We consider a model in which projects are to be assigned to agents based on their preferences, and where projects have capacities, i.e., can each be assigned to a minimum and maximum number of agents. The extreme cases of our model are the social choice model (the same project is assigned to all...

In a two-sided matching market when agents on both sides have preferences the stability of the solution is typically the most important requirement. However, we may also face some distributional constraints with regard to the minimum number of assignees or the distribution of the assignees...