  As machine learning informs increasingly consequential decisions, different
metrics have been proposed for measuring algorithmic bias or unfairness. Two
popular fairness measures are calibration and equality of false positive rate.
Each measure seems intuitively important, but notably, it is usually impossible
to satisfy both measures. For this reason, a large literature in machine
learning speaks of a fairness tradeoff between these two measures. This framing
assumes that both measures are, in fact, capturing something important. To
date, philosophers have not examined this crucial assumption, and examined to
what extent each measure actually tracks a normatively important property. This
makes this inevitable statistical conflict, between calibration and false
positive rate equality, an important topic for ethics. In this paper, I give an
ethical framework for thinking about these measures and argue that, contrary to
initial appearances, false positive rate equality does not track anything about
fairness, and thus sets an incoherent standard for evaluating the fairness of
algorithms.
