Geodesic
The toy model with two strong players in a weighted voting game
Mathematica Applicanda, Tome 42 (2014) no. 2, pp. 259-272.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The aim of this article is to compare a specific toy voting model with the results derived from the normal approximation techniques by Słomczyński et al in the previous papers. For this purpose we have constructed a model in which the optimal quota for the qualified majority has been estimated. The optimal quota is set in such a way that the voting power of each member of the voting body, measured by the (normalised) Penrose-Banzhaf index, is proportional to its voting weight. We present the ‘France-Germany’ model of two strong players each of which is c > 1 times stronger than each of the others and we estimate the quota in the case of c = 2. We check that these results are consistent with a formula derived from the normal approximation, where the quota we are looking for is the inflection point of the density function for this distribution.
DOI : 10.14708/ma.v42i2.524
Classification : Primary 91B12, Secondary 91B14 (2000)
Mots-clés : two strong players in a weighted voting game, optimal quota, normal approximation 
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Andrzej Tomski. The toy model with two strong players in a weighted voting game. Mathematica Applicanda, Tome 42 (2014) no. 2, pp.  259-272. doi : 10.14708/ma.v42i2.524. http://geodesic.mathdoc.fr/articles/10.14708/ma.v42i2.524/

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