One of the most noticeable trends in recent years has been the increasing reliance of public decision-making processes (bureaucratic, legislative and legal) on algorithms, i.e. computer-programmed step-by-step instructions for taking a given set of inputs and producing an output. The question raised by this article is whether the rise of such algorithmic governance creates problems for the moral or political legitimacy of our public decision-making processes. Ignoring common concerns with data protection and privacy, it is argued that algorithmic governance does pose a significant threat to the legitimacy of such processes. Modelling my argument on Estlund’s threat of epistocracy, I call this the ‘threat of algocracy’. The article clarifies the nature of this threat and addresses two possible solutions (named, respectively, ‘resistance’ and ‘accommodation’). It is argued that neither solution is likely to be successful, at least not without risking many other things we value about social decision-making. The result is a somewhat pessimistic conclusion in which we confront the possibility that we are creating decision-making processes that constrain and limit opportunities for human participation.