It is also called Tideman method. See details.
cdc_rankedpairs(x, allow_dup = TRUE, min_valid = 1)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.
whether ballots with duplicated score values are taken into account. Default is TRUE.
default is 1. If the number of valid entries of a ballot is less than this value, it will not be used.
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 the 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 winner, 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 3 elements. The 1st
is the reason of failure. If winner exists, it will be blank. The 2nd
is the tally result (it may contain unsolved ties).
The 3rd is the lock-in result; if the method fails,
it will be NULL.
The method first summarizes the result of pairwise comparison, the order used is the order of winning votes from large to small. So if pairwise comparison has ties (that is, the number of voters who prefer a than b is equal to the number of voters who prefer b than a, the method will fail, and the winner will be NULL).
The second step is called tally. If a wins b with 100 votes, b wins c with 80 votes, then we put a-b-100 ahead of b-c-80. Suppose a wins b with 100 votes, a wins c with 100 votes, then we have a tie; so we have to check the relation between b and c. If b wins c, then we put a-c-100 ahead of a-b-100. Suppose a wins b with 100 votes, d wins b with 100 votes, then again we have a tie and have to check the a-d relation. If d wins a, then we put d-b-100 ahead of a-b-100. Suppose a wins b with 100 votes, e wins f with 100 votes, then the ties cannot be solved, so the winner will be NULL.
The third step, after the above mentioned tally, is called lock-in. As the relations have been sorted according to their strength from large to small in the tally step, we now add them one by one. The rule is: if a relation is contradictory with those already locked in relations, this relation will be discarded.
For example, suppose we have already add relation a > b and b > c, then the two relations are locked in. As a result, we should not add b > a. Also, as a > b and b > c indicate a > c, so we should not add c > a. After this process, we will finally find the winner who defeats all others.
Tideman, T. 1987. Independence of clones as a criterion for voting rules. Social Choice and Welfare, 4(3), 185-206.
# NOT RUN {
raw <- rbind(c('m', 'n', 'c', 'k'), c('n', 'c', 'k', 'm'),
c('c', 'k', 'n', 'm'), c('k', 'c', 'n', 'm'))
raw <- list2ballot(m = raw, n = c(42, 26, 15, 17))
vote <- create_vote(raw, xtype = 2, candidate = c('m', 'n', 'c', 'k'))
y <- cdc_rankedpairs(vote)
# }
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