A retrospective analysis of Montana's 2020 congressional redistricting map

TL;DR

The paper addresses how to characterize Montana's two-district space after the 2020 census by enumerating county-line partitions and by evaluating sampling methods (Redist enumpart, SMC, and GerryChain ReCom). It combines population-deviation, compactness (ER, LW, PbP), and political-outcome analyses across enumerated plans and multiple ensembles, revealing biases in sampling toward more compact plans and showing how the adopted map compares to the full set and to sampled ensembles. Key findings include the adopted map's strong population balance (ER=$11$, PbP scores $0.21$ and $0.53$, LW=$0.644$) and its generally non-extreme placement in political-outcome distributions, though its compactness posture differs from some ensembles. The study demonstrates the value and limitations of sampling-based inferences in redistricting, highlighting the importance of understanding the sampling distribution when interpreting the adopted map’s properties and potential political consequences.

Abstract

The 2020 decennial census data resulted in an increase from one to two congressional representatives in the state of Montana. The state underwent its redistricting process in 2021 in time for the November 2022 congressional elections, carving the state into two districts. This paper analyzes the redistricting process and compares the adopted congressional map to the space of all other possible maps. In particular, we look at the population deviation, compactness and political outcomes of these maps. We also consider how well two popular sampling techniques, that sample from the space of possible maps, approximate the true distributions of these measures.

Figures (20)

• Figure 1: Montana's two adopted congressional districts and population density by county.
• Figure 2: MT counties shown with graphs.
• Figure 3: Histogram of population deviations of the 98,350,198 possible plans from MT_122 with pop_dev $< 10$%.
• Figure 4: Maps with varying ER scores within the ensemble of enumerated plans.
• Figure 5: Histograms of ER, LW and PbP score for the 98 million plans with population deviation less than 0.1. The adopted map has ER = 11, LW = 0.64 and min PbP = 0.21.