论文标题

完整简单游戏中维度增长的注释

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

论文作者

Kurz, Sascha

论文摘要

从简单游戏到加权游戏的远程性可以通过维度的概念或更通用的布尔维度来衡量。众所周知,这两个概念在选民人数中都可以指数级。对于完整的简单游戏,直到最近才表明该维度也可以指数级。在这里,我们表明,具有两种类型的选民以及一般简单游戏的布尔维度的完整简单游戏也是如此,这是一个空旷的问题。

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 notions can be exponential in the number of voters. For complete simple games it was only recently shown 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.

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