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).

中文翻译：

---

关于完整简单游戏中维度增长的说明

从简单游戏到加权游戏的距离可以通过维度或更一般的布尔维度的概念来度量。众所周知，这两种措施在选民人数上都是成倍增长的。对于完整的简单游戏，直到最近O'Dwyer和Slinko（2017）才表明尺寸也可以是指数级的。在这里我们表明，对于具有两种类型选民的完全简单游戏以及一般完全简单游戏的布尔维度，情况也是如此，这在O'Dwyer和Slinko（2017）中被提出为开放问题。