 Kenneth Arrow’s “impossibility” theorem—or “general possibility” theorem, as he called it—answers a very basic question in the theory of collective decision-making. Say there are some alternatives to choose among. They could be policies, public projects, candidates in an election, distributions of income and labour requirements among the members of a society, or just about anything else. There are some people whose preferences will inform this choice, and the question is: which procedures are there for deriving, from what is known or can be found out about their preferences, a collective or “social” ordering of the alternatives from better to worse? The answer is startling. Arrow’s theorem says there are no such procedures whatsoever—none, anyway, that satisfy certain apparently quite reasonable assumptions concerning the autonomy of the people and the rationality of their preferences. The technical framework in which Arrow gave the question of social orderings a precise sense and its rigorous answer is now widely used for studying problems in welfare economics. The impossibility theorem itself set much of the agenda for contemporary social choice theory. Arrow accomplished this while still a graduate student. In 1972, he received the Nobel Prize in economics for his contributions.