Enumeration and sampling analysis of Montana’s 2020 congressional redistricting map

Abstract

The 2020 decennial census data resulted in an increase from one to two congressional representatives in the state of Montana. The new districts nearly followed county lines and provide a rare instance of an enumerable redistricting problem. We use the enumerated set of maps to analyze the redistricting process and compare the adopted congressional map to the space of all other possible maps, the full set of 1-person deviation maps and several ReCom (spanning tree) generated ensembles. Along with considering the usual selection of statistics on these maps (population deviation, compactness, minority representation and political outcomes) we look at Montana’s definition of competitive districts and analyze the best ER upper bound for the ReCom algorithm in this simple case.

Appendix of Tables and Figures

See Tables 6, 7 and Figs. 22, 23, 24, 25, 26 and 27.

Table 6 For the Western and Eastern adopted congressional districts the percent of voters who voted for the Democratic Party candidate out of those who voted for either the Democratic or Republican Party candidate only in each of the 10 elections used by the DAC plus the 2022 Congressional election and the 16-20 Compilation. Note that in 2022, 22% of voters voted for the Independent Party candidate in the Congressional election in the Eastern District. These results can be found on the MT SOS page [27]

Table 7 MT counties with shared border. Ordered in increasing length of shared perimeter. Edges corresponding to those counties above the dashed line are removed from the MT_141 graph to form the graph MT_122

Fig. 22

Histograms for the number of democrats elected in each of the 17,083 possible redistricting maps with ER $\le 21$ and population deviation $<0.03$ for the 10 statewide races considered by the DAC plus the compilation election. The green dashed line is at twice the statewide percentage of voters who voted democratic, hence the number of democrats who would be elected for state-wide proportional representation. Though this is not an integer, it gives an idea of how far the adopted map and the ensemble of maps are from statewide proportionality

Fig. 23

Ensemble 21 was created with the GerryChain proposal ReCom. The full ensemble has 100,000 maps, 5,222 of which are unique. Hard constraints of ER $\le 21$ and pop_dev $<0.03$. The accept function was ‘always_accept’. The adopted map served as the one starting partition

Fig. 24

Ensemble 18 was created with the GerryChain proposal ReCom. The full ensemble has 100,000 maps, 2904 of which are unique. The hard constraints in this MCMC run were ER $\le 18$ and pop_dev $<0.03$. The accept function was ‘always_accept’. The adopted map served as the one starting partition

Fig. 25

Ensemble 15 was created with the GerryChain proposal ReCom. The full ensemble has 100,000 maps, 638 of which are unique. The hard constraints in this MCMC run were ER $\le 15$ and pop_dev $<0.03$. The accept function was ‘always_accept’. The adopted map served as the one starting partition

Fig. 26

Ensemble 12 was created with the GerryChain proposal ReCom. The full ensemble has 100,000 maps, 68 of which are unique. There are only 69 maps in the enumerated set. The hard constraints in this MCMC run were ER $\le 12$ and pop_dev $<0.03$. The accept function was ‘always_accept’. The adopted map served as the one starting partition

Fig. 27

Scatter plots of (x, y) where x and y are the proportion of voters who voted democratic in each of the two districts ordered so that $x\le y$ in the 10 statewide elections and the 16-20 Compilation election. These are calculated over all 17,083 redistricting solutions with ER $\le 21$ and population deviation $< 0.03$ in blue. The red circle is the adopted map while the white circles are the 17 redistricting solutions with population deviation 1 person and ER score < 29. The star is the 1-person deviation map pictured in Fig. 7 with ER score 20