Abstract: The study of degressively proportional allocations has attracted growing attention since degressive proportionality became the guiding principle for determining the composition of the European Parliament. One of the key unresolved practical issues is the identification of a single allocation among all admissible ones in a manner supported by a sound theoretical justification. Although this problem has been widely discussed in the literature, no generally accepted method has yet been established that combines objectivity, reproducibility, and theoretical consistency. This paper contributes to the debate by introducing a method founded on an extension of the notion of quota sequences, familiar from the theory of proportional apportionment, to integer-valued degressively proportional allocations satisfying given boundary conditions. The resulting allocation may then be derived through procedures analogous to those used in classical proportional allocation methods. Owing to its general formulation, the proposed approach is not limited to the allocation of seats in the European Parliament, but can also be applied to a broad spectrum of allocation problems involving the distribution of goods, resources, or responsibilities.

Keywords: apportionment problem, degressive proportionality, fair division, elections, European Parliament, voting

Pages: 1899-1906