Balanced allocation methods for claims problems with indivisibilities

We study claims problems in which a certain amount of indivisible units (of an homogeneous good) has to be distributed among a group of agents, when this amount is not enough to fully satisfy agents' demands. We are interested in finding solutions satisfying robustness and fairness properties. To do that, we define the M-down methods, which are the unique robust (composition down and consistency) and fair (balancedness or conditional full compensation ) rules. Besides, we also establish the relationships between these M-down methods and the constrained equal awards rule.