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Dimension, egalitarianism and decisiveness of European voting systems

Carreras F., Freixas J., Magaňa A.

Operations Research and Decisions

2016

Vol. 26, No. 2

31--52

An analysis of three major aspects has been carried out that may apply to any of the successive voting systems used for the European Union Council of Ministers, from the first one established in the Treaty of Rome in 1958 to the current one established in Lisbon. We mainly consider the voting systems designed for the enlarged European Union adopted in the Athens summit, held in April 2003 but this analysis can be applied to any other system. First, it is shown that the dimension of these voting systems does not, in general, reduce. Next, the egalitarian effects of superposing two or three weighted majority games (often by introducing additional consensus) are considered. Finally, the decisiveness of these voting systems is evaluated and compared.

Weighted multi-criteria simple games and voting systems

Monroy L., Fernandez F. R.

Foundations of Computing and Decision Sciences

2007

Vol. 32, No. 4

295-313

Multi-criteria simple games provide mathematical models for describing and analyzing group decision problems when the decision makers consider multiple qualitative criteria simultaneously. Voting systems and related social choice situations may be modelled as multi-criteria simple games. The goal of this paper is to propose a generalization of the notion of weighted simple games within this context. The basic concepts and the model are first introduced. Two different weighted representations for a multi-criteria simple game is established and its dimension is defined. Furthermore, we provide an extension of the classic Theorem of Taylor and Zwicker for these types of games, which permits both, the weighted representation of a multi-criteria simple game and a bound of its dimension to be obtained.