 There are social welfare functions that satisfy all conditions of Arrow’s theorem, reformulated for graded inputs. With an odd number \(n\) of people, for instance, the social welfare function median grading fills the bill. Given a profile \(\langle G_{i}\rangle\) of grade functions, the median grade for an alternative \(x\) is the grade that is in the middle, when we list all the grades \(G_{1}(x), \ldots, G_{n}(x)\) for \(x\) in order, from top to bottom. The social ordering associated with this profile goes by the alternatives’ median grades: \(x f\langle G_{i}\rangle y\) means that the median grade for \(x\) is either the same as the median grade for \(y\), or else it is higher.