Arrow’s domain condition U says that the domain of the social welfare function includes every list of \(n\) weak orderings of \(X\). For example, suppose the alternatives are \(A\), \(B\), and \(C\), and that the people are 1, 2, and 3. There are 13 weak orderings of three alternatives, so the unrestricted domain contains 2197 (that is, \(13^{3}\)) lists of weak orderings of \(A\), \(B\), and \(C\). A social welfare function \(f\) for these alternatives and people, if it satisfies U, maps each one of these “logically possible” preference profiles onto a collective preference among \(A\), \(B\), and \(C\).