Fair Facility Location for Socially Equitable Representation

We consider the problem of effectively finding a subset of reps (representatives) from a large group of agents belonging to a metric space while considering three distinct notions of fairness. First, each agent should be close to a rep (while precisely how close depends on population densities). Second, reps should satisfy a given social equity constraint specifying the number of representatives with each property value. Finally, reps should be similar, in their property value, to that of the community of agents whom they represent.