Allocation of seats in the European Parliament and a degressive proportionality

Abstract

Distribution of seats in The European Parliament postulated by Treaty of Lisbon should be degressively proportional. The meaning of degressively proportional concept can be found in two principles annexed to the draft of European Parliament resolution. The first, referred as the principle of fair division, states that "the larger the population of a Member State, the greater is entitlement to a large number of seats". The other condition, referred to as the principle of relative proportionality, holds that "the larger the population of a country, the more inhabitants are represented by each of its Members of the EU". We postulate a clear and fair method which determines uniquely a distribution of seats in the European Parliament which fulfil the requirements of degressive proportionality. More generally, let $l_i$ be any non-increasing sequence of real positive numbers. We say that a sequence of natural numbers $m_{i}$ is degressively proportional with respect to the sequence $l_{i}$, if $m_{i}$ and $l_{i}/m_{i}$ are non-increasing sequences. Our method can be instrumental in uniquely determining a degressively proportional sequence $m_{i}$ with respect to $l_{i}$ which fulfils given conditions.