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...

Distributional constraints are important in many market design settings. Prominent examples include the minimum manning requirements at each Army branch in military cadet matching and diversity considerations in school choice, whereby school districts impose constraints on the demographic...