cdc_schulze {votesys}

Schulze Method

Description

Schulze method is essentially a widest path problem. With the Condorcet matrix, we must find the so called the strongest path a > b > c > d, and the winner is a. The strength of a path is the strength of its weakest link.

Usage

cdc_schulze(x, allow_dup = TRUE, min_valid = 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.

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, may be NULL.

• (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 2 elements. The 1st is the strength comparison matrix. The 2nd is the strength comparison matrix in binary mode, 1 for win, 0 for else.

References

• Schulze, M. 2010. A new monotonic, clone-independent, reversal symmetric, and Condorcet-consistent single-winner election method. Social Choice and Welfare, 36(2), 267-303.

Examples

raw <- list2ballot(
    x = list(
        c('a', 'c', 'b', 'e', 'd'), 
        c('a', 'd', 'e', 'c', 'b'), 
        c('b', 'e', 'd', 'a', 'c'), 
        c('c', 'a', 'b', 'e', 'd'), 
        c('c', 'a', 'e', 'b', 'd'), 
        c('c', 'b', 'a', 'd', 'e'), 
        c('d', 'c', 'e', 'b', 'a'), 
        c('e', 'b', 'a', 'd', 'c')
    ), 
    n = c(5, 5, 8, 3, 7, 2, 7, 8)
)
vote <- create_vote(raw, xtype = 3, candidate = c('a', 'b', 'c', 'd', 'e'))
win1 <- cdc_simple(vote) # no winner
win2 <- cdc_schulze(vote) # winner is e
win2 <- cdc_schulze(win1)