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Compute pairwise results from ranked preference data

Source: R/pairwise.R
pairwise_calculator.Rd

Computes all pairwise comparisons from a set of ranked preferences using prefio::adjacency(). For each pair of items, reports the number of voters who preferred each item and the Two-Candidate Preferred (TCP) ratio. Also identifies the Condorcet winner and loser where they exist.

Usage

pairwise_calculator(x, preferences_col = NULL, frequency_col = NULL)

Arguments

x

A preferences object, or a data frame / tibble containing a preferences-typed column.

preferences_col

<tidy-select> When x is a data frame, the column containing the preferences. Passed directly to prefio::adjacency().

frequency_col

<tidy-select> Optional column containing ballot frequencies. Passed directly to prefio::adjacency().

Value

An S3 object of class "pairwise" with four components:

pairwise_matrix

N×N integer matrix from prefio::adjacency().

two_candidate_preferred

Tibble with one row per pair, columns: item_a, item_b, wins_a, wins_b, total, tcp_a, tcp_b, h2h_winner.

condorcet_winner

Name of the Condorcet winner, or NA if none.

condorcet_loser

Name of the Condorcet loser, or NA if none.

Details

TCP ratio (tcp_a, tcp_b) is computed as wins / (wins_a + wins_b). The denominator is the number of voters who expressed a preference between the specific pair, not the total number of voters. This correctly handles partial rankings where some voters did not rank all items.

Condorcet winner: the item that beats every other item head-to-head (tcp > 0.5 in all pairs it appears in). At most one can exist.

Condorcet loser: the item that loses to every other item head-to-head (tcp < 0.5 in all pairs it appears in). At most one can exist. Neither winner nor loser may exist when preference cycles are present.

See also

pairwise_heatmap() to visualise the results.

Examples

library(prefio)

prefs <- data.frame(
  A = c(1, 1, 1, 2, 2),
  B = c(2, 2, 3, 1, 3),
  C = c(3, 3, 2, 3, 1)
) |>
  wide_preferences(col = vote, ranking_cols = A:C)

result <- pairwise_calculator(prefs, preferences_col = vote)
print(result)
#> Pairwise analysis (3 items)
#> 
#> Head-to-head results (first 5 rows):
#>  item_a item_b wins_a wins_b total tcp_a tcp_b h2h_winner
#>       A      B      4      1     5 80.0% 20.0%          A
#>       A      C      4      1     5 80.0% 20.0%          A
#>       B      C      3      2     5 60.0% 40.0%          B
#> 
#> Condorcet winner: A
#> Condorcet loser:  C