Class Zero-Sum Beliefs
February 2026: Analysis
Preregistration
Hypotheses
- H1: Class-based zero-sum beliefs positively predict cross-race working-class solidarity.
- H2: Class-based zero-sum beliefs positively predict support for redistributive economic policy.
- H3: The relationship between class-based zero-sum beliefs and support for redistributive economic policy is at least partially explained by cross-race working-class solidarity.
- H4: The effect of class-based zero-sum beliefs on cross-race solidarity will be moderated by race-based zero-sum beliefs such that the positive relationship will hold only for those who are low on race-based zero-sum beliefs.
Analysis plan
- Mediation model: Class-based zero-sum beliefs as the predictor; support for redistributive policy as the outcome; cross-race class-solidarity as the mediator.
- A-path linear model: Class-based zero-sum beliefs as the predictor; cross-race class-solidarity as the outcome variable; race-based zero-sum beliefs as the moderator.
Eligibility
total_n = nrow(df_cbzs)Total N = 501
Preregistered exclusions:
- check_1: select somewhat disagree
- check_2: bot-check
elg_n = nrow(df_cbzs_elg)
df_cbzs %>%
group_by(att_1,att_2) %>%
summarise(N = n()) %>%
ungroup() %>%
mutate(Perc = round(100*(N/sum(N)),2)) %>%
ungroup() %>%
arrange(desc(Perc)) %>%
kbl() %>%
kable_styling(bootstrap_options = "hover",
full_width = F,
position = "left")## `summarise()` has grouped output by 'att_1'. You can override using the
## `.groups` argument.| att_1 | att_2 | N | Perc |
|---|---|---|---|
| 1 | 1 | 488 | 97.41 |
| 1 | 0 | 11 | 2.20 |
| 0 | 1 | 2 | 0.40 |
Eligible N = 488
Demographics
Gender
df_cbzs_elg %>%
mutate(gender = ifelse(is.na(gender) | gender == "","other",gender)) %>%
group_by(gender) %>%
summarise(N = n()) %>%
ungroup() %>%
mutate(Perc = round(100*(N/sum(N)),2)) %>%
ungroup() %>%
arrange(desc(Perc)) %>%
kbl() %>%
kable_styling(bootstrap_options = "hover",
full_width = F,
position = "left")| gender | N | Perc |
|---|---|---|
| woman | 276 | 56.56 |
| man | 209 | 42.83 |
| other | 3 | 0.61 |
Race
| race | N | Perc |
|---|---|---|
| White | 465 | 95.29 |
| multiracial | 23 | 4.71 |
Age
Mean age: 43.6.
Income
median_income_num <- df_cbzs_elg %>%
mutate(income_num = as.numeric(income)) %>%
summarise(median = median(income_num, na.rm = TRUE)) %>%
pull(median)
df_cbzs_elg %>%
ggplot(aes(x = income)) +
geom_bar() +
geom_vline(xintercept = median_income_num,
color = "lightblue", linetype = "dashed") +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_blank(),
axis.ticks = element_blank(),
axis.line = element_line(color = "grey66"),
axis.text.y = element_text(color = "black"),
axis.text.x = element_text(color = "black", face = "bold"),
axis.title.x = element_blank(),
axis.title.y = element_blank()) +
coord_flip()
Education
| edu | N | Perc |
|---|---|---|
| noHS | 2 | 0.41 |
| GED | 138 | 28.28 |
| 2yearColl | 58 | 11.89 |
| 4yearColl | 187 | 38.32 |
| MA | 74 | 15.16 |
| PHD | 27 | 5.53 |
| NA | 2 | 0.41 |
SES
| ses | N | Perc |
|---|---|---|
| Lower Class | 51 | 10.45 |
| Lower Middle Class | 156 | 31.97 |
| Middle Class | 214 | 43.85 |
| Upper Middle Class | 63 | 12.91 |
| Upper Class | 4 | 0.82 |
Working-class identification
To what extent do you identify as working-class? (0 = Not at All Working-Class; 50 = Moderately Working-Class; 100 = Very Strongly Working-Class)
df_cbzs_elg %>%
ggplot(aes(x = class_id)) +
geom_histogram(fill = "lightblue",
binwidth = 5,
color = NA) +
scale_x_continuous(breaks = seq(0,100,10),
limits = c(-10,110)) +
ylab("count") +
geom_vline(xintercept = mean(df_cbzs_elg$class_id,na.rm = T),
color = "black",
linetype = "dashed",
size = 1.1) +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_blank(),
axis.ticks = element_blank(),
axis.line = element_line(color = "grey66"),
axis.text.y = element_text(color = "black"),
axis.text.x = element_text(color = "black",
face = "bold"),
axis.title.x = element_text(color = "black",
face = "bold"))
Politics
Political ideology
Participants were asked about the extent to which they subscribe to the following ideologies on a scale of 1-7 (select NA if unfamiliar): Conservatism, Liberalism, Democratic Socialism, Libertarianism, Progressivism.
