benford_2016_usa_elections.R

library(readr)
library(dplyr)
library(ggplot2)

get_first_digit <- function(x) {
    return(substr(x, 1, 1))
}

votes <- read_csv("https://github.com/Prooffreader/election_2016_data/raw/master/data/presidential_general_election_2016_by_county.csv")

# Not interested in 0 votes
votes <- votes[votes$votes != 0, ]

votes$first_digit <- sapply(votes$votes, get_first_digit)

votes_dist <- votes %>% 
    group_by(name, first_digit) %>%
    summarise(n = n())

votes_candidate <- votes_dist %>%
    group_by(name) %>%
    summarise(n_counties = sum(n))

votes_dist <- left_join(votes_dist, votes_candidate, by = "name")
votes_dist$observed <- votes_dist$n / votes_dist$n_counties

# Expected probs
benford <- log10(1 + (1 / 1:9))

# Get only 4 main candidates
votes_dist <- votes_dist[votes_dist$n_counties > 2500, ]

votes_dist$expected <- benford

plt1 <- ggplot(votes_dist) +
    geom_line(aes(x = first_digit, y = expected), group = 1) +
    geom_point(aes(x = first_digit, y = observed)) +
    facet_wrap(~ name) +
    ggtitle("Bendford's law applied to USA 2016 Elections by county") +
    ylab("Observed ratio") + xlab("First digit")
plot(plt1)