A random assignment is ordinally efficient if it is not stochastically dominated with respect to individual preferences over sure objects. When there are no private endowments, the set of ordinally efficient random assignments is characterized by the eating algorithm (Bogomolnaia and Moulin,...

The natural preference domain for many practical settings of the assignment problems is the one in which agents are allowed to be indifferent between objects, the weak preference domain. Most of the existing work on assignment problems assumes strict preferences. There are important exceptions,...