American Presidential Voting Habits, Spots and Trends

Introduction

We just finished another presidential election year, full of surprises and upsets, or maybe upsets and surprises. Either way, the voting part is over, the counting part is ongoing, and unlike 2020, the vanquished had a sense of dignity and sanity. All sorts of experts have crawled out from under their rocks to either claim credit or assign blame. I’m not interested in that. I’m interested in the story data can tell.

I asked myself what Presidential elections looked like from a “pure” numbers perspective, so I collected some data. The voting-eligible population (VEP) came from the University of Florida Election Lab. The vote counts came from either the Wikipedia pages for each election, 1980, 1984, 1988, 1992, 1996, 2000, 2004, 2008, 2012, 2016, and 2020 or the Election Atlas state pages for 2024. The 2024 numbers are all preliminary and should be interpreted with caution. I also collected the number of Electoral College votes each state had in each election to use as weights for modeling. This was looked up from several sources, including Wikipedia.

The data consisted of election year, state names, and counts of VEP and votes for the Democrat, Republican, and Other candidates. I subtracted the sum of the votes from the VEP to get Nonvoting counts. This was all done in Excel, where I also formatted the data into “long” format. I loaded the clean data. You can get it, yourself in this Google sheet.

Before I go any further, I will be using R for this work, so I need to load a bunch of R packages.

library(googlesheets4)

Warning: package ‘googlesheets4’ was built under R version 4.4.2

library(glmmTMB)
library(performance)
library(car)

Loading required package: carData

library(performance)
library(MuMIn)
library(emmeans)

Welcome to emmeans.
Caution: You lose important information if you filter this package's results.
See '? untidy'

library(effectsize)
library(tidyverse)

── Attaching core tidyverse packages ──────────────────────────────────────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4     ✔ readr     2.1.5
✔ forcats   1.0.0     ✔ stringr   1.5.1
✔ ggplot2   3.5.1     ✔ tibble    3.2.1
✔ lubridate 1.9.3     ✔ tidyr     1.3.1
✔ purrr     1.0.2     
── Conflicts ────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
✖ dplyr::recode() masks car::recode()
✖ purrr::some()   masks car::some()
ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errors

library(reshape2)

Warning: package ‘reshape2’ was built under R version 4.4.2

Attaching package: ‘reshape2’

The following object is masked from ‘package:tidyr’:

    smiths

Vote.dat <- read_sheet("https://docs.google.com/spreadsheets/d/1oySzPkmaVMBHHwAib4kLuca_7XQrXg5x67hQmLKUpTA/edit")

The googlesheets4 package is requesting access to your Google account.
Enter '1' to start a new auth process or select a pre-authorized account.
1: Send me to the browser for a new auth process.
2: maloneywriting18@gmail.com

1

Waiting for authentication in browser...
Press Esc/Ctrl + C to abort
Authentication complete.

✔ Reading from Vote.sheet.
✔ Range Sheet1.

Vote.dat$State <- factor(Vote.dat$State)
Vote.dat$Selection <- factor(Vote.dat$Selection)

Feel free to use the above link to do a manual import if you’d prefer that.

So, let’s take a look at the raw data.

messy.plot <- ggplot(Vote.dat, aes(x = jitter(Year), y = Votes/VEP, group = Selection, color = Selection)) + 
  scale_color_manual(values = c("#4477AA", "#228833", "#CCBB44", "#EE6677"),
                     limits = c("Democrat", "Other", "Nonvoting", "Republican")) +
  geom_point(size = 3) +
  theme(panel.background = element_rect(fill = "white"),
        axis.line = element_line(size = 1, color = "black")) +
  scale_y_continuous(labels = scales::percent) +
  scale_x_continuous(breaks = c(1980, 1984, 1988, 1992, 1996, 2000, 2004, 2008, 2012, 2016, 2020, 2024)) +
  ylab("Frequency (per VEP)") + xlab("Year")

messy.plot

Summarizing

That’s a real mess. Let’s try generating a summary.

