Abstract

This is a study of gerrymandering in Alabama. We well test three methods of shape-based compactness scores, assess the 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: gerrymandering, compactness, convex hull, alabama, political representation Comma-separated list of keywords (tags) for searchability. Geographers often use one or two keywords each for: theory, geographic context, and methods.
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.

This study is exploratory in design, with the goal of evaluating usefulness of a new gerrymandering metric based on the convex hull of a congressional district and representative capability inside the convex hull compared to the congressional district.

Materials and procedure

Computational environment

I plan on using…
groundhog() for reproducible computational environments (consistent versions of R and its packages)
here() for reproducible path names
tidyverse() includes dplyr() for database-style data frames
sf() provides support for spatial vector data implementing the OSGeo simple features standards we are accustomed to
stars() spatial-temporal raster data in R
tmap() thematic maps, including static maps or interactive leaflet maps

## Loading required package: conflicted

## Loading required package: groundhog

## groundhog says: No default repository found, setting to 'http://cran.r-project.org/'

## Attached: 'Groundhog' (Version: 3.2.2)

## Tips and troubleshooting: https://groundhogR.com

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2     
## here() starts at /Users/samuelbarnard/Desktop/springTerm25/openGISci/OR-Gerrymander-Alabama
## 
## Linking to GEOS 3.13.0, GDAL 3.8.5, PROJ 9.5.1; sf_use_s2() is TRUE
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## Linking to liblwgeom 3.0.0beta1 r16016, GEOS 3.11.0, PROJ 9.1.0

## Warning in fun(libname, pkgname): GEOS versions differ: lwgeom has 3.11.0 sf
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Data and variables

We plan on using data sources…

Set up districts file from districts.gpkg:

## 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

Layers from `districts.gpkg`

`precincts20`

Title: Voting Precincts 2020
Abstract: Alabama voting data for 2020 elections by precinct.
Spatial Coverage: Alabama OSM:161950
Spatial Resolution: voting precincts
Spatial Reference System: EPSG: 4269, NAD 1983 geographic coordinate system
Temporal Coverage: voting precincts used for tabulating the 2020 election
Temporal Resolution: annual election (2020)
Lineage: Saved as geopackage format. Processing prior to download is explained in validation report and readme
Distribution: Data available at Redistricting Data Hub with free login.
Constraints: Permitted for noncommercial and nonpartisan use only. Copyright and use constraints explained here
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	…	…	…	…	…

Load variables:

## Reading layer `precincts20' from data source 
##   `/Users/samuelbarnard/Desktop/springTerm25/openGISci/OR-Gerrymander-Alabama/data/raw/public/alabama_dataset/districts.gpkg' 
##   using driver `GPKG'
## Simple feature collection with 1972 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: -88.47323 ymin: 30.14442 xmax: -84.88825 ymax: 35.00803
## Geodetic CRS:  NAD83

`districts23`

Title: US Congressional Districts 2023
Abstract: Alabama congressional districts for the 2024 election.
Spatial Coverage: Alabama OSM:161950
Spatial Resolution: congressional districts
Spatial Reference System: EPSG: 3857, NAD 1984 Web Mercator projection
Temporal Coverage: districts approved in 2023 for use in 2024.
Temporal Resolution:
Lineage: Loaded into QGIS as ArcGIS feaure service layer and saved in geopackage format. Extraneous data fields were removed and the FIX GEOMETRIES tool was used to correct geometry errors.
Distribution: Alabama State GIS via ESRI feature service
Constraints: Public Domain data free for use and redistribution.
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
DISTRICT	…	US Congressional District Number	…	…	…	…	…
POPULATION	…	total population (2020 census)	…	…	…	…	…
WHITE	…	total white population (2020 census)	…	…	…	…	…
BLACK	…	total Black or African American population (2020 census)	…	…	…	…	…

Load variables:

## Reading layer `districts23' from data source 
##   `/Users/samuelbarnard/Desktop/springTerm25/openGISci/OR-Gerrymander-Alabama/data/raw/public/alabama_dataset/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:  NAD83

