Abstract

This is a study of gerrymandering in Alabama. We will test three methods of shape-based compactness scores, assess representativeness of districts based on prior presidential elections and race. We will then extend prior studies by calculating representativeness of the convex hull of district polygons.

Study Metadata

Key words: Alabama, gerrymandering, compactness, convex hull, political representation
Subject: Social and Behavioral Sciences: Geography: Geographic Information Sciences
Date created: 2025-02-17
Date modified: 2025-02-17
Spatial Coverage: Alabama OSM:161950
Spatial Resolution: Census Block Groups
Spatial Reference System: EPSG:4269 NAD 1983 Geographic Coordinate System
Temporal Coverage: 2020-2024 population and voting data
Temporal Resolution: Decennial census

Study design

This is an original study based on literature on gerrymandering metrics.

It is an exploratory study to evaluate usefulness of a new gerrymandering metric based on the convex hull of a congressional district and the representativeness inside the convex hull compared to the congressional district.

Materials and procedure

Computational environment

I plan on using package … for …

Data and variables

WE plan on using data sources …. , … ….

Several data layers are compiled and provided in the districts geopackage.

districts_file <- here("data", "raw", "public", "districts.gpkg")
st_layers(districts_file)

## Driver: GPKG 
## Available layers:
##    layer_name geometry_type features fields crs_name
## 1 districts21 Multi Polygon        7      4   WGS 84
## 2 districts23 Multi Polygon        7      4    NAD83
## 3 precincts20 Multi Polygon     1972      8    NAD83

Districts 2021

The congressional districts enacted in 2021 were used in the 2022 mid-term elections, and then deemed unconstitutional gerrymanders by the Supreme Court.

Load the districts.

districts21 <- st_read(districts_file, layer="districts21")

## Reading layer `districts21' from data source 
##   `C:\GitHub\josephholler\OR-Gerrymander-Alabama\data\raw\public\districts.gpkg' 
##   using driver `GPKG'
## Simple feature collection with 7 features and 4 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: -88.47323 ymin: 30.14443 xmax: -84.88825 ymax: 35.00803
## Geodetic CRS:  WGS 84

Map the districts

tmap_mode(mode = "plot")

## ℹ tmap mode set to "plot".

districts21map <- districts21 |> 
  tm_shape() +
  tm_polygons(fill_alpha = 0,
              col = "red") +
  tm_labels(text = "DISTRICT",
          col="red",
          bgcol = "white",
          bgcol_alpha = 0.5,
          on_surface = TRUE,
          just = c("center", "center")
          )

## 
## ── tmap v3 code detected ───────────────────────────────────────────────────────
## [v3->v4] `tm_text()`: migrate the layer options 'just' to 'options =
## opt_tm_text(<HERE>)'[tm_text()] Argument `on_surface` unknown.

districts21map

Precincts 2020

includeMarkdown(here("data", "metadata", "precincts20.md"))

Title: Voting Precincts 2020
Abstract: Alabama voting data for 2020 elections by precinct.
Spatial Coverage: Alabama
Spatial Resolution: Voting precincts
Spatial Reference System: EPSG 4269 NAD 1983 geographic coordinate system
Temporal Coverage: precincts used for tabulating the 2020 census
Temporal Resolution: annual election
Lineage: Saved a sgeopackage format. Processing prior to download is explained in al_vest_20_validation_report.pdf and readme_al_vest_20.txt
Distribution: Data available at Redistricting Data Hub with free login
Constraints: Permitted for noncommercial and nonpartisan use only. Copright and use constrains explained in redistrictingdatahub_legal.txt
Data Quality: State any planned quality assessment
Variables: For each variable, enter the following information. If you have two or more variables per data source, you may want to present this information in table form (shown below)
- Label: variable name as used in the data or code
- Alias: intuitive natural language name
- Definition: Short description or definition of the variable. Include measurement units in description.
- Type: data type, e.g. character string, integer, real
- Accuracy: e.g. uncertainty of measurements
- Domain: Expected range of Maximum and Minimum of numerical data, or codes or categories of nominal data, or reference to a standard codebook
- Missing Data Value(s): Values used to represent missing data and frequency of missing data observations
- Missing Data Frequency: Frequency of missing data observations: not yet known for data to be collected

