Homogenous Precinct Analyses

Ray Block Jr., Penn State University

Winter 2021

Overview

Each “analysis” lesson will be about a specific technique.

Today’s lesson is about a type of analysis that explores whether there is a relationship between municipality characteristics and voting patterns. Specifically, we discuss:

the (math-based) logic of Homogenous Precinct analyses
an example (using Lisa Handley’s dataset)
a replication (and extension) in RStudio
how to interpret the results of these analyses

1. The (Math-Based) Logic of Homogenous Precinct Analyses

The (math-based) logic

Set of methods for testing the relationship between municipality characteristics and voting patterns

Compares voting patterns between:

homogeneous precincts (e.g., those with a high concentration of a particular racial/ethnic group)
non-homogenous precincts (for the same group)

The (math-based) logic

If, for example, there is a precinct composed entirely of minority voters,
and if the voters within that precinct give most of their votes to a particular candidate,
then we can conclude that most minority voters support (i.e., prefer) that candidate

The (math-based) logic

How homogenous do precincts need to be?

The problem: precincts are usually not exclusively one race/ethnicity
A (not “the”) solution: for analysis purposes, precincts that are \(\geq\) 90% minority are considered “homogeneous”

But your homogeneity thresholds might (have to) differ!

The (math-based) logic

The goal is to say that a contest is racially polarized because

an overwhelming majority of minority voters preferred one candidate, and/or
an overwhelming majority of White voters preferred a different candidate.
- How do we know? Because these were the prevailing patterns in homogenous precincts.

2. An example (using sample data from Lisa Handley’s dataset)

An Example (using Handley’s Data)

Results for precincts that are \(\geq\) 90% Black

An Example (using Handley’s Data)

For \(\geq\) 90% White precincts (i.e., 100% – Black VAP)

An Example (using Handley’s Data)

If we combine results from the previous tables…

An Example (using Handley’s Data)

Based on these analyses…

This contest is racially polarized

How do we know? Because…

an overwhelming majority of voters in mostly Black precincts (94.9%) preferred candidate A
while the vast majority of voters in mostly White precincts (86.5%) supported candidate B.

3. Replicating (and Extending) the Homogenous Precinct Analysis in RStudio

Replication & extension in RStudio

Importing the data…

library(readr)
my_data <- read_csv("HomogenousPrecinct/PracticeData.csv")
data(my_data)

Install the readr package and load it to your “library”
Find the “PracticeData.csv” file (specify path)
Use the “read_csv” command to translate the file into R
Put R version of data into a new “object” (“my_data”)

Replication & extension in RStudio

Generating and recoding variables

Install the dplyr package and load it to your “library”

library("dplyr")

Replication & extension in RStudio

Use dplyr’s “mutate” and “ifelse” commands to do the percentage and homogenous precinct variables

my_recodes <- (my_data %>%
  mutate(pBlackVAP=(blackVAP/totalVAP)*100) %>%
  mutate(pWhiteVAP=(whiteVAP/totalVAP)*100) %>%
  mutate(pTurnoutVAP=(total_votes/totalVAP)*100) %>%
  mutate(pVoteA=(candidateA/total_votes)*100) %>%
  mutate(pVoteB=(candidateB/total_votes)*100) %>%
  mutate(MostlyBlack=ifelse(pBlackVAP >= 90, 1, 0),
         MostlyWhite=ifelse(pWhiteVAP >= 90, 1, 0))
  )
data(my_recodes)

Put the re-coded version of the data into a new “object” (called “my_recodes” here). Use this from now on.

