On the impossibility of non-trivial accuracy under fairness constraints

TL;DR

This paper demonstrates that for certain data sources, achieving fairness via equality of opportunity inherently limits accuracy to trivial classifiers, and it explores conditions where fairness and accuracy can coexist.

Contribution

It strengthens previous results by removing privacy constraints and identifies when fairness constraints force classifiers to be trivial, also analyzing the trade-off between fairness and accuracy.

Findings

For some data sources, the optimal fair classifier is trivial.

The paper provides conditions under which fairness and accuracy are compatible.

It extends prior work by removing privacy constraints from the analysis.

Abstract

One of the main concerns about fairness in machine learning (ML) is that, in order to achieve it, one may have to trade off some accuracy. To overcome this issue, Hardt et al. proposed the notion of equality of opportunity (EO), which is compatible with maximal accuracy when the target label is deterministic with respect to the input features. In the probabilistic case, however, the issue is more complicated: It has been shown that under differential privacy constraints, there are data sources for which EO can only be achieved at the total detriment of accuracy, in the sense that a classifier that satisfies EO cannot be more accurate than a trivial (i.e., constant) classifier. In our paper we strengthen this result by removing the privacy constraint. Namely, we show that for certain data sources, the most accurate classifier that satisfies EO is a trivial classifier. Furthermore, we study the trade-off between accuracy and EO loss (opportunity difference), and provide a sufficient condition on the data source under which EO and non-trivial accuracy are compatible.