I was having a conversation about dropping the minimum threshold (currently 5% of the vote) for political parties to get representation in Parliament. The obvious question is how would seat allocation change, which of course involved a calculation. There is a calculator in the Electoral Commission website, but trying to understand how things work (and therefore coding) is my thing, and the Electoral Commission has a handy explanation of the Sainte-Laguë allocation formula used in New Zealand. So I had to write my own seat allocation function:
allocate_seats <- function(votes) {
parties <- names(votes)
denom <- seq(1, 121, 2)
quotients <- vapply(denom, FUN = function(x) votes/x, FUN.VALUE = rep(1, length(votes)))
quotients <- t(quotients)
colnames(quotients) <- parties
priority <- rank(-quotients)
seat_ranking <- matrix(priority, nrow = nrow(quotients), ncol = ncol(quotients))
seat_ranking <- ifelse(seat_ranking <= 120, seat_ranking, NA)
colnames(seat_ranking) <- parties
return(list(quotients = quotients, ranking = seat_ranking))
}
Testing it with the preliminary election results (that is, no including special votes) gives:
votes2017 <- c(998813, 776556, 162988, 126995, 10959, 48018, 23456)
names(votes2017) <- c('National', 'Labour', 'NZ First', 'Green', 'ACT',
'Opportunities', 'Māori')
seats2017 <- allocate_seats(votes2017)
seats2017$ranking
# National Labour NZ First Green ACT Opportunities Māori
# [1,] 1 2 6 9 98 22 46
# [2,] 3 4 19 26 NA 67 NA
# [3,] 5 7 33 42 NA 112 NA
# [4,] 8 11 47 59 NA NA NA
# [5,] 10 13 60 77 NA NA NA
# [6,] 12 15 73 93 NA NA NA
# [7,] 14 17 86 110 NA NA NA
# [8,] 16 21 100 NA NA NA NA
# [9,] 18 24 113 NA NA NA NA
#[10,] 20 27 NA NA NA NA NA
# ...
In our current setup The Opportunities and Māori parties did not reach the minimum threshold (nor won an electorate as ACT violating the spirit of the system), so did not get any seats. Those 4 seats that would have gone to minor parties under no threshold ended up going to National and Labour (2 each). It sucks.