Independence of irrelevant alternatives imposes three conditions on the social ordering of any subset U of social states: By individualism the ordering depends only on individual tastes, by ordinalism it depends only on preference orderings, and by localism it does not depend on states outside U. We keep individualism and replace ordinalism by the assumption that individuals have interval utility functions. If we also keep localism we still get an impossibility theorem (the main result). If we relax localism as well we can get a social welfare function. But even a minimal relaxation of localism makes the social ordering of each two states (x, y) depend on utilities for n other states, where there are n individuals.