This paper focuses on the analysis of degressively proportional allocation of seats in the European Parliament. We propose an approach, which involves a linear function holding boundary conditions on the minimum and the maximum number of seats for countries with the smallest and the greatest populations. On this basis and applying a branch and bound algorithm, we search the set of all feasible solutions to find degressively proportional allocations of seats such that the sum of the squared differences or the sum of the absolute differences between these allocations and the values provided by the defined linear function is minimized.