We study the allocation of indivisible objects (e.g. school seats) to agents by lotteries. Agents have preferences over different objects and have different priorities at different objects. The priorities can contain indifferences, some agents may have the same priority at some object. A lottery...

In college admissions and student placements at public schools, the admission decision can be thought of as assigning indivisible objects with capacity constraints to a set of students such that each student receives at most one object and monetary compensations are not allowed. In these...