How fair do people perceive government decisions based on algorithmic predictions?And to what extent can the government delegate decisions to machines without sacrificing perceived procedural fairness?Using a set of vignettes in the context of predictive policing, school admissions, and refugee-matching, we explore how different degrees of human-machine interaction affect fairness perceptions and procedural preferences.We implement four treatments varying the extent of responsibility delegation to the machine and the degree of human involvement in the decision-making process, ranging from full human discretion, machine-based predictions with high human involvement, machine-based predictions with low human involvement, and fully machine-based decisions.We find that machine-based predictions with high human involvement yield the highest and fully machine-based decisions the lowest fairness scores.Different accuracy assessments can partly explain these differences.Fairness scores follow a similar pattern across contexts, with a negative level effect and lower fairness perceptions of human decisions in the context of predictive policing.Our results shed light on the behavioral foundations of several legal human-in-the-loop rules.