Apportionment Strategies for the European Parliament

• Autores: G. Gambarelli, C. Bertini, I. Stach Janas
• Localización: Abstracts of the Fifth Spanish Meeting on Game Theory and Applications / coord. por Jesús Mario Bilbao Arrese , Francisco Ramón Fernández García , 2002, ISBN 84-472-0733-1, pág. 10
• Idioma: inglés
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• Resumen

  • A solution is proposed to the problem of assigning seats to new countries applying for membership of the European Parliament. This solution is obtained by weighting the populations and Gross Domestic Products of all members. A strategy of optimization for each single country is also studied.

    The apportionment of seats to incoming members to the European parliament has always been a source of discussion, as no fixed rule has so far been established. The trend in the past has been to take into account the size of population, in an attempt to guarantee representation for the major political parties of each country (cf. Luxembourg) and avoid any reduction in the number of seats held by existing members. The innovation at the Nice European Council was the application of a large number of countries having weaker economies than those of existing members. This involves a considerable increase in the total number of Euro MBPs, many of whom could have influenced decisions of a specifically economic nature to the disadvantage of current members. A solution to this impasse could be to restructure the distribution of seats for all countries using a formula, which takes into account both populations and Gross Domestic Products (GDP). The most direct method consists of adequate weighting of this data.

    For instance, let populations and GDP percentages of the i-th country shown by Pi and Gi . Suppose that we decide to weight the population with 30% and GDP with 70%. In this case the seat percentages Si of the i-th country would be Si = 0.3Pi + 0.7Gi. Generally speaking, if a is the weighting we wish to assign to the population (0 . a . 1), the resulting seat percentages are Si = aPi + (1 . a)Gi. To transform the seat percentages into real ones, a suitable rounding method can be used (for instance Hondt�fs proportional system, or Hamilton�fs Great Divisors, or Gambarelli�fs minimax apportionment [1999] and so on).

    Once this method of apportionment has been accepted, it is a question of fixing the value of a to weight the populations and GDP. The value of a strongly characterizes the seat distribution. In fact if a = 0, the seats are assigned proportionally on the basis of the countries�f economic powers, without taking into account the size of population at all. Viceversa if a = 1. Then, a discussion on this can be expected between countries with strong economies and those with weak economies. From an initial examination, it would seem in the interests of countries with higher GDP percentages than their population percentages (Denmark, Finland etc.), to have lower values of a (possibly 0). Viceversa, for countries with lower GDP percentages (Poland, Romania etc.) it would seem in their interests to have high values of a (possibly 1). However, this rule does not always apply.

    In this presentation a paradox on the matter is illustrated. The work proceeds with an application of these ideas to the new Parliament size, examined in the Nice Council of 2000. The program quoted in [Bilbao, 2000] has been used for our computations. The seat distribution percentages and the related power indices are studied with parameter a varying from 0 to 1 in 10% steps.

    Other studies are presented in reference to different majority quotas, optimum weight intervals, overcrossing between countries and so on. Here, we limit ourselves to quote that the Netherlands and Ireland, although they have a GDP percentage higher than their population percentage, they do not have the maximum advantage if only the GDP is taken into account (i.e. if a = 0). For these countries the maximum advantage (in terms of Martin-Banzhaf-Coleman index) is achieved with a balanced division (a = 0.3).