From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution

In bankruptcy problems, the minimal rights of a claimant is what is left of the endowment when all claimants but himself have received their full claims. By the Minimal Rights First property, it is irrelevant if we distribute the minimal rights first or proceed on the original problem. By adapting the property to the assignment problem, we obtain two characterizations of the Fair Division solution.