Arrow’s conditions often are called axioms, and his approach is said to be axiomatic. This might be found misleading. Unlike axioms of logic or geometry, Arrow’s conditions are not supposed to express more or less indubitable truths, or to constitute an implicit definition of the object of study. Arrow himself took them to be questionable “value judgments” that “express the doctrines of citizens’ sovereignty and rationality in a very general form” (Arrow 1951 [1963]: 31). Indeed, as we will see in Section 4, and as Arrow himself recognized, sometimes it is not even desirable that social welfare functions should satisfy all conditions of the impossibility theorem.