# Some background functions
weighted.average <- function(x, w){
## Sum of the weights
sum.w <- sum(w, na.rm = T)
## Sum of the weighted $x_i$
xw <- sum(w*x, na.rm = T)
## Return the weighted average
return(xw/sum.w)
}

weighted.se.mean <- function(x, w, na.rm = T){
## Remove NAs
if (na.rm) {
i <- !is.na(x)
w <- w[i]
x <- x[i]
}
## Calculate effective N and correction factor
n_eff <- (sum(w))^2/(sum(w^2))
correction = n_eff/(n_eff-1)
## Get weighted variance
numerator = sum(w*(x-weighted.average(x,w))^2)
denominator = sum(w)
## get weighted standard error of the mean
se_x = sqrt((correction * (numerator/denominator))/n_eff)
return(se_x)
}

# Making the weighted summary
Vote.sum <- Vote.dat %>%
  mutate(pasteup = paste(Year, Selection)) %>%
  mutate(ratio = Votes/VEP) %>%
  group_by(pasteup) %>%
  summarize(weighted_means = weighted.average(ratio, Electoral.Votes)) %>%
  cbind(Vote.dat %>%
          mutate(pasteup = paste(Year, Selection)) %>%
          mutate(ratio = Votes/VEP) %>%
          group_by(pasteup) %>%
          summarize(weighted_CL = weighted.se.mean(ratio, Electoral.Votes) * qt(0.975, 50)))
Vote.sum <- Vote.sum[, c(1, 2, 4)]
Vote.sum <- cbind(colsplit(Vote.sum$pasteup, " ", c("Year", "Selection")), Vote.sum[,2:3])
Vote.sum$Selection <- factor(Vote.sum$Selection)
Vote.sum

What I did was take weighted means by year of all the states for votes cast for the Democratic or Republican candidate or any other candidate, along with the remainder (non-voting VEP), divided by the VEP. The means were weighted by the Electoral College votes that state had in that election year. I then calculated the weighted standard errors of the mean, using a function written by Alex Stephenson. I converted these to 95% confidence limits by multiplying by the appropriate quantile of t at 0.975 and 50 degrees of freedom. Why did I weight the popular votes? It’s a concession to reality. People might hand-wring and whine all they like about how horrid the Electoral College might be, but it’s not going away any time soon. Understanding US presidential politics requires taking it into account.

So, I have a table, I don’t find tables useful. What are useful are charts.

summary.plot <- ggplot(Vote.sum, aes(x = Year, y = weighted_means, group = Selection, color = Selection)) + 
  geom_line(linewidth = 1) +
  scale_color_manual(values = c("#4477AA", "#228833", "#CCBB44", "#EE6677"),
                     limits = c("Democrat", "Other", "Nonvoting", "Republican")) +
  geom_point(size = 3) +
  geom_errorbar((aes(ymin=weighted_means - weighted_CL, ymax = weighted_means + weighted_CL))) +
  theme(panel.background = element_rect(fill = "white"),
        axis.line = element_line(size = 1, color = "black"),
        legend.position = c(0.8, 0.3)) +
  scale_y_continuous(labels = scales::percent) +
  scale_x_continuous(breaks = c(1980, 1984, 1988, 1992, 1996, 2000, 2004, 2008, 2012, 2016, 2020, 2024)) +
  ylab("Frequency (per VEP)")

summary.plot

I didn’t just pull the colors out of my cute patootie. They’re from Paul Tol’s site that describes many wonderful (and color-blind safe) color schemes, arranged with the now-traditional coloring of blue for Democrats and red for Republicans.

A little non-statistical analysis

We can analyze the above chart without even considering statistics. I’m going to be mostly just descriptive. The first thing to note is that the most popular “candidate”, by far, for the last 44 years has been nobody. Since at least 1980, there has never been a president elected by the majority of Americans eligible to vote. Let us wring hands. Hand wringing time is over. While it’s true that “get out of my face” has usually been the most popular selection, it’s equally true that this option has been chosen less and less as time has gone on. Whatever is wrong with America, more Americans have been getting out to vote. True enough, 2024 was another election of apathy, but it’s hard to call the future based on a single-point deflection. The overall trend has been for non-voting to drop by a little less than 1 percentage point every election. The Democrats and Republicans are basically in a dead heat in dividing this gain up between themselves. The overall Democrat gain since 1980 has been greater than the overall Republican gain, but currently they are indistinguishable. On the other hand, the slow increase in voting doesn’t seem to have been distributed to “Other” options.

