Allocation of the EU Parliament seats via integer linear programming and revised quotas

We deal with the problem of assigning seats to the European Parliament within the special requirements imposed by the rules of the EU. Since the usual rounding techniques, like in the divisor methods, may fail to satisfy these requirements, we propose to use integer linear programming (ILP) to provide at the same time rounding and satisfaction of the requirements. Using ILP makes central the choice of quotas to which the seats should be as close as possible. We investigate how the special requirements can affect the very definition of quotas, and define projective quotas. Finally we compare the various methods by using the EU Parliament data.