means <- df_cbzs_elg %>%
dplyr::select(PID,ideo_con:ideo_prog) %>%
pivot_longer(-PID,
names_to = "ideo",
values_to = "score") %>%
filter(!is.na(score)) %>%
group_by(ideo) %>%
summarise(score = mean(score)) %>%
ungroup()
df_cbzs_elg %>%
dplyr::select(PID,ideo_con:ideo_prog) %>%
pivot_longer(-PID,
names_to = "ideo",
values_to = "score") %>%
filter(!is.na(score)) %>%
ggplot() +
geom_density(aes(x = score), fill = "lightblue",color = NA) +
scale_x_continuous(limits = c(1,7),
breaks = seq(1,7,1)) +
geom_vline(data = means,mapping = aes(xintercept = score),
color = "black",
linetype = "dashed",
size = 1.1) +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_blank(),
axis.ticks = element_blank(),
axis.line = element_line(color = "grey66"),
axis.text.y = element_text(color = "black"),
axis.text.x = element_text(color = "black",
face = "bold")) +
facet_wrap(~ideo,nrow = 2)
Party affiliation
| party_id | N | Perc |
|---|---|---|
| Independent | 169 | 34.63 |
| Democrat | 164 | 33.61 |
| Republican | 155 | 31.76 |
Measures
Class-based Zero-Sum Beliefs
- If the upper class becomes richer, this comes at the expense of the working class
- If the upper class makes more money, then the working class makes less money
- If the upper class does better economically, this does NOT come at the expense of the working class [R]
alpha = 0.92
df_cbzs_elg %>%
ggplot(aes(x = zs_class)) +
geom_density(fill = "lightblue",
color = NA) +
scale_x_continuous(breaks = seq(1,7,1),
limits = c(1,7)) +
ylab("density") +
geom_vline(xintercept = mean(df_cbzs_elg$zs_class,na.rm = T),
color = "black",
linetype = "dashed",
size = 1.1) +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_blank(),
axis.ticks = element_blank(),
axis.line = element_line(color = "grey66"),
axis.text.y = element_text(color = "black"),
axis.text.x = element_text(color = "black",
face = "bold"),
axis.title.x = element_text(color = "black",
face = "bold"))
Race-based Zero-Sum Beliefs
- If non-white become richer, this comes at the expense of white people
- If non-white people make more money, then white people make less money
- If non-white people do better economically, this does NOT come at the expense of white people [R]
alpha = 0.82
df_cbzs_elg %>%
ggplot(aes(x = zs_race)) +
geom_density(fill = "lightblue",
color = NA) +
scale_x_continuous(breaks = seq(1,7,1),
limits = c(1,7)) +
ylab("density") +
geom_vline(xintercept = mean(df_cbzs_elg$zs_race,na.rm = T),
color = "black",
linetype = "dashed",
size = 1.1) +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_blank(),
axis.ticks = element_blank(),
axis.line = element_line(color = "grey66"),
axis.text.y = element_text(color = "black"),
axis.text.x = element_text(color = "black",
face = "bold"),
axis.title.x = element_text(color = "black",
face = "bold"))
Class Solidarity
- I feel a sense of solidarity with non-White (e.g., Black, Asian, Hispanic) working class people.
- The problems facing White and non-White working class people are similar enough for us to be allies.
- What happens to non-White working class communities has something to do with what happens to White working class people.
alpha = 0.61
df_cbzs_elg %>%
ggplot(aes(x = crs)) +
geom_density(fill = "lightblue",
color = NA) +
scale_x_continuous(breaks = seq(1,7,1),
limits = c(1,7)) +
ylab("density") +
geom_vline(xintercept = mean(df_cbzs_elg$crs,na.rm = T),
color = "black",
linetype = "dashed",
size = 1.1) +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_blank(),
axis.ticks = element_blank(),
axis.line = element_line(color = "grey66"),
axis.text.y = element_text(color = "black"),
axis.text.x = element_text(color = "black",
face = "bold"),
axis.title.x = element_text(color = "black",
face = "bold"))
Support for redistributive policy
Participants saw one of the following policies and indicated their support for it (1 = Strongly Oppose to 7 = Strongly Support)
Minimum wage increase
Congress has not increased the federal minimum wage, currently set at $7.25, since 2009. Some Congresspeople are proposing a policy that would gradually raise the federal minimum wage to $20 an hour by 2028. After 2028, the minimum wage would be adjusted each year to keep pace with growth in the median wage, a measure of wages for typical workers.