Another thing to note is that the Republicans and Democrats seem to have switched performances from 1980 to the present. From 1980 to 2004, Republican performance fluctuated wildly from year to year. The Democrats, on the other hand, were experiencing very slow but very regular gains until 2000. From these inflection points to the present day, this has switched. The Democrats now have wild swings while the Republicans’ oscillations have calmed down (although with more variation than the early-period Democrats showed). How to explain this or what it means for the future I leave to more knowledgeable people. What I can say is that it looks like both parties experienced a significant sea change roughly 2000-2004, and it is having long-lasting effects on each of them. What these changes were, I can’t even speculate. Feel free.

Calling the Horse Races

Let’s dive deeper and look at each election in turn. Reagan’s tenure was marked by moving from strong to stronger. Unusually for incumbents, he gained percentage in his re-election bid. However, this was not at the expense of Mondale, who also got a (very tiny) gain vs. Carter’s performance. Instead, Reagan may have attracted some non-voters and a large portion of people who had voted for Anderson (who?). Poppy Bush’s election was an exercise in coat-tail riding. The nonvoters bounced back up, and Dukakis got another (very tiny) gain over the Democrats’ share of the previous election,

Indeed, from 1980 to 2000 “a very tiny gain” could accurately describe the Democratic party’s entire presidential performance, even in years they took the White House. In every election, it was a very small improvement in attracting a proportion of the voting-eligible population, while the Republicans see-sawed up and down in popularity. For example, Clinton took office in a tidal wave of spoilage. Ross Perot’s leap seems to have been fueled by some Republican-leaning voters and bigger chunk of people who otherwise wouldn’t have bothered to vote at all. But Perot was a gadfly candidate. Bush was the anointed leader of the Republican party, so there was a squabble on that side of the political spectrum. Clinton rode in on this disunity.

Perot’s huge-for-a-third-dude showing cannot be explained only by attracting nonvoters. In 1998, there was a giant leap in apathy, which probably hurt Dole more than it hurt Clinton. However, Clinton didn’t experience a spike in popularity. He managed to do a bit better than last time. This set the stage for 2000.

This was an extremely close election. What is interesting is that there was very little apparent motivation of the nonvoters. It ended up in a mess. Bush’s re-election was more definite and it was accompanied by the Democratic party starting to improve more quickly its slug-like crawl upwards since 1980. However, Bush was able to attract more of the nonvoters (and possibly Other voters) than did Kerry. What is interesting is that this election saw a big drop in nonvoters, which goes against the general trend of an increase in apathy or at very best a small decrease during a re-election attempt. However, these voters didn’t turn out for Kerry.

In 2008, Obama ended up continuing a straight-line trend started by the prior two failed Democrat attempts. There was a small tend downwards in nonvoters, but the Republicans lost share as well, indicating some possible aisle-crossing by voters. Obama’s second turn was a typical successful re-election, with more people choosing to sit it out, but not enough to force a loss. The Republicans were still experiencing the Bush 2-inspired decline.

2016 was another close election. It’s well-documented that Trump did not achieve the total popular majority of votes cast. The weighted means still reflect this. This is not anomalous. It is because weighted means can “distribute” proportional Electoral outcomes within each state as well as fractions. What we do see is that Gary Johnson had a bit of a spike, which may have been acquired from a mixture of nonvoters and both Democrat and Republican leaning voters.

The Biden election is illustrative of what might be an important trend. Once again, the number of nonvoters fell (to its lowest level), and the primary beneficiary seems to have been Biden. It was the first time in the period I looked at that an actual candidate managed to get more popular votes than “this election isn’t worth voting in”!

Finally, Iit should be noted that the 2024 results are based in part on projections and estimates and ought not be over-interpreted. However, the biggest winner is “Nobody is worth my vote.” Apathy and disengagement won again, with one of its biggest spikes since 1996. However, this time, the Republicans weren’t riding a massive bottom-out trend. If the projections are to be believed, Trump also lost share from his previous attempt. He merely lost less than did Harris vs. Biden’s performance. Trump managed to get less of the voting-eligible public than he did in 2020. Unfortunately, Harris managed to do even worse. I can’t explain why. I won’t try to explain why. I can only show the what. The why requires more in-depth knowledge than I have.

