The ever-increasing application of algorithms to decision-making in a range of social contexts has prompted demands for algorithmic accountability. Accountable decision-makers must provide their decision-subjects with justifications for their automated system's outputs, but what kinds of broader principles should we expect such justifications to appeal to? Drawing from political philosophy, I present an account of algorithmic accountability in terms of the democratic ideal of "public reason". I argue that situating demands for algorithmic accountability within this justificatory framework enables us to better articulate their purpose and assess the adequacy of efforts toward them.