Student debt relief
Some Congresspeople are proposing a policy that would help to address the student loan debt crisis by forgiving up to $50,000 in loans per borrower. Approximately 42 million Americans, or about 1 in 6 American adults, owe a cumulative $1.6 trillion in student loans. Student loans are now the second-largest slice of household debt after mortgages, bigger than credit card debt.
Housing
Some Congresspeople are proposing a housing affordability policy that would help ensure that every American has a place to live. The policy would allow for smaller, lower cost homes like duplexes, townhouses, and garden apartments to be built and developed, allowing new nonprofit homes and reducing overall housing prices.
Climate change
Some Congresspeople are proposing a Green New Deal bill which would phase out the use of fossil fuels, with the government providing clean energy jobs for people who can’t find employment in the private sector. All jobs would pay at least $20 an hour, and include healthcare benefits and collective bargaining rights.
df_cbzs_elg %>%
ggplot(aes(x = support)) +
geom_histogram(fill = "lightblue",
binwidth = 1,
color = NA) +
scale_x_continuous(breaks = seq(1,7,1),
limits = c(0,8)) +
ylab("count") +
geom_vline(xintercept = mean(df_cbzs_elg$support,na.rm = T),
color = "black",
linetype = "dashed",
size = 1.1) +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_blank(),
axis.ticks = element_blank(),
axis.line = element_line(color = "grey66"),
axis.text.y = element_text(color = "black"),
axis.text.x = element_text(color = "black",
face = "bold"),
axis.title.x = element_text(color = "black",
face = "bold"))
Correlations
Analysis Plan
Mediation Model
Predictor: Class ZSB
Mediator: Cross-race solidarity
Outcome: Support for policy
Bootstraps: 10,000
form.m <- reformulate("zs_class", response = "crs")
form.y <- reformulate(c("zs_class", "crs"), response = "support")
# Fit linear models
m.fit <- lm(form.m, data = df_cbzs_elg) # a-path
y.fit <- lm(form.y, data = df_cbzs_elg) # b and c'-paths
# Fit outcome model WITHOUT mediator to get c-path (total effect)
y.fit.total <- lm(
reformulate("zs_class", response = "support"),
data = df_cbzs_elg
)
# Mediation analysis with bootstrapping (10,000 sims)
med.fit <- mediation::mediate(
model.m = m.fit,
model.y = y.fit,
treat = "zs_class",
mediator = "crs",
boot = TRUE,
sims = 10000
)
med_tbl <- tibble(
Effect = c("ACME (indirect)", "ADE (direct)",
"Total Effect", "Prop. Mediated"),
Estimate = c(med.fit$d0, med.fit$z0,
med.fit$tau.coef, med.fit$n0),
CI.lower = c(med.fit$d0.ci[1], med.fit$z0.ci[1],
med.fit$tau.ci[1], med.fit$n0.ci[1]),
CI.upper = c(med.fit$d0.ci[2], med.fit$z0.ci[2],
med.fit$tau.ci[2], med.fit$n0.ci[2]),
p.value = c(med.fit$d0.p, med.fit$z0.p,
med.fit$tau.p, med.fit$n0.p)
)
kbl(med_tbl) %>%
kable_styling(bootstrap_options = "hover",
full_width = F,
position = "left")| Effect | Estimate | CI.lower | CI.upper | p.value |
|---|---|---|---|---|
| ACME (indirect) | 0.0742914 | 0.0407380 | 0.1146186 | 0 |
| ADE (direct) | 0.3027089 | 0.1931744 | 0.4167262 | 0 |
| Total Effect | 0.3770003 | 0.2696739 | 0.4859205 | 0 |
| Prop. Mediated | 0.1970594 | 0.1053765 | 0.3347072 | 0 |
# Helper to generate significance stars
p_stars <- function(p) {
if (p < .001) return("***")
if (p < .01) return("**")
if (p < .05) return("*")
return("")
}
# Extract coefficients & p-values
a_coef <- coef(m.fit)["zs_class"]
