Combining Fairness and Optimality when Selecting and Allocating Projects

We consider the problem of the conjoint selection and allocation of projects to a population of agents, e.g. students are assigned papers and shall present them to their peers. The selection can be constrained either by quotas over subcategories of projects, or by the preferences of the agents themselves. We explore fairness and optimality issues and refine the analysis of the rank-maximality and popularity optimality concepts. We show that they are compatible with reasonable fairness requirements related to rank-based envy-freeness and can be adapted to select globally good projects according to the preferences of the agents.