The ideals program in algorithmic fairness

I consider statistical criteria of algorithmic fairness from the perspective of the ideals of fairness to which these criteria are committed. I distinguish and describe three theoretical roles such ideals might play. The usefulness of this program is illustrated by taking Base Rate Tracking and its ratio variant as a case study. I identify and compare the ideals of these two criteria, then consider them in each of the aforementioned three roles for ideals. This ideal program may present a way forward in the normative evaluation of candidate statistical criteria of algorithmic fairness.