Label	Alias	Definition	Type	Accuracy	Domain	Missing Data Value(s)	Missing Data Frequency
VTDST20	…	Voting district ID	…	…	…	…	…
GEOID20	…	Unique geographic ID	…	…	…	…	…
G20PRETRU	…	total votes for Trump in 2020	…	…	…	…	…
G20PREBID	…	total votes for Biden in 2020	…	…	…	…	…

Decennial Census

We acquire decennial census data in block groups using the tidycensus package. First, query metadata for the pl public law data series.

census_metadata_file <- here("data", "metadata", "census2020pl_vars.csv")
if(file.exists(census_metadata_file)){
  census2020pl_vars <- read.csv(census_metadata_file)
} else {
  census2020pl_vars <- load_variables(2020, "pl")
  write.csv(census2020pl_vars, here("data", "metadata", "census2020pl_vars.csv"))
}

The issue in the 2023 court cases on Alabama’s gerrymandering was a racial gerrymander discriminating against people identifying as Black or African American. Therefore, we will analyze people of voting age (18 or older) identifying as Black and or African as one race in any combination with other races. This data is found in table P3.

Query the public law data series table P3 on “race for the population 18 years and over”.

blockgroup_file <- here("data", "raw", "public", "block_groups.gpkg")

# if the data is already downloaded, just load it
# otherwise, query from the census and save
if(file.exists(blockgroup_file)){
  blockgroups <- st_read(blockgroup_file)
} else {
  blockgroups <- get_decennial(geography = "block group",
                               sumfile = "pl",
                               table = "P3",
                               year = 2020,
                               state = "Alabama",
                               output = "wide",
                               geometry = TRUE,
                               keep_geo_vars = TRUE)
  st_write(blockgroups, blockgroup_file)
}

## Reading layer `block_groups' from data source 
##   `C:\GitHub\josephholler\OR-Gerrymander-Alabama\data\raw\public\block_groups.gpkg' 
##   using driver `GPKG'
## Simple feature collection with 3925 features and 83 fields (with 1 geometry empty)
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: -88.47323 ymin: 30.22333 xmax: -84.88908 ymax: 35.00803
## Geodetic CRS:  NAD83

Prior observations

We have previously investigated the compactness scores of Alabama’s congressional districts as well as the percentage of Biden voters from the 2020 elections and the percentage of the population 18 years or older that is not Hispanic and is Black or African American.

We have never calculated the minimum bounding circle or convex hulls of Alabama’s congressional districts.

Bias and threats to validity

This study is explicitly an investigation to the modifiable areal unit problem. Aspects of the study are extremely sensitive to the combination of edge effects and scale, whereby complex borders formed by natural features, e.g. coastlines or rivers, vary greatly in perimeter depending on the scale of analysis. We hope that in part, this study establishes a method that is more robust (less sensitive) to the threats to validity caused by scale and edge effects in studies of gerrymandering and district shapes.

Data transformations

Districts 2021

Transform Districts into NAD 1983 coordinate system, and calculate the percentage of population identifying as Black.

districts21 <- districts21 |> st_transform(4269) |> 
  mutate(pctBlack = round(BLACK / POPULATION * 100, 1))

Block groups census data

Census data needs to be transformed from the WGS 1984 geographic coordinate system to the NAD 1983 geographic coordinate system.

blockgroups <- st_transform(blockgroups, 4269)

Find the total of people identifying as Black or African American as one race or any combination of multiple races. First, make a list of all the variables inclusive of people identifying as Black or African American.

black_vars <- census2020pl_vars |> 
  dplyr::filter(str_detect(name, "P3"),
                str_detect(label, "Black")) |> 
  select(-concept)

black_vars |> kable()

