The algorithmic accountability literature to date has primarily focused on procedural tools to govern automated decision-making systems. That prescriptive literature elides a fundamentally empirical question: whether and under what circumstances, if any, is the use of algorithmic systems to make public policy decisions perceived as legitimate? The present study begins to answer this question. Using factorial vignette survey methodology, we explore the relative importance of the type of decision, the procedural governance, the input data used, and outcome errors on perceptions (...) of the legitimacy of algorithmic public policy decisions as compared to similar human decisions. Among other findings, we find that the type of decision—low importance versus high importance—impacts the perceived legitimacy of automated decisions. We find that human governance of algorithmic systems increases perceptions of the legitimacy of algorithmic decision-making systems, even when those decisions are likely to result in significant errors. Notably, we also find the penalty to perceived legitimacy is greater when human decision-makers make mistakes than when algorithmic systems make the same errors. The positive impact on perceived legitimacy from governance—such as human-in-the-loop—is greatest for highly pivotal decisions such as parole, policing, and healthcare. After discussing the study’s limitations, we outline avenues for future research. (shrink)