Whether it is sensible to impose U or any other domain condition on a social welfare function depends very much on the particulars of the choice problem being studied. Sometimes, in the nature of the alternatives under consideration, and the way in which individual preferences among them are determined, imposing U certainly is not appropriate. If for instance the alternatives are different ways of dividing up a pie among some people, and it is known prior to selecting a social welfare function that these people are selfish, each caring only about the size of his own piece, then it makes no obvious sense to require of a suitable function that it can handle cases in which some people prefer to have less for themselves than to have more. The social welfare function will never be called on to handle such cases for the simple reason that they will never arise. Arrow made this point as follows: