irv_method {votesys}

Instant-Runoff Voting Method

Description

Instant-runoff voting (IRV) method is also called alternative voting, transferable voting, ranked-choice voting, single-seat ranked-choice voting, or preferential voting. In the 1st round, the candidate with absolute majority (that is, with more than 50 percent) wins. If no absolute winner exists, the one who gets the least votes is deleted, all other candidates enter into the 2nd round. Again, if no absolute winner exists, let the one with the least votes go and start the 3rd round... Finally, an absolute winner will appear. Ties are solved with different methods in reality; however, this function applies the following rules: (a) if more than one candidate gets the least votes, let all of them go; (b) if all the candidates get the same number of votes in a certain round, then all of them are winners. Note: the function accepts object of class vote and the method can only be used when x$approval_able is TRUE, that is, there is no duplicated values in the score matrix; otherwise, the winner will be NULL.

Usage

irv_method(x, min_valid = 1)

Arguments

x

an object of class vote.

min_valid

default is 1. If the number of valid entries of a ballot is less than this value, the ballot will not be used.

Value

a list object.

• (1) call the function call.

• (2) method the counting method.

• (3) candidate candidate names.

• (4) candidate_num number of candidate.

• (5) ballot_num number of ballots in x.

• (6) valid_ballot_num number of ballots that are used to compute the result.

• (7) winner the winners, may be NULL.

• (8) absolute whether the winner wins absolute majority in the 1st round.

• (9) other_info the IRV may run for 2 or more rounds. So here the summary information of each round is recorded. The length of the list is equal to the number of rounds.

References

• Reilly, B. 2004. The global spread of preferential voting: Australian institutional imperialism? Australian Journal of Political Science, 39(2), 253-266.

Examples

raw <- c(
   rep(c('m', 'n', 'c', 'k'), 42), rep(c('n', 'c', 'k', 'm'), 26), 
   rep(c('c', 'k', 'n', 'm'), 15), rep(c('k', 'c', 'n', 'm'), 17)
) 
raw <- matrix(raw, ncol = 4, byrow = TRUE)
vote <- create_vote(raw, xtype = 2, candidate = c('m', 'n', 'k', 'c'))
y <- irv_method(vote) # winner is k