State legislative election results

State House election results are made available here by Princeton University folks – which is apart of a larger ecosystem of tools/resources for investigating gerrymandering. Results are limited to lower houses for states with bicameral state legislatures.

library(tidyverse)
election_results <- read.csv(url(git_url)) %>% 
  janitor::clean_names() %>%
  mutate(d_voteshare = round(d_voteshare, 3))

A sample of the data set is detailed below. Results are presented year, state, and state house district; the d_voteshare column specifies the vote share received by the Democratic candidate.

election_results %>%
  filter(state == 'CA', year == 1980) %>%
  slice(1:5) %>%
  select(-incumbent) %>%
  knitr::kable()

A super simple imputation method: Per approach described in Gelman and King (1994), winning parties of uncontested elections are re-assigned a vote share of 0.75, and losing parties 0.25.

election_results1 <- election_results %>%
  mutate(d_voteshare = ifelse(d_voteshare == 1, 0.75, d_voteshare),
         d_voteshare = ifelse(d_voteshare == 0, 0.25, d_voteshare))

Summarizing election results

Next, we summarize election results per legislature. Summary stats include:

• the number of seats in legislature,
• the number/proportion of seats won by Democrats,
  
• the average vote share received by Democratic candidates; and
• the median Democratic vote share.

Important to emphasize here is that the v_mean value specifies the average Democratic vote share across individual state house races in a given year, and not the aggregate statewide house results.

full_summary <- election_results1 %>%
  group_by(state, year) %>%
  mutate(dseat = ifelse(dem_votes > gop_votes, 1, 0),
         rseat = ifelse(dem_votes < gop_votes, 1, 0),
         d_above = ifelse(d_voteshare > mean(d_voteshare),
                          1, 0)) %>%
  
  summarize(district_n = n(),
            d_seats = sum(dseat),
            r_seats = sum(rseat),
            v_mean = mean(d_voteshare),
            v_median = median(d_voteshare),
            d_above = sum(d_above)) %>%
  mutate(seat_bar = d_seats/district_n) %>%
  ungroup()

Election results for Colorado during the 2010s are presented below. So, Dems took the majority – and then some – in the Colorado State House during the previous decade.

full_summary %>%
  filter(state == 'CO',
         year > 2008) %>%
  select(-r_seats) %>% 
  mutate(across(c(v_mean, v_median, seat_bar), ~round(., 2))) %>%
  knitr::kable()

The plots below illustrate the shifting partisan balance for a selection of state houses since 1972.

south <- c('CO', 'FL', 'AL', 'TX', 
           'AR', 'TN', 'OK', 'KY')

full_summary %>%
  filter(state %in% south) %>%
  ggplot() +
  geom_line(aes(x = year, 
                y = d_seats/district_n * 100), 
            color = '#437193', size = 1) +
  geom_line(aes(x = year, 
                y = r_seats/district_n * 100), 
            color = '#ae4952', size = 1) +
  facet_wrap(~state, ncol = 4) +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  scale_x_continuous(breaks=seq(1972, 2018, 8)) +
  ggtitle('State house partisan trends')

Historical vote distributions

details1 <- election_results1 %>%
  #filter(party %in% c('D', 'R')) %>% 
  
  left_join(full_summary) %>%
  group_by(state, year) %>%
  
  mutate(swing = 0.5 + v_mean - d_voteshare,
         rank = rank(d_voteshare, ties.method = 'first'),
         seat_share = rank/n(),
         seat_share = 1 - seat_share) %>%
  
  ## still not correct exactly --
  mutate(swing = ifelse(seat_share == seat_bar, v_mean, swing)) %>%
  arrange(seat_share) %>%
  ungroup()

Vote distributions for election results in Wisconsin since 1972 are illustrated below. Districts have been sorted in increasing order of Democratic vote share.

details1 %>% 
  filter(state == 'WI') %>%
  
  ggplot() +
  geom_point(aes(x = factor(rank), 
                 y = d_voteshare),
             color = 'steelblue',
             size = .5) + 
  
  geom_hline(yintercept = 0.5, lty = 3) +
  facet_wrap(~year, ncol = 6) +
  theme_minimal() +
  theme(axis.text.x=element_blank()) +
  xlab('Districts ordered from least to most Democratic') +
  ylab('Percentage of votes for a Democrat') +
  labs(title = 'Wisconsin State House election results',
       subtitle = 'Democratic vote share by district, ranked')

Seats-votes curves

There are a host of metrics that aim to capture partisan asymmetries in vote distributions (see Warrington 2019 for a comparison). Here, we focus on mean-median scores and partisan bias scores, mainly because they are closely tied to the seats-votes curve.

The mean-median score is the difference between a party’s median vote share and its mean vote share – divergence between these two values suggests a vote distribution that is skewed in favor of a particular party. In contrast, the partisan bias score is the difference between (1) a party’s actual seat share and (2) that party’s hypothetical seat share if it garnered 50% of the statewide vote share. Both metrics are calculated below:

full_summary1 <- full_summary %>%
  mutate(mm = 0.5 + v_mean - v_median,
         pb = (d_above - 1) /district_n) ## 

As an example, we consider results from the Wisconsin State House in 2018. Again, results are presented from the perspective of Democrats.

xmm <- full_summary1 %>% filter(state == 'WI', year == 2018) 

Per plot below, the green bar specifies the mean-median value; the red bar specifies the partisan bias score. So, if a seats-votes curve populates quadrant I, Democrats are over-represented in the legislature based on their statewide vote share; quadrant III, under-represented. The star specifies actual election results. Extreme values in either quadrant are symptomatic of gerrymandering.

see <- details1 %>%
  filter(state == 'WI', year == 2018)  

see %>%
  ggplot() +
  geom_hline(yintercept = .50) +
  geom_vline(xintercept = .50) +
  geom_step(aes(x = swing, 
                y = seat_share,
                color = factor(year)),
            size = 1) + 
  geom_point(aes(x = v_mean, 
                 y = seat_bar),
             pch="\u2605",
             size = 4) +
  
  annotate('segment', 
           x = 0.5, 
           y = xmm$pb, 
           xend = 0.5, 
           yend = 0.5,
           color = '#913a40', size = 3, alpha = .5) +
  annotate('segment', 
           x = xmm$mm, 
           y = 0.5, 
           xend = 0.5, 
           yend = 0.5,
           color = '#3c811a', size = 3, alpha = .5) +
  
  theme_minimal() +
  theme(legend.position = 'right')+
  ggthemes::scale_color_stata() +
  coord_equal(xlim = c(0.3, 0.7),
              ylim = c(0.3, 0.7)) + 
  ggtitle('Seate-Votes Curve: Wisconsin 2018') +
  ylab('Democratic share of lower house seats') +
  xlab('Democratic vote share')

A historical example from the state of Colorado –