X	name	label
151	P3_004N	!!Total:!!Population of one race:!!Black or African American alone
158	P3_011N	!!Total:!!Population of two or more races:!!Population of two races:!!White; Black or African American
163	P3_016N	!!Total:!!Population of two or more races:!!Population of two races:!!Black or African American; American Indian and Alaska Native
164	P3_017N	!!Total:!!Population of two or more races:!!Population of two races:!!Black or African American; Asian
165	P3_018N	!!Total:!!Population of two or more races:!!Population of two races:!!Black or African American; Native Hawaiian and Other Pacific Islander
166	P3_019N	!!Total:!!Population of two or more races:!!Population of two races:!!Black or African American; Some Other Race
174	P3_027N	!!Total:!!Population of two or more races:!!Population of three races:!!White; Black or African American; American Indian and Alaska Native
175	P3_028N	!!Total:!!Population of two or more races:!!Population of three races:!!White; Black or African American; Asian
176	P3_029N	!!Total:!!Population of two or more races:!!Population of three races:!!White; Black or African American; Native Hawaiian and Other Pacific Islander
177	P3_030N	!!Total:!!Population of two or more races:!!Population of three races:!!White; Black or African American; Some Other Race
184	P3_037N	!!Total:!!Population of two or more races:!!Population of three races:!!Black or African American; American Indian and Alaska Native; Asian
185	P3_038N	!!Total:!!Population of two or more races:!!Population of three races:!!Black or African American; American Indian and Alaska Native; Native Hawaiian and Other Pacific Islander
186	P3_039N	!!Total:!!Population of two or more races:!!Population of three races:!!Black or African American; American Indian and Alaska Native; Some Other Race
187	P3_040N	!!Total:!!Population of two or more races:!!Population of three races:!!Black or African American; Asian; Native Hawaiian and Other Pacific Islander
188	P3_041N	!!Total:!!Population of two or more races:!!Population of three races:!!Black or African American; Asian; Some Other Race
189	P3_042N	!!Total:!!Population of two or more races:!!Population of three races:!!Black or African American; Native Hawaiian and Other Pacific Islander; Some Other Race
195	P3_048N	!!Total:!!Population of two or more races:!!Population of four races:!!White; Black or African American; American Indian and Alaska Native; Asian
196	P3_049N	!!Total:!!Population of two or more races:!!Population of four races:!!White; Black or African American; American Indian and Alaska Native; Native Hawaiian and Other Pacific Islander
197	P3_050N	!!Total:!!Population of two or more races:!!Population of four races:!!White; Black or African American; American Indian and Alaska Native; Some Other Race
198	P3_051N	!!Total:!!Population of two or more races:!!Population of four races:!!White; Black or African American; Asian; Native Hawaiian and Other Pacific Islander
199	P3_052N	!!Total:!!Population of two or more races:!!Population of four races:!!White; Black or African American; Asian; Some Other Race
200	P3_053N	!!Total:!!Population of two or more races:!!Population of four races:!!White; Black or African American; Native Hawaiian and Other Pacific Islander; Some Other Race
205	P3_058N	!!Total:!!Population of two or more races:!!Population of four races:!!Black or African American; American Indian and Alaska Native; Asian; Native Hawaiian and Other Pacific Islander
206	P3_059N	!!Total:!!Population of two or more races:!!Population of four races:!!Black or African American; American Indian and Alaska Native; Asian; Some Other Race
207	P3_060N	!!Total:!!Population of two or more races:!!Population of four races:!!Black or African American; American Indian and Alaska Native; Native Hawaiian and Other Pacific Islander; Some Other Race
208	P3_061N	!!Total:!!Population of two or more races:!!Population of four races:!!Black or African American; Asian; Native Hawaiian and Other Pacific Islander; Some Other Race
211	P3_064N	!!Total:!!Population of two or more races:!!Population of five races:!!White; Black or African American; American Indian and Alaska Native; Asian; Native Hawaiian and Other Pacific Islander
212	P3_065N	!!Total:!!Population of two or more races:!!Population of five races:!!White; Black or African American; American Indian and Alaska Native; Asian; Some Other Race
213	P3_066N	!!Total:!!Population of two or more races:!!Population of five races:!!White; Black or African American; American Indian and Alaska Native; Native Hawaiian and Other Pacific Islander; Some Other Race
214	P3_067N	!!Total:!!Population of two or more races:!!Population of five races:!!White; Black or African American; Asian; Native Hawaiian and Other Pacific Islander; Some Other Race
216	P3_069N	!!Total:!!Population of two or more races:!!Population of five races:!!Black or African American; American Indian and Alaska Native; Asian; Native Hawaiian and Other Pacific Islander; Some Other Race
218	P3_071N	!!Total:!!Population of two or more races:!!Population of six races:!!White; Black or African American; American Indian and Alaska Native; Asian; Native Hawaiian and Other Pacific Islander; Some Other Race

Next, calculate new columns. Black is a sum of all 32 columns shown above, in which any of the racial categories by which someone identifies is Black or African American.
Total is a copy of the population 18 years or over, variable P3_001N.
PctBlack is calculated as Black / Total * 100
CheckPct is calculated as the percentage of the population 18 years or older that is either white of one race only (P3_003N) or Black or African American as calculated above. In Alabama, we can expect that this will be close to 100% for most block groups, and should never exceed 100%.

