As rapid advances in Artificial Intelligence and the rise of some of history's most potent corporations meet the diminished neoliberal state, people are increasingly subject to power exercised by means of automated systems. Machine learning and related computational technologies now underpin vital government services. They connect consumers and producers in new algorithmic markets. They determine how we find out about everything from how to vote to where to get vaccinated, and whose speech is amplified, reduced, or restricted. And a new wave of products based on Large Language Models (LLMs) will further transform our economic and political lives. Automatic Authorities are automated computational systems used to exercise power over us by determining what we may know, what we may have, and what our options will be. In response to their rise, scholars working on the societal impacts of AI and related technologies have advocated shifting attention from how to make AI systems beneficial or fair towards a critical analysis of these new power relations. But power is everywhere, and is not necessarily bad. On what basis should we object to new or intensified power relations, and what can be done to justify them? This paper introduces the philosophical materials with which to formulate these questions, and offers preliminary answers. It starts by pinning down the concept of power, focusing on the ability that some agents have to shape others' lives. It then explores how AI enables and intensifies the exercise of power so understood, and sketches three problems with power and three ways to solve those problems. It emphasises, in particular, that justifying power requires more than satisfying substantive justificatory criteria; standards of proper authority and procedural legitimacy must also be met. We need to know not only what power may be used for, but how it may be used, and by whom.