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

Sascha Kurz

Mathematical Social Sciences, 2021, vol. 110, issue C, 14-18

Abstract: The remoteness from a simple game to a weighted game can be measured by the concept of the dimension or the more general Boolean dimension. It is known that both measures can be exponential in the number of voters. For complete simple games it was only recently shown in O’Dwyer and Slinko (2017) that the dimension can also be exponential. Here we show that this is also the case for complete simple games with two types of voters and for the Boolean dimension of general complete simple games, which was posed as an open problem in O’Dwyer and Slinko (2017).

Keywords: Complete simple games; Weighted games; Dimension; Boolean dimension (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:110:y:2021:i:c:p:14-18

DOI: 10.1016/j.mathsocsci.2021.01.001

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