Artificial intelligence (AI) is supposed to help us make better choices. Some of these choices are small, like what route to take to work, or what music to listen to. Others are big, like what treatment to administer for a disease or how long to sentence someone for a crime. If AI can assist with these big decisions, we might think it can also help with hard choices, cases where alternatives are neither better, worse nor equal but on a par. The aim of this paper, however, is to show that this view is mistaken: the fact of parity shows that there are hard limits on AI in decision making and choices that AI cannot, and should not, resolve.