Understanding Significance Tests From a Non-Mixing Markov Chain for Partisan Gerrymandering Claims

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.