Sometimes, in the nature of the alternatives under consideration and how individual preferences among them are determined, not all individual preferences can arise. When studying such a case within Arrow’s framework there is no need for a social welfare function that can handle each and every \(n\)-tuple of individual orderings. Some but not all profiles are admissible, and the domain is said to be restricted. In fortunate cases, it is then possible to find a social welfare function that meets all assumptions and conditions of Arrow’s theorem—apart, of course, from U. Such domains are said to be Arrow consistent. This Section considers some important examples of Arrow consistent domains.