have equal populations (specifically, within 0.5% of equality)
be geographically compact
preserve county and municipality boundaries as much as possible
preserve the cores of prior districts
not be drawn using partisan information
Interpretation of requirements
We enforce a maximum population deviation of 0.5%.
We apply a county constraint.
We preprocess the map to ensure the cores of prior districts are preserved, as described below.
To preserve the cores of prior districts, we merge all precincts which are more than two precincts away from a district border, under the 2010 plan.
Precincts in counties which are split by existing district boundaries are merged only within their county.
Simulation Notes
We sample 5,000 districting plans for Nebraska across four runs of the SMC algorithm.
In addition to a county constraint applied to the residual counties left over from the cores operation, we apply an additional Gibbs constraint of strength 2 to avoid splitting counties.
Validation
SMC: 5,000 sampled plans of 3 districts on 1,402 units
`adapt_k_thresh`=0.985 • `seq_alpha`=0.5
`est_label_mult`=1 • `pop_temper`=0
Plan diversity 80% range: 0.13 to 0.43
✖ WARNING: Low plan diversity
R-hat values for summary statistics:
pop_overlap total_vap plan_dev comp_edge comp_polsby pop_hisp pop_white
1.00193 1.00300 1.00084 1.00125 1.00083 0.99979 1.00117
pop_black pop_aian pop_asian pop_nhpi pop_other pop_two vap_hisp
1.00111 1.00140 1.00090 1.00018 1.00100 1.00102 0.99983
vap_white vap_black vap_aian vap_asian vap_nhpi vap_other vap_two
1.00182 1.00093 1.00209 1.00088 1.00022 1.00209 1.00042
pre_16_rep_tru pre_16_dem_cli uss_18_rep_fis uss_18_dem_ray gov_18_rep_ric gov_18_dem_kri atg_18_rep_pet
1.00100 0.99995 1.00120 1.00027 1.00104 1.00003 1.00176
sos_18_rep_evn sos_18_dem_dan pre_20_rep_tru pre_20_dem_bid uss_20_rep_sas uss_20_dem_jan arv_16
1.00127 1.00022 1.00132 1.00093 1.00145 1.00014 1.00100
adv_16 arv_18 adv_18 arv_20 adv_20 county_splits muni_splits
0.99995 1.00132 1.00014 1.00118 1.00064 1.00102 1.00070
ndv nrv ndshare e_dvs e_dem pbias egap
1.00000 1.00117 1.00061 1.00063 1.00077 0.99996 1.00140
Sampling diagnostics for SMC run 1 of 4 (1,250 samples)
Eff. samples (%) Acc. rate Log wgt. sd Max. unique Est. k
Split 1 1,239 (99.1%) 5.7% 0.20 778 ( 98%) 8
Split 2 1,196 (95.7%) 3.5% 0.36 709 ( 90%) 5
Resample 903 (72.2%) NA% 0.34 756 ( 96%) NA
Sampling diagnostics for SMC run 2 of 4 (1,250 samples)
Eff. samples (%) Acc. rate Log wgt. sd Max. unique Est. k
Split 1 1,237 (99.0%) 5.7% 0.21 792 (100%) 8
Split 2 1,199 (96.0%) 3.7% 0.37 700 ( 89%) 5
Resample 1,013 (81.0%) NA% 0.36 757 ( 96%) NA
Sampling diagnostics for SMC run 3 of 4 (1,250 samples)
Eff. samples (%) Acc. rate Log wgt. sd Max. unique Est. k
Split 1 1,238 (99.0%) 6.5% 0.20 778 ( 98%) 7
Split 2 1,209 (96.7%) 4.3% 0.34 690 ( 87%) 4
Resample 1,039 (83.1%) NA% 0.32 775 ( 98%) NA
Sampling diagnostics for SMC run 4 of 4 (1,250 samples)
Eff. samples (%) Acc. rate Log wgt. sd Max. unique Est. k
Split 1 1,238 (99.1%) 4.6% 0.20 807 (102%) 10
Split 2 1,212 (97.0%) 2.9% 0.33 705 ( 89%) 6
Resample 1,065 (85.2%) NA% 0.31 784 ( 99%) NA
• Watch out for low effective samples, very low acceptance rates (less than 1%), large std. devs. of the
log weights (more than 3 or so), and low numbers of unique plans. R-hat values for summary statistics
should be between 1 and 1.05.
• Low diversity: Check for potential bottlenecks. Increase the number of samples. Examine the diversity
plot with `hist(plans_diversity(plans), breaks=24)`. Consider weakening or removing constraints, or
increasing the population tolerance. If the accpetance rate drops quickly in the final splits, try
increasing `pop_temper` by 0.01.
NOTE: Low diversity warning is spurious. Cores constraint limits max VI distance. Did 4 independent runs rather than 2 to maximize diversity.
Redistricting requirements
In Nebraska, districts must, under a legislative resolution:
Interpretation of requirements
We enforce a maximum population deviation of 0.5%. We apply a county constraint. We preprocess the map to ensure the cores of prior districts are preserved, as described below.
Data Sources
Data for Nebraska comes from the ALARM Project's 2020 Redistricting Data Files.
Pre-processing Notes
To preserve the cores of prior districts, we merge all precincts which are more than two precincts away from a district border, under the 2010 plan. Precincts in counties which are split by existing district boundaries are merged only within their county.
Simulation Notes
We sample 5,000 districting plans for Nebraska across four runs of the SMC algorithm. In addition to a county constraint applied to the residual counties left over from the cores operation, we apply an additional Gibbs constraint of strength 2 to avoid splitting counties.
Validation
NOTE: Low diversity warning is spurious. Cores constraint limits max VI distance. Did 4 independent runs rather than 2 to maximize diversity.
Checklist
TODOlines from the template code have been removedenforce_style()to format my coderedist_mapandredist_plansobjects, and summary statistics) have been edited@christopherkenny