Description Usage Arguments Value References Examples

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.

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

`x` |
it accepts the following types of input:
1st, it can be an object of class |

`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. |

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.

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

1 2 3 4 5 6 7 8 9 10 | ```
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)
``` |

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