<p>The demands of fair machine learning are often expressed in probabilistic terms. Yet, most of the systems of concern are deterministic in the sense that whether a given subject will receive a given score on the basis of their traits is, for all intents and purposes, either zero or one. What, then, can justify this probabilistic talk? We argue that the statistical reference classes used in fairness measures can be understood as defining the probability that hypothetical persons, who are representative of social roles, will receive certain goods. We call these hypothetical persons “representative individuals.” We claim that what we owe to actual, concrete individuals—whose individual chances of receiving the good in the system might be extreme (i.e., either zero or one)—is that their representative individual has an appropriate probability of receiving the good in question. While less immediately intuitive than other approaches, we argue that the representative individual approach has important advantages over other ways of making sense of this probabilistic talk in the context of fair machine learning.</p>