Replication & extension in RStudio

Here is a quick a glance at the revised data (with recodes)

Replication & extension in RStudio

Use the “filter” command (in dplyr) to sort through the data

precincts that are homogenously Black

black_precincts <- my_recodes %>%
  filter(MostlyBlack==1) %>%
  select(pVoteA, pVoteB)
data(black_precincts)
print(black_precincts)

Replication & extension in RStudio

Use the “filter” command (in dplyr) to sort through the data

precincts that are homogenously White

white_precincts <- my_recodes %>%
  filter(MostlyWhite==1) %>%
  select(pVoteA, pVoteB)
data(white_precincts)
print(white_precincts)

Replication & extension in RStudio

Check for polarization using the following hypotheses:

H₀: \(\bar{Y}\)(homogenous) \(=\) \(\bar{Y}\)(non-homogenous)
H₁: \(\bar{Y}\)(homogenous) \(\neq\) \(\bar{Y}\)(non-homogenous)

where \(\bar{Y}\) represents a racial/ethnic group’s vote share (e.g., support for candidate A vs. candidate B), sorted by precinct type (e.g., homogenous vs. otherwise)

Replication & extension in RStudio

Evaluating the hypotheses using t-tests

t.test(data=my_recodes, pVoteA ~ MostlyBlack)

t.test(data=my_recodes, pVoteB ~ MostlyBlack)

Replication & extension in RStudio

Evaluating the hypotheses using t-tests

t.test(data=my_recodes, pVoteA ~ MostlyWhite)

t.test(data=my_recodes, pVoteB ~ MostlyWhite)

Replication & extension in RStudio

Data visualization (i.e., showing the results graphically)

library(ggplot2)
my_recodes %>%
  group_by(MostlyBlack) %>%
  summarise(meanA=mean(pVoteA),
            ciA=1.96*sd(pVoteA)/sqrt(n())) %>%
  ggplot(aes(x=factor(MostlyBlack, labels=c("Other", "Mostly Black")), y=meanA))+
  geom_bar(stat="identity")+ 
  geom_errorbar(aes(ymin=meanA-ciA, ymax=meanA+ciA), width=0.2) +
  labs(title="Support for Candidate A", x="Type of precinct", y="Average vote share")

Note: I used the above code to create all the graphs (subbing out the precinct-type and candidate-votes variables)

Replication & extension in RStudio

…in plain English (add a table explaining what the code does, line by line)

Replication & extension in RStudio

Clear evidence of polarization (when comparing vote choice in homogenously Black precincts to other precincts)

Replication & extension in RStudio

Qualified evidence of polarization (when comparing vote choice in homogenously White precincts to other precincts)

4. Interpreting Results from Homogenous Precinct Analysis

Interpreting the results

Recall that,

H₀: \(\bar{Y}\)(homogenous) \(=\) \(\bar{Y}\)(non-homogenous)
H₁: \(\bar{Y}\)(homogenous) \(\neq\) \(\bar{Y}\)(non-homogenous)

…where \(\bar{Y}\) represents a racial/ethnic group’s vote share (e.g., support for candidate A vs. candidate B), sorted by precinct type (e.g., homogenous vs. otherwise)

We have sufficient evidence to reject H₀

Interpreting the results

If voting is polarized

If polarization is statistically significant and minority voters are sufficiently concentrated, the state must create district(s) that provide minority voters with an opportunity to elect candidates of choice.
In this example, we evaluated the degree to which voting patterns are polarized in the Handley data.
More generally, my goal was to show how you can assess the “fairness” of proposed districts using the results from RPV analysis.

Interpreting the results

Limitations of Homogeneous Precinct Analysis

Problematic threshold: In many jurisdictions there are no precincts that can be classified as homogeneous (based on the strict 90% cutoff point).
Limited information: Homogeneous precincts are often only a small, possibly unrepresentative, sample of the population.
- Details about voters in more racially/ ethnically diverse areas not always incorporated into the analyses.

References (FYI)

Handley, Lisa. “Vote Dilution: Measuring Voting Patterns by Race/Ethnicity.” Presentation delivered at the National Conference of State Legislatures.

SCOTUS Blog. 2020. Section 2 of the Voting Rights Act: Vote Dilution and Vote Deprivation.