ABSTRACT Recently, Chikina, Frieze, and Pegden proposed a way to assess significance in a Markov chain without requiring that Markov chain to mix. They presented their theorem as a rigorous test for partisan gerrymandering. We clarify that their ε-outlier test is distinct from a traditional global outlier test and does not indicate, as they imply, that a particular electoral map is associated with an extreme level of “partisan unfairness.” In fact, a map could simultaneously be an ε-outlier and have a typical partisan fairness value. That is, their test identifies local outliers but has no power for assessing whether that local outlier is a global outlier. How their specific definition of local outlier is related to a legal gerrymandering claim is unclear given Supreme Court precedent.

中文翻译：

---

了解非混合马尔可夫链对游击队格里曼德主张的重要性检验

摘要最近，Chikina，Frieze和Pegden提出了一种方法来评估Markov链中的重要性，而无需将Markov链混合在一起。他们提出了他们的定理，作为对党派共事的严格检验。我们澄清说，他们的ε-离群值测试与传统的全球离群值测试不同，并且没有暗示它们暗示特定的选举地图与“党派不公平”的极端水平相关。实际上，地图可能同时是ε异常值，并且具有典型的党派公平值。也就是说，他们的测试可以识别局部离群值，但无权评估该局部离群值是否为全局离群值。鉴于最高法院的判例，目前尚不清楚他们对当地离群值的具体定义如何与合法的嫁接要求有关。