The systems that most countries use to elect presidents are deeply flawed. In particular, candidates A and B may each be more popular than C (in the sense that either would beat C in a head-to-head contest), but nevertheless each may lose to C if they both run. The systems therefore fail to reflect voters’ preferences adequately. In this lecture, I will illustrate this point with examples from U.S. and French political history. I will also propose an election system that is far superior to the current ones.