 To express different assumptions about which information is truly encoded by a profile of welfare functions and which information is not (and should thus be seen, at best, as an artifact of the numerical representation), it is helpful to introduce the notion of meaningful statements. Some examples of statements about individual welfare that are candidates for meaningful statements are the following (the present formulations come from List 2003a; for earlier analyses, see Bossert 1991 and Bossert and Weymark 1996: Section 5):