blockgroups_calc <- blockgroups |> 
  rowwise() |> 
  mutate(Black = sum(c_across(all_of(black_vars$name)))) |> 
  ungroup() |> 
  mutate(bgarea = st_area(geom),
         Total = P3_001N,
         PctBlack = Black / Total * 100,
         CheckPct = (Black + P3_003N) / Total * 100
         ) |> 
  select(GEOID, bgarea, Black, Total, PctBlack, CheckPct)

Save the results as blockgroups_calc.gpkg

st_write(blockgroups_calc, 
         here("data", "derived", "public", "blockgroups_calc.gpkg"),
         append=FALSE)

Map the percentage of the population 18 or over that is Black or African American.

tmap_mode(mode = "plot")
blkgrp_black_map <- tm_shape(blockgroups_calc) + 
  tm_polygons(
    fill = "PctBlack",
    col_alpha = 0.2,
    lwd = 0.1,
    col = "grey90"
  )

blkgrp_black_map

Make an interactive map of the 2021 districts over the black population

tmap_mode(mode = "view")

## ℹ tmap mode set to "view".

blkgrp_black_map +
  districts21map

## Registered S3 method overwritten by 'jsonify':
##   method     from    
##   print.json jsonlite
## Variable bgcol and bgcol_alpha not supported by view mode

Analysis

Estimate the white and black voting age populations using AWR with block groups. Why do this when POPULATION, BLACK, and WHITE variables are already in the table? First, this is the total population, but we should care more about the voting age population. Second, we may want to categorize and calculate BLACK differently from the state of Alabama.

It turns out that R optimizes the first dataset in a spatial query or overlay, with a spatial index, and not the second. Therefore, add the more complex data to st_intersection first, and you’ll see remarkably different run times.

Spatial indices in R: https://r-spatial.org/r/2017/06/22/spatial-index.html

districts21_estimates <- st_intersection(blockgroups_calc, districts21) |> 
  mutate(
    awTot = Total * as.numeric(st_area(geom) / bgarea),
    awBlack = Black * as.numeric(st_area(geom) / bgarea)
  ) |> 
  st_drop_geometry() |> 
  group_by(DISTRICT) |> 
  summarize(bgTotal = sum(awTot),
            bgBlack = sum(awBlack))

districts21_join_bg <- districts21 |> 
  left_join(districts21_estimates, by = "DISTRICT") |> 
  mutate(pctBlackbg = round(bgBlack / bgTotal * 100, 1))

Report results. We find very similar percentages of Black or African American people.

districts21_join_bg |> st_drop_geometry() |> kable()

DISTRICT	POPULATION	WHITE	BLACK	pctBlack	bgTotal	bgBlack	pctBlackbg
1	717754	461324	186921	26.0	557342.4	142843.24	25.6
2	717755	433244	217392	30.3	558173.9	168697.51	30.2
3	717754	479432	176953	24.7	564208.0	141086.63	25.0
4	717754	582698	51929	7.2	556586.0	42949.26	7.7
5	717754	499707	124642	17.4	561381.6	101418.26	18.1
6	717754	498843	138019	19.2	551752.6	104977.72	19.0
7	717754	265204	400306	55.8	567451.7	312326.83	55.0

districts21_estimates <- st_intersection(blockgroups_calc, st_convex_hull(districts21)) |> 
  mutate(
    awTot = Total * as.numeric(st_area(geom) / bgarea),
    awBlack = Black * as.numeric(st_area(geom) / bgarea)
  ) |> 
  st_drop_geometry() |> 
  group_by(DISTRICT) |> 
  summarize(chTotal = sum(awTot),
            chBlack = sum(awBlack))

Join convex hull estimates to Districts with blockgroup estimates.

districts21_join_ch <- districts21_join_bg |> 
  left_join(districts21_estimates, by = "DISTRICT") |> 
  mutate(pctBlackch = round(chBlack / chTotal * 100, 1),
         diffPct = pctBlackbg - pctBlackch,
         absdiffPct = abs(diffPct))

Calculate compactness scores based on:

the area and perimeter
the area and the area of the convex hull
the area and the area of the minimum bounding circle

This block takes some time to run due to the st_minimum_bounding_circle function.

