cdc_minmax {votesys}

Minmax Method

Description

Minmax method (also known as Simpson-Kramer method, successive reversal method) means three different methods. The first is winning votes method. In pairwise comparison, if a wins b, a gets 0 point, the number of points for b is the number of voters who prefer a than b. The second method is to use margins. In pairwise comparison, a gets b - a points and b gets a - b points. The third method is pairwise opposition method. The number of points for a is the number of voters who prefer b than a; the number of points for b is the number of voters who prefer a than b. Although the point-assigning methods are different for the above three methods, they nonetheless do the same thing: to check to what extent one candidate is defeated by others. So the summarizing method is the same: for each candidate, we extract the maximum target points, and the one with the minimum points wins.

Usage

cdc_minmax(x, allow_dup = TRUE, min_valid = 1, variant = 1)

Arguments

x

it accepts the following types of input: 1st, it can be an object of class vote. 2nd, it can be a user-given Condorcet matrix, 3rd, it can be a result of another Condorcet method, which is of class condorcet.

allow_dup

whether ballots with duplicated score values are taken into account. Default is TRUE.

min_valid

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

variant

should be 1, 2 or 3. 1 (default) for winning votes method, 2 for margins method, 3 for pairwise comparison method.

Value

a condorcet object, which is essentially a list.

• (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. When x is not a vote object, it may be NULL.

• (6) valid_ballot_num number of ballots that are actually used to compute the result. When x is not a vote object, it may be NULL.

• (7) winner the winners.

• (8) input_object the class of x.

• (9) cdc the Condorcet matrix which is actually used.

• (10) dif the score difference matrix. When x is not a vote object, it may be NULL.

• (11) binary win and loss recorded with 1 (win), 0 (equal) and -1 (loss).

• (12) summary_m times of win (1), equal (0) and loss (-1).

• (13) other_info a list of 4 elements. The 1st is the method, which is equal to variant. The 2nd is the winning votes matrix. The 3rd is the margins matrix. The 4th is the pairwise comparison matrix.

References

• https://en.wikipedia.org/wiki/Minimax_Condorcet_method

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'))
win1 <- cdc_simple(vote)
win2 <- cdc_minmax(vote) # winner is n
win3 <- cdc_minmax(win1, variant = 2)
win4 <- cdc_minmax(win3$cdc, variant = 3)