Map 2023 districts

## ℹ tmap mode set to "plot".
## 
## 
## ── 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.

`blockgroups2020`

Title: Block Groups 2020
Abstract: Vector polygon geopackage layer of Census tracts and demographic data.
Spatial Coverage: Alabama OSM:161950
Spatial Resolution: census block groups
Spatial Reference System: EPSG: 4269, NAD 1983 geographic coordinate system
Temporal Coverage: 2020 census
Temporal Resolution: 10 year census (2020)
Lineage: Data downloaded from US Census API “pl” public law summary file using tidycensus in R
Distribution: US Census API
Constraints: Public Domain data free for use and redistribution.
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
GEOID	…	code to uniquely identify tracts	…	…	…	…	…
P4_001N	…	total population, 18 years or older	…	…	…	…	…
P4_006N	…	total: not Hispanic or Latino, Population of one race, Black or African American alone, 18 years or older	…	…	…	…	…
P5_003N	…	Total institutionalized population in correctional facilities for adults, 18 years or older	…	…	…	…	…

Load data:

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

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 public law data series table P3.

Query table P3 on "race for the population 18 years and over".

## Reading layer `block_groups' from data source 
##   `/Users/samuelbarnard/Desktop/springTerm25/openGISci/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

I have previously conducted an analysis with this data using QGIS to determine compactness along with race and party affiliation data.

However, I only conducted my analysis with an area-weighted re-aggregation approach, and did not incorporate convex hulls.

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

Step 1:

districts23 needs to be re-projected to EPSG:4269 NAD 1983 coordinate system using st_transform() for the purpose of geodesic analysis.

From here, we can calculate the percentage of population identifying as Black using mutate().

Step 2:

Census data (blockgroups2020) also needs to be re-projected from the WGS 1984 geographic coordinate system to the NAD 1983 geographic coordinate system.

Step 3:

Find the total of people identifying as Black or African American as one race or any combination of multiple races.

a. First, make a list of all the variables inclusive of people identifying as Black or African American.

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

b. 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%.

c. Save the results in `blockgroups_calc.gpkg`

## Deleting layer `blockgroups_calc' using driver `GPKG'
## Writing layer `blockgroups_calc' to data source 
##   `/Users/samuelbarnard/Desktop/springTerm25/openGISci/OR-Gerrymander-Alabama/data/derived/public/blockgroups_calc.gpkg' using driver `GPKG'
## Writing 3925 features with 6 fields and geometry type Multi Polygon.

Step 4:

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

## ℹ tmap mode set to "plot".

Map approved 2023 districts over the black population

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

Analysis

Approach 1: AWR

Use area weighted re-aggregation to estimate white and black voting age populations in 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 (sf)

## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries

Report results. Percentages of Black or African American people vary significantly from district to district.

DISTRICT	POPULATION	WHITE	BLACK	pctBlack	bgTotal	bgBlack	pctBlackbg
1	717754	527330	116462	16.2	556559.0	90288.76	16.2
2	717754	303461	353228	49.2	559640.2	272078.98	48.6
3	717754	508080	146376	20.4	564183.0	116778.64	20.7
4	717754	585183	49721	6.9	558441.9	42522.09	7.6
5	717754	495427	126226	17.6	560573.5	102750.67	18.3
6	717755	517634	125785	17.5	552556.9	96865.75	17.5
7	717754	283337	378364	52.7	564941.7	293014.56	51.9

Approach 2: Convex hull

## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries

Join convex hull estimates to districts with blockgroup estimates.

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

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

Also, to knit, will we need to replacest_perimeter() with st_length(st_cast(geom, "MULTILINESTRING"))?

Results

Visualization 1: Correlation matrix and small plots for gerrymandering indicators

	pctBlackbg	diffPct	absdiffPct	compact_shp	compact_hull	compact_circ
pctBlackbg	1.0000000	0.8656916	0.2755931	-0.2814174	-0.1247704	0.0389629
diffPct	0.8656916	1.0000000	-0.0363323	0.1128061	0.1850875	0.1185339
absdiffPct	0.2755931	-0.0363323	1.0000000	-0.6801495	-0.5295192	0.2456776
compact_shp	-0.2814174	0.1128061	-0.6801495	1.0000000	0.9557498	0.4197650
compact_hull	-0.1247704	0.1850875	-0.5295192	0.9557498	1.0000000	0.5039445
compact_circ	0.0389629	0.1185339	0.2456776	0.4197650	0.5039445	1.0000000

Visualization 2: Plot with representational difference and compactness

This is a scatterplot with (absolute) difference in representation on x axis and compactness on y axis. This plot presents the three different compactness scores simultaneously with different colors.

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

There is a positive relationship between minimum bounding circle compactness and absolute convex hull representational difference. There is a negative relationship between convex hull compactness and absolute convex hull representational difference. There is a negative relationship between shape compactness and absolute convex hull representational difference. Shape and convex hull exhibit a positive correlation.