Modeling

We could stop right there, but I looked at the chart and wondered if there were any possibly verifiable trends in what I think I saw. That’s when I pulled out the formal modeling tools.

The data was repeated measurements (by state and District of Columbia) of 12 presidential elections. When I see repeated measures, I like to use a mixed-level model. If you want to know more, you can start here. The data is count data. Yes, I presented it as frequencies, but a frequency is a count divided by a reference count. The preferred way to analyze count data is with a Poisson distribtion. However, the Poisson distribution presumes that the mean and the variance of the data are the same, or dispersion = 1, to use jargon. A dispersion over 1 is overdispersed, and under 1 is underdispersed. Since I did not yet know if the data were over or under-dispersed, I chose R’s glmmTMB package, since it has options that can handle either eventuality. I started with a first pass model that used the Poisson family.

options(contrasts = rep("contr.Sum",2))
start.mod <- glmmTMB(Votes ~ Selection * Year + (1 | State) + offset(log(VEP)), weights = Electoral.Votes, family = poisson, data = Vote.dat)

Warning in (function (start, objective, gradient = NULL, hessian = NULL,  :
  NA/NaN function evaluation

I got a warning. It’s often due to differences in variable scale. The offending variable is probably Year, which can be fixed.

Vote.dat$Year.s <- scale(Vote.dat$Year)
start.mod <- glmmTMB(Votes ~ Selection * Year.s + (1 | State) + offset(log(VEP)), weights = Electoral.Votes, family = poisson, data = Vote.dat)

And I had to check the dispersion.

check_overdispersion(start.mod)

# Overdispersion test

       dispersion ratio =    1112634.483
  Pearson's Chi-Squared = 2713715504.977
                p-value =        < 0.001

Overdispersion detected.

Yes, definitely overdispersed. There are fancy ways to handle this, like the Conway-Maxwell-Poisson family, but the current implementation of this family can be slower than a geologic age to run. Fortunately, the reliable old negative binomial family will handle overdispersion. Since the sample had over 2000 entries, I felt comfortable exploring different random effects vis the states. I compared models that included random intercepts and random slopes for both Selection and Year, with and without correlated intercepts.

nb.mod1 <- glmmTMB(Votes ~ Selection * Year.s + (1 | State) + offset(log(VEP)), weights = Electoral.Votes, family = nbinom2, data = Vote.dat)
nb.mod2 <- glmmTMB(Votes ~ Selection * Year.s + (Selection | State) + offset(log(VEP)), weights = Electoral.Votes, family = nbinom2, data = Vote.dat)

Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old) :
  Model convergence problem; singular convergence (7). See vignette('troubleshooting'), help('diagnose')

nb.mod3 <- glmmTMB(Votes ~ Selection * Year.s + (Year.s | State) + offset(log(VEP)), weights = Electoral.Votes, family = nbinom2, data = Vote.dat)
nb.mod4 <- glmmTMB(Votes ~ Selection * Year.s + (Selection + Year.s | State) + offset(log(VEP)), weights = Electoral.Votes, family = nbinom2, data = Vote.dat)

Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old) :
  Model convergence problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')
Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old) :
  Model convergence problem; singular convergence (7). See vignette('troubleshooting'), help('diagnose')

nb.mod5 <- glmmTMB(Votes ~ Selection * Year.s + (Selection * Year.s | State) + offset(log(VEP)), weights = Electoral.Votes, family = nbinom2, data = Vote.dat)

Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old) :
  Model convergence problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')
Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old) :
  Model convergence problem; singular convergence (7). See vignette('troubleshooting'), help('diagnose')

nb.mod6 <- glmmTMB(Votes ~ Selection * Year.s + (Selection || State) + offset(log(VEP)), weights = Electoral.Votes, family = nbinom2, data = Vote.dat)
nb.mod7 <- glmmTMB(Votes ~ Selection * Year.s + (Year.s || State) + offset(log(VEP)), weights = Electoral.Votes, family = nbinom2, data = Vote.dat)
nb.mod8 <- glmmTMB(Votes ~ Selection * Year.s + (Selection + Year.s || State) + offset(log(VEP)), weights = Electoral.Votes, family = nbinom2, data = Vote.dat)

Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old) :
  Model convergence problem; false convergence (8). See vignette('troubleshooting'), help('diagnose')

nb.mod9 <- glmmTMB(Votes ~ Selection * Year.s + (Selection * Year.s || State) + offset(log(VEP)), weights = Electoral.Votes, family = nbinom2, data = Vote.dat)

I compared models that included random intercepts and random slopes for both Selection and Year, with and without correlated intercepts. Different models were compared by second-order Akaike information criterion . I admit, doing this is not rigorous. There’s controversy over whether AICc can be calculated at all for a mixed model, but I’m not being paid for this, so I wasn’t going to take the time to do more in-depth model comparisons.

Alist <- c(AICc(nb.mod1),
           AICc(nb.mod2),
           AICc(nb.mod3),
           AICc(nb.mod4),
           AICc(nb.mod5),
           AICc(nb.mod6),
           AICc(nb.mod7),
           AICc(nb.mod8),
           AICc(nb.mod9))
Alist

[1] 742668.5 739833.8 742668.2       NA       NA 740009.8 742666.3 739999.4 739731.6

The model with the lowest AICc is the 9th model, so that’s what I adopted. You may have noticed a few lines back that I set the contrasts to “contr.Sum”. These are simple sum-to-zero contrasts, aka effect coding. R’s default is dummy coding or treatment contrasts, which are fine if you’re not worrying about analyzing interactions. We have an interaction, so I’m using effect coding.

Vote.model <- nb.mod9
summary(Vote.model)

 Family: nbinom2  ( log )
Formula:          Votes ~ Selection * Year.s + (Selection * Year.s || State) +      offset(log(VEP))
Data: Vote.dat
Weights: Electoral.Votes

      AIC       BIC    logLik  deviance  df.resid 
 739731.4  739830.0 -369848.7  739697.4      2431 

Random effects:

Conditional model:
 Groups Name                          Variance  Std.Dev. Corr                               
 State  (Intercept)                   0.0095931 0.09794                                     
        Selection[S.Democrat]         0.0457551 0.21390  0.00                               
        Selection[S.Nonvoting]        0.0474525 0.21784  0.00 0.00                          
        Selection[S.Other]            0.0721619 0.26863  0.00 0.00 0.00                     
        Year.s                        0.0005149 0.02269  0.00 0.00 0.00 0.00                
        Selection[S.Democrat]:Year.s  0.0059620 0.07721  0.00 0.00 0.00 0.00 0.00           
        Selection[S.Nonvoting]:Year.s 0.0036982 0.06081  0.00 0.00 0.00 0.00 0.00 0.00      
        Selection[S.Other]:Year.s     0.0063977 0.07999  0.00 0.00 0.00 0.00 0.00 0.00 0.00 
Number of obs: 2448, groups:  State, 51

Dispersion parameter for nbinom2 family (): 3.74 

Conditional model:
                               Estimate Std. Error z value Pr(>|z|)    
(Intercept)                   -1.782538   0.014308 -124.58   <2e-16 ***
Selection[S.Democrat]          0.450019   0.030783   14.62   <2e-16 ***
Selection[S.Nonvoting]         0.872299   0.031316   27.85   <2e-16 ***
Selection[S.Other]            -1.838467   0.038281  -48.03   <2e-16 ***
Year.s                        -0.079030   0.004922  -16.06   <2e-16 ***
Selection[S.Democrat]:Year.s   0.184270   0.012791   14.41   <2e-16 ***
Selection[S.Nonvoting]:Year.s -0.001572   0.010808   -0.15    0.884    
Selection[S.Other]:Year.s     -0.288923   0.013224  -21.85   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

r2(Vote.model)

# R2 for Mixed Models

  Conditional R2: 0.453
     Marginal R2: 0.417

Anova(Vote.model, type = "III")

Analysis of Deviance Table (Type III Wald chisquare tests)

Response: Votes
                    Chisq Df Pr(>Chisq)    
(Intercept)      15520.80  1  < 2.2e-16 ***
Selection         3253.50  3  < 2.2e-16 ***
Year.s             257.86  1  < 2.2e-16 ***
Selection:Year.s   630.28  3  < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Don’t spend much time trying to interpret coefficients. I’m going to estimate marginal means and trends, which are much easier to interpret. Marginal means (trends for slopes) estimate based on the model and take into account the effects of all parts of the model on a response. They summares what the model is saying in a way that is more intuitive than attempting to puzzle out multiple coefficients. If you want to really go down a rabbit hole, there’s a very complete description you can read elsewhere.

