In eight states, a "nesting rule" requires that each state Senate district be exactly composed of two adjacent state House districts. In this paper we investigate the potential impacts of these nesting rules with a focus on Alaska, where Republicans have a 2/3 majority in the Senate while a Democratic-led coalition controls the House. Treating the current House plan as fixed and considering all possible pairings, we find that the choice of pairings alone can create a swing of 4-5 seats out of 20 against recent voting patterns, which is similar to the range observed when using a Markov chain procedure to generate plans without the nesting constraint. The analysis enables other insights into Alaska districting, including the partisan latitude available to districters with and without strong rules about nesting and contiguity.

中文翻译：

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嵌套区的数学：以阿拉斯加为例

在八个州中，“嵌套规则”要求每个州参议院区都必须由两个相邻的州众议院区组成。在本文中，我们以阿拉斯加为研究对象，研究了这些嵌套规则的潜在影响。在阿拉斯加，共和党在参议院中占2/3多数，而民主党领导的联盟控制众议院。将当前的众议院计划定为固定条件并考虑所有可能的配对，我们发现仅配对的选择就可以在最近的投票模式下从20个席位中产生4-5个席位，这与使用马尔可夫链时观察到的范围相似没有嵌套约束的计划生成过程。该分析使您能够对阿拉斯加的选区有其他见解，包括有或没有有关于嵌套和连续性的严格规则的选区人可用的游击党纬度。