When Can Memorization Improve Fairness?

We study to which extent additive fairness metrics (statistical parity, equal opportunity and equalized odds) can be influenced in a multi-class classification problem by memorizing a subset of the population. We give explicit expressions for the bias resulting from memorization in terms of the label and group membership distribution of the memorized dataset and the classifier bias on the unmemorized dataset. We also characterize the memorized datasets that eliminate the bias for all three metrics considered. Finally we provide upper and lower bounds on the total probability mass in the memorized dataset that is necessary for the complete elimination of these biases.