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

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  • Kurz, Sascha

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).

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  • Kurz, Sascha, 2021. "A note on the growth of the dimension in complete simple games," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 14-18.
    • Handle: RePEc:eee:matsoc:v:110:y:2021:i:c:p:14-18
    DOI: 10.1016/j.mathsocsci.2021.01.001
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    References listed on IDEAS

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    1. Sascha Kurz & Nikolas Tautenhahn, 2013. "On Dedekind’s problem for complete simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 411-437, May.
    2. O’Dwyer, Liam & Slinko, Arkadii, 2017. "Growth of dimension in complete simple games," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 2-8.
    3. Carreras, Francesc & Freixas, Josep, 1996. "Complete simple games," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 139-155, October.
    4. Freixas, Josep & Kurz, Sascha, 2014. "On minimum integer representations of weighted games," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 9-22.
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    Cited by:

    1. Molinero, Xavier & Riquelme, Fabián & Roura, Salvador & Serna, Maria, 2023. "On the generalized dimension and codimension of simple games," European Journal of Operational Research, Elsevier, vol. 306(2), pages 927-940.

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