If you look at the R² (Nakagawa’s R²), this model isn’t too bad a fit. Marginal R² estimates the total contribution of the fixed effects, conditional includes the random effects (individual state effects).

I’m not interested in comparing outcomes for a single given election. That’s not very informative from this high up in the clouds. Comparing the trends, on the other hand, interests me.

Vote.emt <- emtrends(Vote.model, ~Selection:Year.s, "Year.s")
Vote.emt

 Selection  Year.s Year.s.trend     SE  df asymp.LCL asymp.UCL
 Democrat        0       0.1052 0.0137 Inf    0.0784    0.1321
 Nonvoting       0      -0.0806 0.0119 Inf   -0.1038   -0.0574
 Other           0      -0.3680 0.0142 Inf   -0.3958   -0.3401
 Republican      0       0.0272 0.0196 Inf   -0.0113    0.0656

Confidence level used: 0.95 

Visualizing

What does this tell us? We can see that this trend is increasing over the 1980-2024 period for Democrats, decreasing for non-voting, and votes for “Other” candidates, and weakly increasing over time for Republicans. What is interesting is that the confidence limits for the Republican trend are negative and positive, suggesting that the overall trend may not significantly differ from zero for this period. But words say so much less than a picture. First, we have to generate some points from the model.

Vote.emm <- emmeans(Vote.model, ~Selection:Year.s, type = "response", offset = log(1), at = 
                      list(Year.s = as.numeric(levels(factor(Vote.dat$Year.s)))))
Vote.preds <- data.frame(Vote.emm) %>%
  mutate(Year = (Year.s * attr(Vote.dat$Year.s, "scaled:scale") + attr(Vote.dat$Year.s, "scaled:center")))
Vote.preds

model.plot <- ggplot(Vote.preds, aes(x = Year, y = response, group = Selection, color = Selection)) + 
  geom_line(linewidth = 1) +
  scale_color_manual(values = c("#4477AA", "#228833", "#CCBB44", "#EE6677"),
                     limits = c("Democrat", "Other", "Nonvoting", "Republican")) +
  geom_ribbon(aes(ymin = asymp.LCL, ymax = asymp.UCL), alpha = 0.05) +
  theme(panel.background = element_rect(fill = "white"),
        axis.line = element_line(size = 1, color = "black"),
        legend.position = c(0.8, 0.3)) +
  scale_y_continuous(labels = scales::percent) +
  scale_x_continuous(breaks = c(1980, 1984, 1988, 1992, 1996, 2000, 2004, 2008, 2012, 2016, 2020, 2024)) +
  ylab("Frequency (per VEP)")

model.plot

The ribbons around each line are the 95% confidence intervals. The trends look like they differ from each other, but is that real?

pairs(Vote.emt)

 contrast                               estimate     SE  df z.ratio p.value
 Democrat Year.s0 - Nonvoting Year.s0      0.186 0.0176 Inf  10.573  <.0001
 Democrat Year.s0 - Other Year.s0          0.473 0.0193 Inf  24.541  <.0001
 Democrat Year.s0 - Republican Year.s0     0.078 0.0281 Inf   2.774  0.0283
 Nonvoting Year.s0 - Other Year.s0         0.287 0.0180 Inf  15.997  <.0001
 Nonvoting Year.s0 - Republican Year.s0   -0.108 0.0256 Inf  -4.217  0.0001
 Other Year.s0 - Republican Year.s0       -0.395 0.0287 Inf -13.775  <.0001

P value adjustment: tukey method for comparing a family of 4 estimates 

If we look at the adjusted p values for every pairwise comparison of trends, yes. Even adjusting for all multiple comparisons, every trend differs from every other trend with a p of < 0.05. How can this be interpreted? Typically, people say “significant” or “not significant” and call it a day. There’s another interpretation of the p value, and that’s the probability of the observed difference occuring by random chance if the difference did not actually exist. For example, if there really were no difference between Republican and Democrat performance, according to this model, we would expect to still see the difference we estimated about 2.8% of the time.

