Kurz and Napel (2015) proved that the voting system of the EU council (based on the 2014 population data) cannot be represented as the intersection of six weighted games, i.e., its dimension is at least 7. This set a new record for real-world voting rules and the authors posed the exact determination as a challenge. Recently, Chen, Cheung, and Ng (2019) showed that the dimension is at most 24. We provide the first improved lower bound and show that the dimension is at least 8.

中文翻译：

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改善欧盟理事会投票规则维度的下限

Kurz 和 Napel (2015) 证明欧盟理事会的投票系统（基于 2014 年人口数据）不能表示为六个加权博弈的交集，即其维数至少为 7。这创下了真实的新记录-世界投票规则和作者提出了确切的决定作为挑战。最近，Chen、Cheung 和 Ng（2019）表明维度最多为 24。我们提供了第一个改进的下界，并表明维度至少为 8。