Count votes using the Condorcet voting method.

The Condorcet method elects the candidate who wins a majority of the ranked vote in every head to head election against each of the other candidates. A Condorcet winner is a candidate who beats all other candidates in pairwise comparisons. Analogously, a Condorcet loser is a candidate who loses against all other candidates. Neither Condorcet winner nor loser might exist.

Usage

condorcet(
  votes,
  runoff = FALSE,
  nseats = 1,
  safety = 1,
  fsep = "\t",
  quiet = FALSE,
  ...
)

Arguments

votes: A matrix or data.frame containing the votes. Rows correspond to the votes, columns correspond to the candidates. If votes is a character string, it is interpreted as a file name from which the votes are to be read. See below.
runoff: Logical. If TRUE and no Condorcet winner exists, the election goes into a run-off, see below.
nseats: the number of seats to be filled in this election
safety: Parameter for a clustering heuristic on a total ranking of the candidates. Conjecture: the default of 1.0 ensures a separation of one s.d. between clusters, when votes are i.u.d. permutations on the candidates.
fsep: If votes is a file name, this argument gives the column separator in the file.
quiet: If TRUE no output is printed.
...: Undocumented intent (preserved from legacy code)

Value

Object of class SafeVote.condorcet

Details

If the runoff argument is set to TRUE and no Condorcet winner exists, two or more candidates with the most pairwise wins are selected and the method is applied to such subset. If more than two candidates are in such run-off, the selection is performed repeatedly, until either a winner is selected or no more selection is possible.

The input data votes is structured the same way as for the stv method: Row i contains the preferences of voter i numbered 1; 2; : : : ; r; 0; 0; 0; 0, in some order, while equal preferences are allowed. The columns correspond to the candidates. The dimnames of the columns are the names of the candidates; if these are not supplied then the candidates are lettered A, B, C, .... If the dataset contains missing values (NA), they are replaced by zeros.

If a ballot has equally-ranked candidates, its rankings are tested for validity: for each preference \(i\) which does not have any duplicate, there are exactly \(i - 1\) preferences \(j\) with \(0 < j < i\). If any ballot x fails this validity test, it is automatically corrected (aka "converted") into a valid ballot using x <- rank(x, ties.method = "min"), and a warning is issued.

This method also computes a Borda ranking of all candidates, using tournament-style scoring. This ranking is "fuzzed" into a safeRank, with approximately 1 s.d. of fuzz when safety=1.0 and voter preferences are i.u.d. A warning is thrown if a safeRank violates the (extended) Condorcet principle: that Candidate \(i\) is more highly ranked than Candidate \(j\) only if a majority of voters agree with this.

Examples

{
data(food_election)
condorcet(food_election)
}
#> 
#> Results of Condorcet voting
#> ===========================                           
#> Number of valid votes:   20
#> Number of invalid votes:  0
#> Number of candidates:     5
#> Number of seats:          1
#> 
#> 
#> |             | Oranges| Pears| Chocolate| Strawberries| Sweets| Total| Score | BordaRank | margin| SafeRank| Winner| Loser|
#> |:------------|-------:|-----:|---------:|------------:|------:|-----:|:-----:|:---------:|------:|--------:|------:|-----:|
#> |Oranges      |       0|     1|         0|            0|      1|     2|  22   |     3     |      6|        2|       |      |
#> |Pears        |       0|     0|         0|            0|      0|     0|   8   |     5     |      0|        2|       |     x|
#> |Chocolate    |       1|     1|         0|            1|      1|     4|  48   |     1     |     20|        1|      x|      |
#> |Strawberries |       1|     1|         0|            0|      1|     3|  28   |     2     |      6|        2|       |      |
#> |Sweets       |       0|     1|         0|            0|      0|     1|  16   |     4     |      8|        2|       |      |
#> 
#> safeRank fuzz on Borda scores: 8.944272
#> Gaps in Borda scores: min 6 mean 9.6 max 20 ; all 6 6 8 8 20
#> Condorcet winner: Chocolate
#> Condorcet loser: Pears
#>