Of course, there is nothing to keep anyone from reinterpreting Arrow’s basic notions, including the set \(X\) of alternatives, in any way they like; a theorem is a theorem no matter what interpretation it is given. It is important to realize, though, that to interpret \(x, y, z, \ldots\) as labels is not standard, and can only make nonsense of much of the theory of social choice to which Arrow’s theorem has given  rise.[4]