Districts 1 and 2 are the least compact across all scores.

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

This analysis is based on work by Professor Joseph Holler of Middlebury College, and concepts and workflows from the course Open GIScience GEOG 0361.

This report is based upon the template for Reproducible and Replicable Research in Human-Environment and Geographical Sciences, DOI:[10.17605/OSF.IO/W29MQ](DOI:%5B10.17605/OSF.IO/W29MQ){.uri}

References

Cheng, Joe, Carson Sievert, Barret Schloerke, Winston Chang, Yihui Xie, and Jeff Allen. 2024. Htmltools: Tools for HTML. https://github.com/rstudio/htmltools.

Müller, Kirill. 2020. Here: A Simpler Way to Find Your Files. https://here.r-lib.org/.

Pebesma, Edzer. 2018. “Simple Features for R: Standardized Support for Spatial Vector Data.” The R Journal 10 (1): 439–46. https://doi.org/10.32614/RJ-2018-009.

———. 2024a. Lwgeom: Bindings to Selected Liblwgeom Functions for Simple Features. https://r-spatial.github.io/lwgeom/.

———. 2024b. Sf: Simple Features for r. https://r-spatial.github.io/sf/.

Pebesma, Edzer, and Roger Bivand. 2023. Spatial Data Science: With applications in R. Chapman and Hall/CRC. https://doi.org/10.1201/9780429459016.

R Core Team. 2024. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.

Tennekes, Martijn. 2018. “tmap: Thematic Maps in R.” Journal of Statistical Software 84 (6): 1–39. https://doi.org/10.18637/jss.v084.i06.

———. 2025. Tmap: Thematic Maps. https://github.com/r-tmap/tmap.

Walker, Kyle, and Matt Herman. 2025. Tidycensus: Load US Census Boundary and Attribute Data as Tidyverse and Sf-Ready Data Frames. https://walker-data.com/tidycensus/.

Wickham, Hadley. 2023. Tidyverse: Easily Install and Load the Tidyverse. https://tidyverse.tidyverse.org.

Wickham, Hadley, Mara Averick, Jennifer Bryan, Winston Chang, Lucy D’Agostino McGowan, Romain François, Garrett Grolemund, et al. 2019. “Welcome to the tidyverse.” Journal of Open Source Software 4 (43): 1686. https://doi.org/10.21105/joss.01686.

Xie, Yihui. 2014. “Knitr: A Comprehensive Tool for Reproducible Research in R.” In Implementing Reproducible Computational Research, edited by Victoria Stodden, Friedrich Leisch, and Roger D. Peng. Chapman; Hall/CRC.

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Gerrymandering in Alabama: Analysis Plan

Samuel Barnard

2025-03-02

Abstract

Study Metadata

Study design

Materials and procedure

Computational environment

Data and variables

Layers from `districts.gpkg`

`precincts20`

`districts23`

`blockgroups2020`

Prior observations

Bias and threats to validity

Data transformations

Step 1:

Step 2:

Step 3:

a. First, make a list of all the variables inclusive of people identifying as Black or African American.

b. Next, calculate new columns.

c. Save the results in `blockgroups_calc.gpkg`

Step 4:

Analysis

Approach 1: AWR

Approach 2: Convex hull

Results

Visualization 1: Correlation matrix and small plots for gerrymandering indicators

Visualization 2: Plot with representational difference and compactness

Discussion

Integrity Statement

Acknowledgements

References

Gerrymandering in Alabama: Analysis Plan

Samuel Barnard

2025-03-02

Abstract

Study Metadata

Study design

Materials and procedure

Computational environment

Data and variables

Layers from districts.gpkg

precincts20

districts23

blockgroups2020

Prior observations

Bias and threats to validity

Data transformations

Step 1:

Step 2:

Step 3:

a. First, make a list of all the variables inclusive of people identifying as Black or African American.

b. Next, calculate new columns.

c. Save the results in blockgroups_calc.gpkg

Step 4:

Analysis

Approach 1: AWR

Approach 2: Convex hull

Results

Visualization 1: Correlation matrix and small plots for gerrymandering indicators

Visualization 2: Plot with representational difference and compactness

Discussion

Integrity Statement

Acknowledgements

References

Layers from `districts.gpkg`

`precincts20`

`districts23`

`blockgroups2020`

c. Save the results in `blockgroups_calc.gpkg`