Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization

Our main result is that the generalized serial rule, which we propose as an adaptation of the serial rule to our setting, is the only rule satisfying sd-efficiency, the sd proportional-division lower-bound, limited invariance, and consistency. Uniqueness persists if we replace the sd proportional-division lower-bound by sd normalized-no-envy, or consistency by converse consistency, or both. The serial rule in Bogomolnaia and Moulin (2001) is characterized as a special case of our generalized serial rule.