Arrow’s problem arises, then, only after some alternatives and people have been fixed. It is for them that an aggregation procedure is sought. Crucially, though, this problem arises before relevant information about the people’s preferences among the alternatives has been gathered, whether that is by polling or some other method for eliciting or determining preferences. The question that Arrow’s theorem answers is, more precisely, this: Which procedures are there for arriving at a social ordering of some given alternatives, on the basis of some given people’s preferences among them, no matter what these preferences turn out to be?