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A numerical method to determine a degressive proportional distribution of seats in the European Parliament

机译:确定欧洲议会席位递减比例分配的一种数值方法

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Distribution of seats in the European Parliament postulated by the Treaty of Lisbon should be degressively proportional. We propose a numerical method which determines uniquely a distribution of seats in the European Parliament which fulfil the requirements of degressive proportionality. More generally, let l _i, 1≤i≤n, be any non-increasing sequence of real positive numbers. We say that a sequence of positive integers m _i is degressively proportional with respect to the sequence l _i, if m _i and limi are non-increasing sequences. For fixed positive integer M we determine inductively a sequence M _i degressively proportional with respect to l _i which is smaller, then any other such sequence with the first element ≥M. Moreover, for every integer ∑i=1nMi≤Y≤nM we determine a degressively proportional sequence m _i with respect to l _i, which has the first element m _1=M and satisfies inequalities Y-(n-2)≤∑i=1nmi≤Y.
机译:《里斯本条约》所假定的欧洲议会席位分配应具有递减比例关系。我们提出一种数值方法,该方法唯一确定满足国会相称比例要求的欧洲议会席位分配。更一般地,令l _i,1≤i≤n是实数的任何非递增序列。我们说,如果m _i和limi是非递增序列,则正整数m _i的序列与序列l _i递减成比例。对于固定的正整数M,我们归纳地确定一个相对于l _i递减成比例的序列M _i,然后确定第一个元素≥M的任何其他此类序列。此外,对于每个整数∑i =1nMi≤Y≤nM,我们确定关于l _i的递减比例序列m _i,该序列具有第一元素m _1 = M且满足不等式Y-(n-2)≤∑i = 1nmi≤Y。

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