With many profiles in play there can be “interprofile” conditions on aggregation procedures. These coordinate the results of aggregation at several profiles at once. One such condition that plays a crucial role in Arrow’s theorem is Independence of Irrelevant Alternatives. It requires that whenever everybody’s preferences among two alternatives are in one profile the same as in another, the collective ordering must also be the same at the two profiles, as far as these alternatives are concerned. There is to be this much similarity among social orderings even as people’s tastes and values change. Sections 3.1 and 4.5 discuss in more detail the meaning of this controversial requirement, and the extent to which it is reasonable to impose it on aggregation procedures.