Sometimes a certain amount is known about everybody’s preferences before these have been elicited. Profiles that are compatible with what is known represent preferences that the people could have, and might turn out actually to have, and it is from these “admissible” profiles that we may hope to derive social orderings. Technically, a domain, in Arrow’s framework, is a set of admissible profiles, each concerning the same alternatives \(X\) and people \(1, \ldots, n\). A social welfare function \(f\) assigns to each profile \(\langle R_{i}\rangle\) in some domain a binary relation \(f\langle R_{i}\rangle\) on \(X\). Intuitively, \(f\) is an aggregation procedure and \(f\langle R_{i}\rangle\) represents the social preferences that it derives from \(\langle R_{i}\rangle\). Arrow’s social welfare functions are sometimes called “constitutions”.