A century ago, John Dewey observed that '[s]team and electricity have done more to alter the conditions under which men associate together than all the agencies which affected human relationships before our time'. In the last few decades, computing technologies have had a similar effect. Political philosophy's central task is to help us decide how to live together, by analysing our social relations, diagnosing their failings, and articulating ideals to guide their revision. But these profound social changes have left scarcely a dent in the model of social relations that most (analytical) political philosophers assume. This essay aims to reverse that trend. It first builds a model of our novel social relations—as they are now, and as they are likely to evolve—and then explores how those differences affect our theories of how to live together. I introduce the 'Algorithmic City'—the network of algorithmically-mediated social relations—then characterise the intermediary power by which it is governed, and contrast that intermediary power with the top-down power of the state in the physical city. I show how algorithmic governance raises new challenges for political philosophy concerning the justification of authority, the foundations of procedural legitimacy, and the possibility of justificatory neutrality.