# cdc_dodgson: Dodgson Method In votesys: Voting Systems, Instant-Runoff Voting, Borda Method, Various Condorcet Methods

## Description

The original Dodgson method checks the number of votes each candidate has to rob from other candidates; the winner is with the smallest number. However, the function `cdc_dodgson` uses two alternative methods rather than the original Dodgson method. The two methods are Tideman score method and Dodgson Quick method. See Details.

## Usage

 `1` ```cdc_dodgson(x, allow_dup = TRUE, min_valid = 1, dq_t = "dq") ```

## 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. `dq_t` the alternative Dodgson methods to be used. Default is "dq", for Dodgson Quick method; it can also be "t", Tideman score method.

## Details

Suppose the candidates are A, B, C and D. If A wins B in pairwise comparison or has equal votes with B, then add 0 to A. If C wins A, then add to A adv(C, A), that is, the number of voters that prefer C than A, minus the number of voters that prefer A than A. Again, if D wins A, then add to A that number. Then, we sum up the points belong to A. We do the same thing to B, C and D. The one gets the least points is the winner. This is what we do in Tideman score method. In Dodgson Quick method, we first compute the number of votes, then divide it by 2 and get the ceiling, and sum all of them up.

## 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 with four elements. The 1st indicates the method used to compute score. The 2nd is the score for pairwise comparison (number of votes one has to rob). The 3rd is Tideman score summary (the smaller the better). The 4th is Dodgson Quick summary (the smaller the better).

## References

• McCabe-Dansted, J. & Slinko, A. 2008. Approximability of Dodgson's Rule. Social Choice and Welfare, Feb, 1-26.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```raw <- list2ballot( x = list( c('A', 'B', 'C', 'D', 'E', 'F'), c('F', 'A', 'B', 'C', 'D', 'E'), c('E', 'D', 'C', 'B', 'F', 'A'), c('B', 'A', 'C', 'D', 'E', 'F'), c('F', 'E', 'D', 'C', 'B', 'A'), c('F', 'B', 'A', 'C', 'D', 'E'), c('E', 'D', 'C', 'A', 'F', 'B'), c('E', 'B', 'A', 'C', 'D', 'F'), c('F', 'D', 'C', 'A', 'E', 'B'), c('D', 'B', 'A', 'C', 'E', 'F'), c('F', 'E', 'C', 'A', 'D', 'B') ), n = c(19, 12, 12, 9, 9, 10, 10 , 10 , 10, 10, 10) ) vote <- create_vote(raw, xtype = 3, candidate = c('A', 'B', 'C', 'D', 'E', 'F')) win1 <- cdc_simple(vote) # no winner win2 <- cdc_dodgson(vote, dq_t = "dq") # A win2 <- cdc_dodgson(win1, dq_t = "dq") # A win3 <- cdc_dodgson(vote, dq_t = "t") # B win3 <- cdc_dodgson(win2, dq_t = "t") # B ```

### Example output

```MATCHING NAMES AND SCORES
COUNTING NA AND DUP VALUES
MAKING CONDORCET TABLE
COLLECTING RESULT
DONE
CREATING CDC MATRIX
------USE CDC MATRIX WITH NA IN x
EXTRACTING INFO
SELECTING
COLLECTING RESULT
DONE
CREATING CDC MATRIX
------USE CDC MATRIX WITH NA IN x
EXTRACTING INFO
SELECTING
COLLECTING RESULT
DONE
CREATING CDC MATRIX
EXTRACTING INFO
SELECTING
COLLECTING RESULT
DONE
CREATING CDC MATRIX
------USE CDC MATRIX WITH NA IN x
EXTRACTING INFO
SELECTING
COLLECTING RESULT
DONE
CREATING CDC MATRIX
EXTRACTING INFO
SELECTING
COLLECTING RESULT
DONE
```

votesys documentation built on May 2, 2019, 1:32 p.m.