A note on the growth of the dimension in complete simple games

Titelangaben

Kurz, Sascha:
A note on the growth of the dimension in complete simple games.
In: Mathematical Social Sciences. Bd. 110 (2021) . - S. 14-18.
ISSN 0165-4896
DOI: https://doi.org/10.1016/j.mathsocsci.2021.01.001

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Abstract

The remoteness from a simple game to a weighted game can be measured by the concept ofthe dimension or the more general Boolean dimension. It is known that both notions can be exponentialin the number of voters. For complete simple games it was only recently shown that the dimensioncan also be exponential. Here we show that this is also the case for complete simple games with two typesof voters and for the Boolean dimension of general complete simple games, which was posed as an open problem.