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.

Theoretical Foundations and Empirical Evaluations of Partisan Fairness in District-Based Democracies

“…Simulation measures seek to compare a redistricting plan with all possible plans for a state, or all that meet the chosen criteria (Chen and Rodden 2013; Chikina, Frieze, and Pegden 2017; Duchin 2018; Magleby and Mosesson 2018). Unfortunately, all possible plans are too large, proper random sampling remains an unsolved problem (Fifield et al 2018; Tam Cho and Rubinstein-Salzedo 2019), and using actual plans from different states is unrealistic (Wang 2016b).…”

Seed-Fill-Shift-Repair: A redistricting heuristic for civic deliberation

“…Chikina, et al [83] prove that a reversible Markov chain can generate a global p-value at a discount (roughly the square root) of the outlier cutoff of any random walk from the Markov chain. Tam Cho and Rubinstein-Salzedo [84] argue that overly tight constraints in the chain can leave the algorithm exploring a space disconnected from the global state space. In their view, finding a local outlier can never allow claims regarding global outliers.…”