Note: To knit, will we need to replace st_perimeter() with st_length(st_cast(geom, "MULTILINESTRING"))?

districts21_results <- districts21_join_ch |> 
  mutate(
    darea = st_area(geom),
    dperim = st_length(st_cast(geom, "MULTILINESTRING")),
#    dperim2 = st_perimeter(geom),
    compact_shp = round( as.numeric((4 * pi * darea) / dperim^2), 2),
    compact_hull = round( as.numeric(darea / st_area(st_convex_hull(geom))), 2),
    compact_circ = round( as.numeric(darea / st_area(st_minimum_bounding_circle(geom))), 2)
  )

Results

Correlation matrix and small plots for gerrymandering indicators

districts21_results_cor <- districts21_results |> 
  st_drop_geometry() |> 
  select(pctBlackbg,
         diffPct,
         absdiffPct,
         compact_shp,
         compact_hull,
         compact_circ)

districts21_results_cor |> cor() |> kable()

	pctBlackbg	diffPct	absdiffPct	compact_shp	compact_hull	compact_circ
pctBlackbg	1.0000000	0.8661204	0.3920151	-0.0932363	0.1063590	0.7166688
diffPct	0.8661204	1.0000000	0.1621541	0.1633225	0.2565140	0.3900650
absdiffPct	0.3920151	0.1621541	1.0000000	-0.6451778	-0.7348077	0.2726012
compact_shp	-0.0932363	0.1633225	-0.6451778	1.0000000	0.8326192	-0.2836411
compact_hull	0.1063590	0.2565140	-0.7348077	0.8326192	1.0000000	-0.0210585
compact_circ	0.7166688	0.3900650	0.2726012	-0.2836411	-0.0210585	1.0000000

districts21_results_cor |> pairs()

Plot representational difference against compactness

Scatterplot with (absolute) difference in representation on x axis and compactness on y axis. Plot the three different compactness scores simultaneously with different colors. Symbolize the districts with different shapes.

districts21_results_plot <- districts21_results |> 
  st_drop_geometry() |> 
  select(DISTRICT, pctBlack, absdiffPct, compact_shp, compact_hull, compact_circ) |> 
  pivot_longer(cols = starts_with("compact"))

districts21_results_plot |> ggplot() +
  aes(x = absdiffPct, y = value) +
  geom_smooth(method="lm", col = "grey30") +
  geom_label(aes(label = DISTRICT, fill = pctBlack)) +
  scale_fill_distiller(type = "div", palette = "PRGn") +

  facet_wrap(~name)

## `geom_smooth()` using formula = 'y ~ x'

There is a negative relationship between convex hull compactness and convex hull difference. There is a negative relationship between convex hull compactness and convex hull difference. There is a negative relationship between minimum bounding circle compactness and convex hull representational difference.
The exceptions are districts 5 and 7. District 7 really is gerrymandered (packed African American), but the minimum bounding circle method does not find it so. District 5 is not really gerrymandered, even though the minimum bounding circle does find it so.

Shape and convex hull exhibit a positive correlation.
Shape and minimum bounding circle exhibit a positive correlation, with the exception of District 5. Convex hull and minimum bounding circle exhibit a positive correlation, with the exception of District 5.

District 5 is a long, but otherwise compact shape.

tm_shape(districts21_results) +
  tm_polygons(fill = "pctBlackbg") +
  tm_text("DISTRICT")

Discussion

Describe how the results are to be interpreted vis a vis each hypothesis or research question.

Integrity Statement

Include an integrity statement - The authors of this preregistration state that they completed this preregistration to the best of their knowledge and that no other preregistration exists pertaining to the same hypotheses and research. If a prior registration does exist, explain the rationale for revising the registration here.

Acknowledgements

Funding Name: name of funding for the project
Funding Title: title of project grant
Award info URI: web address for award information
Award number: award number

This report is based upon the template for Reproducible and Replicable Research in Human-Environment and Geographical Sciences, DOI: 10.17605/OSF.IO/W29MQ

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Gerrymandering in Alabama: Analysis Plan

Joseph Holler

2025-02-24

Abstract

Study Metadata

Study design

Materials and procedure

Computational environment

Data and variables

Districts 2021

Precincts 2020

Decennial Census

Prior observations

Bias and threats to validity

Data transformations

Districts 2021

Block groups census data

Analysis

Results

Correlation matrix and small plots for gerrymandering indicators

Plot representational difference against compactness

Discussion

Integrity Statement

Acknowledgements

References