wilson-score.R

library(dplyr)

Wilson <- function(n, k, alpha=0.95) {
    phat <- k/n
    score <- qnorm(1-(1-alpha)/2)
    lbound <- (phat+score**2/(2*n)-score*sqrt((phat*(1-phat)+score**2/(4*n))/n))/(1+score**2/n)
    return(lbound)
}

seed(2019)
x <- sample(1:500,200,replace=T)
y <- sample(1:500,200,replace=T)

votes <- data.frame(x,y) %>%
    rowwise() %>%
    mutate(pos=min(x,y),total=max(x,y)) %>%
    select(total, pos) %>%
    mutate(Wilson=Wilson(total,pos)) %>%
    arrange(desc(Wilson))

head(votes)
tail(votes)