Machine learning algorithms are expected to improve referral decisions. In this article I discuss the legitimacy of deferring referral decisions in primary care to recommendations from such algorithms. The standard justification for introducing algorithmic decision procedures to make referral decisions is that they are more accurate than the available practitioners. The improvement in accuracy will ensure more efficient use of scarce health resources and improve patient care. In this article I introduce a proceduralist framework for discussing the legitimacy of algorithmic (...) referral decisions and I argue that in the context of referral decisions the legitimacy of an algorithmic decision procedure can be fully accounted for in terms of the instrumental values of accuracy and fairness. I end by considering how my discussion of procedural algorithmic legitimacy relates to the debate on algorithmic fairness. (shrink)