A fast exact algorithm for the allocation of seats for the EU Parliament

•The problem of the allocation of seats for the EU Parliament is considered.•A fast exact algorithm is constructed that finds all feasible solutions.•An extensive analysis of allocations and of the algorithm is presented.

In this paper, we analyse the problem of allocation of seats for the EU Parliament. To solve it, we propose a fast exact algorithm which overwhelms limitations of the existing methods. It allows us to examine all feasible allocations of seats within few minutes. On this basis, an in-depth analysis of the problem is provided and some of its properties are revealed (e.g., the number of feasible allocations of seats holding the Treaty of Lisbon), which have never been presented in the scientific literature. Furthermore, the proposed algorithm is not limited to dealing with the problem of allocation of seats for the EU Parliament, but it can be applied in the expert system for any other similar problem, especially under degressive proportionality constraints.