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1 2007

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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.