Analysis on Electoral College

In the results table, the median of all standard deviations is assigned to those who have no standard deviation defined.

polls <- polls_us_election_2016 %>%
  filter(state != "U.S." & !grepl("CD", state) & enddate >= "2016-10-31" &
           (grade %in% c("A+", "A", "A-", "B+") | is.na(grade))) %>%
  mutate(spread = rawpoll_clinton/100 - rawpoll_trump/100)

results <- polls %>%
  group_by(state) %>%
  summarize(avg = mean(spread), sd = sd(spread), n = n()) %>%
  mutate(state = as.character(state))
results <- results %>%
  mutate(sd = ifelse(is.na(sd), median(results$sd, na.rm=TRUE), sd))

Showing 10 closest races, the battleground states:

results %>% mutate(sigma = sd/sqrt(n),
                   B = sigma^2/ (sigma^2 + tau^2),
                   posterior_mean = B*mu + (1-B)*avg,
                   posterior_se = sqrt( 1 / (1/sigma^2 + 1/tau^2))) %>%
  arrange(abs(posterior_mean)) %>% head(10)

A tibble: 10 × 8

state	avg	sd	n	sigma	B	posterior_mean	posterior_se
<chr>	<dbl>	<dbl>	<int>	<dbl>	<dbl>	<dbl>	<dbl>
Florida	0.003557143	0.01634960	7	0.006179569	0.03023074	0.003449608	0.006085446
North Carolina	-0.007300000	0.03062083	9	0.010206942	0.07838031	-0.006727824	0.009798769
Ohio	-0.010416667	0.02522478	6	0.010297974	0.07967275	-0.009586742	0.009879227
Iowa	-0.019733333	0.04366478	3	0.025209875	0.34158821	-0.012992659	0.020455942
Nevada	0.016857143	0.04406809	7	0.016656171	0.18465312	0.013744419	0.015039949
Michigan	0.020950000	0.02026068	6	0.008271386	0.05289547	0.019841840	0.008049655
Arizona	-0.032644444	0.02695474	9	0.008984912	0.06182651	-0.030626152	0.008702728
Pennsylvania	0.035333333	0.01160528	9	0.003868426	0.01206867	0.034906907	0.003845012
New Mexico	0.038933333	0.02255187	6	0.009206761	0.06471732	0.036413672	0.008903860
Georgia	-0.044850000	0.02381155	4	0.011905776	0.10371155	-0.040198537	0.011271497

Monte Carlo simulation to generate 10,000 outcomes from simulated elections, to make probability statements with Bayesian approach.
Considerations: $\mu$ = 0, $\tau$ = 0.02, $\sigma_{b}$ = 0.03

mu <- 0
tau <- 0.02
biassd <- 0.03

results <- left_join(results, results_us_election_2016, by="state")

clinton_EV <- replicate(1000, {
  results %>% mutate(sigma = sqrt(sd^2/n + biassd^2),
                     B = sigma^2/ (sigma^2 + tau^2),
                     posterior_mean = B*mu + (1-B)*avg,
                     posterior_se = sqrt( 1 / (1/sigma^2 + 1/tau^2)),
                     simulated_result = rnorm(length(posterior_mean), posterior_mean, posterior_se),
                     clinton = ifelse(simulated_result > 0, electoral_votes, 0)) %>%    # award votes if Clinton wins state
    summarize(clinton = sum(clinton)) %>%    # total votes for Clinton
    .$clinton + 7    # 7 votes for Rhode Island and DC
})
mean(clinton_EV > 269)    # over 269 votes wins election

0.816

Histogram of the Monte Carlos outcomes:

data.frame(clinton_EV) %>%
  ggplot(aes(clinton_EV)) +
  geom_histogram(binwidth = 1) +
  geom_vline(xintercept = 269) +    # real valor
  theme(axis.text = element_text(size=14))