Allocation of seats in the European Parliament and a degressive proportionality

摘要

Distribution of seats in The European Parliament postulated by Treaty ofLisbon should be degressively proportional. The meaning of degressivelyproportional concept can be found in two principles annexed to the draft ofEuropean Parliament resolution. The first, referred as the principle of fairdivision, states that "the larger the population of a Member State, the greateris entitlement to a large number of seats". The other condition, referred to asthe principle of relative proportionality, holds that "the larger thepopulation of a country, the more inhabitants are represented by each of itsMembers of the EU". We postulate a clear and fair method which determinesuniquely a distribution of seats in the European Parliament which fulfil therequirements of degressive proportionality. More generally, let $l_i$ be anynon-increasing sequence of real positive numbers. We say that a sequence ofnatural numbers $m_{i}$ is degressively proportional with respect to thesequence $l_{i}$, if $m_{i}$ and $l_{i}/m_{i}$ are non-increasing sequences.Our method can be instrumental in uniquely determining a degressivelyproportional sequence $m_{i}$ with respect to $l_{i}$ which fulfils givenconditions.