Plotting Zero Sum Beliefs and their Relationship with Political Polarization

Author

Affiliation

Kurt Roben

Binghamton University

Abstract

This paper is an investigation into whether the relationship between zero sum economic beliefs or zero sum social identity beliefs are more positively associated with political extremity in adolescents. Zero Sum beliefs are a perception that one party’s gains come at the expense of another party’s losses, and in past studies it has been linked to political intergroup fighting (Roberts, 2022), (Davidai, 2023). Political extremity was measured by an adolescent’s affective polarization, or the disproportion between an individual’s positive feelings towards their own political group and negative feelings towards the opposing party (Druckman, 2021).To give this concept a score, a question was implemented into a survey asking participants if they believed the opposing party’s views were so misguided that they threaten the nation’s well being. In order to measure zero sum views, 9 likert-scale questions relating to economic and social identity zero sum beliefs were added to the survey. After assigning both separate economic and social identity zero sum scores based on participants responses to these questions, they were entered into a regression model to predict participants polarization score. We hypothesized that zero sum social identity will be more positively associated with political extremity. Most of the questions are centered on group conflicts, so those who view group conflicts as having winners and losers are much more likely to view political groupings as winners vs losers, leading to more negative views of the opposing political party. It was found that agreement with Economic zero sum beliefs did not have a correlation with extreme political views, but agreement with Social Identity Beliefs had a weak, negative correlation.

Keywords

Political Polarization, Economic Zero Sum Beliefs, Social Identity Zero Sum Beliefs, Spearman Rho correlation, Mental Health

1 1 Results

1.1 1.1 Load

install.packages("readxl")
install.packages("dplyr")
install.packages("ggplot2")
install.packages("stats")
install.packages("NHANES")
library(readxl)
library(dplyr)
library(ggplot2)
library(stats)
library(NHANES)
alldata <- read_excel("10.20.2025.Data.Team3.clean.xlsx")
alldata[alldata == -99] <- NA
alldata[alldata == -50] <- NA

#explanation: these files are necessary to run the following code chunks smoothly.

1.2 1.2 Import

alldata <- read_excel("10.20.2025.Data.Team3.clean.xlsx")
#explanation- This allows the data to be accessed in positcloud. 

1.3 1.3 Transform

alldata[alldata == -99] <- NA
alldata[alldata == -50] <- NA
E_zerosums <- c("ZSPRE_HEALTH", "ZSPRE_ECONOMY", "ZSPRE_ENVIRO1", "ZSPRE_ENVIRO2")
S_zerosums <- c("ZSPRE_IMM", "ZSPRE_WOMEN1", "ZSPRE_WOMEN2", "ZSPRE_DEI1", "ZSPRE_DEI2")
alldata <- alldata %>%
  mutate(across(all_of(c(E_zerosums, S_zerosums)), as.numeric))
alldata <- alldata %>%
  mutate(
    E_avgscore = rowMeans(select(., all_of(E_zerosums)), na.rm = TRUE),
    S_avgscore = rowMeans(select(., all_of(S_zerosums)), na.rm = TRUE),
  )
alldata <- alldata %>%
  mutate(POLITICALAFFIL = as.numeric(POLITICALAFFIL))
dem_data <- alldata %>% 
 filter (POLITICALAFFIL == 2)
dem_data <- dem_data %>% 
  mutate(POLARIZE_REP = as.numeric(POLARIZE_REP))
#explanation: For future use, naming and defining these variables is crucial. It allows you to call on it for future use, and it also gives you both of the participants zerosum score. Filtering the data for democrats only elimanates all non target demographics. Mutatitng the data allows for polarize rep to be called on and used by posit cloud in a numeric way.

1.4 1.4 Model

cor.test(dem_data$E_avgscore, dem_data$POLARIZE_REP, method = "spearman")

Warning in cor.test.default(dem_data$E_avgscore, dem_data$POLARIZE_REP, :
Cannot compute exact p-value with ties

    Spearman's rank correlation rho

data:  dem_data$E_avgscore and dem_data$POLARIZE_REP
S = 27482, p-value = 0.2196
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
-0.173158 

ggplot(dem_data, aes(x = E_avgscore, y = POLARIZE_REP)) + 
  geom_point(position = "jitter", alpha = 0.25) + geom_smooth(method = "lm") +
  xlab("Environmental Zero Sum Belief Average") +
  ylab("Political Opinion Towards Republicans") + 
  ggtitle("Environmental zero sum belief and Polarized Opinion")

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

A scatterplot depicting the relationship between a participants economic zero sum belief average and their extreme political polarization scores with a line of best fit to show the lack of correlation.

#explanation: The spearman method is run first in order to calculate the values. Dem_ data, which was created earlier, is then used to plot E_avgscore on the x axis and POLARIZE_REP (democrat feelings towards republicans) on the y axis. geom_point is used for scatterplots, and geom_smooth is used in order to create a line of best fit included in the graph.

cor.test(dem_data$S_avgscore, dem_data$POLARIZE_REP, method = "spearman")

Warning in cor.test.default(dem_data$S_avgscore, dem_data$POLARIZE_REP, :
Cannot compute exact p-value with ties

    Spearman's rank correlation rho

data:  dem_data$S_avgscore and dem_data$POLARIZE_REP
S = 31602, p-value = 0.01122
alternative hypothesis: true rho is not equal to 0
sample estimates:
       rho 
-0.3489968 

ggplot(dem_data, aes(x = S_avgscore, y = POLARIZE_REP)) + 
  geom_point(position = "jitter", alpha = 0.25) + geom_smooth(method = "lm") +
  xlab("Social Zero Sum Belief Average") +
  ylab("Political Opinion Towards Republicans") +
  ggtitle("Social Identity zero sum beliefs and Polarized Opinion")

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

A scatterplot depicting the relationship between a participants social identity zero sum belief average and their extreme political polarization scores with a line of best fit to show the weak, negative correlation.

#explanation: the spearman method is run first in order to calculate the values. Dem_ data, which was created earlier, is then used to plot S_avgscore on the x axis and POLARIZE_REP (democrat feelings towards republicans) on the y axis. geom_point is used for scatterplots, and geom_smooth is used in order to create a line of best fit included in the graph.

2 Discussion

Upon analysis of our data, we found that Democrats with higher levels of agreement with Social Identity Zero Sum statements may be more likely to hold less extreme views towards Republicans. Furthermore, it was found that Democrats’ agreement with Economic Zero Sum statements has no correlation with their extreme opinions of the opposite political party. When analyzing the data for Republicans, we found only two participants to be eligible to analyze, which is not a large enough data set. We originally hypothesized that both economic and social identity beliefs would have a correlation with an individual’s polarization level, and we also hypothesized that we would be able to use their average zero sum score to predict their polarization level. This hypothesis did not hold true, as economic zero sum beliefs have no correlation with polarization and only a weak negative correlation was found for social identity beliefs. While the results are limited, it does raise interesting questions about the small, negative correlation found between social identity beliefs and extreme polarization