So, we can generally infer that the differences we think we see are probably real. However, are they meaningful? The p value can’t tell us how large a difference is. It can only tell us how likely it is. Fortunately, standardized effect sizes exist to explore this question.

Vote.eff <- eff_size(Vote.emt, sigma = sigma(Vote.model), edf = df.residual(Vote.model))
Vote.eff

 contrast                               effect.size      SE  df asymp.LCL asymp.UCL
 Democrat Year.s0 - Nonvoting Year.s0        0.0497 0.00470 Inf   0.04049    0.0589
 Democrat Year.s0 - Other Year.s0            0.1266 0.00525 Inf   0.11625    0.1368
 Democrat Year.s0 - Republican Year.s0       0.0209 0.00753 Inf   0.00611    0.0356
 Nonvoting Year.s0 - Other Year.s0           0.0768 0.00493 Inf   0.06719    0.0865
 Nonvoting Year.s0 - Republican Year.s0     -0.0288 0.00684 Inf  -0.04223   -0.0154
 Other Year.s0 - Republican Year.s0         -0.1057 0.00778 Inf  -0.12093   -0.0904

sigma used for effect sizes: 3.739 
Confidence level used: 0.95 

These effect sizes are Cohen’s d, which boils down to how far away the trends are from each other, adjusted by how uncertain the estimates of the trends are. The numbers aren’t very informative by themselves. Fortunately has been extensive work to define meaningful categories of effect sizes for political science. I think that the categories proposed by Erik Ghneer Larsen are reasonable. However, he presented them in relation to Pearson’s r. Fortunately, it is possible to convert between the two. Unfortunately, the standard conversion of d to r is biased to produce low outcomes, because it converts to the point-biserial r and presumes that d was estimated with a binomial predictor. Year.s is a continuous predictor. Therefore, I converted d to the probability of superiority common language effect size and then converted this to r using the formula found in Dunlap, 1994.

Vote.d_to_r <- data.frame(summary(Vote.eff)$contrast, summary(Vote.eff)$effect.size,
                          d_to_p_superiority(summary(Vote.eff)$effect.size),
                          sin(((d_to_p_superiority(summary(Vote.eff)$effect.size)) -.5) * pi))
colnames(Vote.d_to_r) <- c("Contrast", "d", "CLES", "r")


Vote.d_to_r <- Vote.d_to_r %>% mutate(Larsen = case_when(
  abs(r) < 0.05 ~ "Less than Small Effect",
  abs(r) >= 0.05 & abs(r) < 0.15 ~ "Small Effect",
  abs(r) >= 0.15 & abs(r) < 0.30 ~ "Medium Effect",
  abs(r) >= 0.30 ~ "Large Effect"
))

Vote.d_to_r

CLES is the “Common Language Effect Size” or “probability of superiority”. This is an estimate of the probability (between 0 and 1) that, for a given trait, a member of one group will be larger than a member of the other group. A CLES of 0.5 means the groups are identical. As you can see, none of the differences are large.

What do we take home?

If you’ve made it this far, you really like chopping through the weeds, but what have we learned. In addition to the race-by-race non-statistical analysis, we can say with some certainty that, since 1980, the Democratic party has been steadily gaining among the voting-eligible population, while Republican gains have been slower. This difference is likely to be real, but it’s not at all large. What is also interesting is that the proportion of people just sitting it out has been slowly decreasing since 1980. Americans have been becoming more engaged.

What about the “Other”? I’ll freely admit that this category fluctuated too wildly to make any deep conclusions. Ross Perot was a major influence, but the Perot spike has never been repeated.

The Future

Short-term, there is no way to predict 2028, certainly not right now. Farther into the future, if the trends I mapped continue, although there is no way to say they must, the Republican party’s gains would be outstripped by the Democrats as more Americans choose to participate in presidential elections. I’m goint to speculate that I’m not the first person to do an analysis like this. I’ve no doubt that professional strategists have already been looking at these trends. This could explain the willingness to adopt severe measures that seems to have driven the Republican party in recent years. If the current paradigm is not destroyed, the Republicans may become irrelevant.