Let X be a finite ordered set and let q~ be a function from X to subsets of a set Y. A subset A of X is called assignable if there is an injection ~b from A to Y that ~(a) ~ q~(a) for all a in A. It is shown that the assignable sets form a matroid on X and using this it is shown that there exists an optimal assignable set A, meaning that if A is any other assignable set then there is an injection f from A to A such thatf(a) > a for all a in A.