 In contemporary social choice theory, it is perhaps fair to say, Arrow’s axiomatic method is more influential than his impossibility theorem itself (on the axiomatic method, see Thomson 2000). The paradigmatic kind of result in formal work is now the ‘characterization theorem’. Here the aim is to identify a set of plausible necessary and sufficient conditions that uniquely characterize a particular solution (or class of solutions) to a given type of collective decision problem. An early example is Kenneth May’s (1952) characterization of majority rule, discussed below.