a_p <- summary(m.fit)$coefficients["zs_class", "Pr(>|t|)"]
b_coef <- coef(y.fit)["crs"]
b_p <- summary(y.fit)$coefficients["crs", "Pr(>|t|)"]
cprime <- coef(y.fit)["zs_class"]
cprime_p <- summary(y.fit)$coefficients["zs_class", "Pr(>|t|)"]
c_total <- coef(y.fit.total)["zs_class"]
c_total_p <- summary(y.fit.total)$coefficients["zs_class", "Pr(>|t|)"]
# Paste coefficient + stars
a_label <- paste0("a = ", round(a_coef, 3), p_stars(a_p))
b_label <- paste0("b = ", round(b_coef, 3), p_stars(b_p))
cprime_label <- paste0("c' = ", round(cprime, 3), p_stars(cprime_p))
c_label <- paste0("c = ", round(c_total, 3), p_stars(c_total_p))
# Plot
ggplot() +
xlim(0, 3) + ylim(0, 2) +
# Nodes
annotate("text", x = 0.5, y = 1, label = "zs_class", fontface = "bold") +
annotate("text", x = 1.5, y = 1, label = "crs", fontface = "bold") +
annotate("text", x = 2.5, y = 1, label = "support", fontface = "bold") +
# a-path (X → M)
annotate("segment",
x = 0.7, xend = 1.3, y = 1, yend = 1,
arrow = arrow(length = unit(0.20, "cm"))) +
annotate("text", x = 1.0, y = 1.15, label = a_label) +
# b-path (M → Y)
annotate("segment",
x = 1.7, xend = 2.3, y = 1, yend = 1,
arrow = arrow(length = unit(0.20, "cm"))) +
annotate("text", x = 2.0, y = 1.15, label = b_label) +
# c'-path (direct effect)
annotate("segment",
x = 0.5, xend = 2.5, y = 0.9, yend = 0.9,
arrow = arrow(length = unit(0.20, "cm"))) +
annotate("text", x = 1.5, y = 0.75, label = cprime_label) +
# c-path (total effect, dashed)
annotate("segment",
x = 0.5, xend = 2.5, y = 1.1, yend = 1.1,
linetype = "dashed",
arrow = arrow(length = unit(0.20, "cm"))) +
annotate("text", x = 1.5, y = 1.25, label = c_label) +
theme_void()
Linear Model
Predictor: Class ZSB
Moderator: Race ZSB
Outcome: Cross-Race Solidarity
m1 <- lm(crs ~ zs_class*zs_race,data = df_cbzs_elg)
eta_table <- eta_squared(m1)
etas_for_table <- c(NA,eta_table$Eta2)
apa_lm <- apa_print(m1)
table_for_print <- apa_lm$table %>%
mutate(eta2 = round(etas_for_table,3))
kbl(table_for_print) %>%
kable_styling(bootstrap_options = "hover",
full_width = F,
position = "left")| term | estimate | conf.int | statistic | df | p.value | eta2 |
|---|---|---|---|---|---|---|
| Intercept | 4.77 | [4.15, 5.39] | 15.03 | 484 | < .001 | NA |
| Zs class | 0.18 | [0.06, 0.30] | 3.03 | 484 | .003 | 0.076 |
| Zs race | -0.24 | [-0.50, 0.01] | -1.90 | 484 | .058 | 0.083 |
| Zs class \(\times\) Zs race | 0.00 | [-0.05, 0.05] | -0.04 | 484 | .970 | 0.000 |
interact_plot(m1,
pred = "zs_class",
modx = "zs_race",
interval = T)
Exploratory Analysis
Linear Model
Predictor: Class ZSB
Moderator: Race ZSB
Outcome: Support for policy
m1 <- lm(support ~ zs_class*zs_race,data = df_cbzs_elg)
eta_table <- eta_squared(m1)
etas_for_table <- c(NA,eta_table$Eta2)
apa_lm <- apa_print(m1)
table_for_print <- apa_lm$table %>%
mutate(eta2 = round(etas_for_table,3))
kbl(table_for_print) %>%
kable_styling(bootstrap_options = "hover",
full_width = F,
position = "left")| term | estimate | conf.int | statistic | df | p.value | eta2 |
|---|---|---|---|---|---|---|
| Intercept | 5.22 | [4.20, 6.24] | 10.10 | 484 | < .001 | NA |
| Zs class | 0.18 | [-0.01, 0.38] | 1.85 | 484 | .065 | 0.116 |
| Zs race | -0.77 | [-1.18, -0.36] | -3.67 | 484 | < .001 | 0.054 |
| Zs class \(\times\) Zs race | 0.09 | [0.01, 0.17] | 2.23 | 484 | .026 | 0.010 |
interact_plot(m1,
pred = "zs_class",
modx = "zs_race",
interval = T)