“Condition U (condition of unrestricted domain): the domain of rule f must contain all logically possible combinations of individual orderings.” Amartya Sen made further explanation of this condition: “condition U and other conditions have different logical status. Given a preference structure, the other conditions specify or restrict what should be done. However, condition U claims that CCR must be feasible to all possible individual preference structure”.
Mueller’s domain (unrestricted area) axiom said: “everyone should choose any preference sequence freely, and collective choice process should reflect these preferences via other axioms”, but it may need further explanation. Here, the concept of “common alternatives” is not critical. The axiom of domain means that social choice process should allow any possible orderings of the three alternatives X, Y and U. This process is not established via expelling some possible orderings.