lower accuracy than the S-NN and DP-NN. This model is
considered fair as it achieved a risk difference below the strict (0.05) and
lenient (0.1) thresholds. However, while the accuracy of the proposed model
improved on previous work from Xu, Yuan and Wu (2019), the risk difference was
found to be worse.
