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Sequential Proportional Approval Voting

seq_pav.Rd

Sequential Proportional Approval Voting (SeqPAV) is a multi-winner method that builds a committee by iteratively maximizing a proportionality-based satisfaction score. After each selection, the weights of voters who approved the chosen candidate are reduced, which promotes proportional representation. The PAV score is computed as the weighted sum of harmonic numbers based on how many elected candidates each voter supports. The process continues until the specified committee size is reached or all candidates are ranked.

This function uses an internal C++ implementation for efficient computation.

Usage

seq_pav(
  voters,
  candidates,
  weights = NULL,
  committee_size = NULL,
  borda_score = TRUE,
  check = FALSE
)

Arguments

voters

(list())
A list of subsets (character vectors), where each subset contains the candidates approved or selected by a voter.

candidates

(character())
A vector of all candidates to be ranked.

weights

(numeric()|NULL)
A numeric vector of non-negative weights representing each voter's influence. Larger weight, higher influence. Must have the same length as voters. If NULL (default), all voters are assigned equal weights of 1, representing equal influence.

committee_size

(integer(1)|NULL)
Number of top-ranked candidates to return. Default (NULL) returns all candidates.

borda_score

(logical(1))
Whether to include a borda_score column in the output, which provides a normalized score based on the candidate's rank. If TRUE (default), the borda_score is calculated as \((p - i) / (p - 1)\), where \(p\) is the total number of candidates and \(i\) is the candidate's rank.

check

(logical(1))
Whether to run additional voter-integrity checks. When TRUE, each voter must approve at least one candidate, approvals must be unique per voter, and all approved candidates must appear in candidates. Use FALSE to skip these checks when inputs are known to be valid.

Value

A data.frame with columns:

  • "candidate": Candidate names.

  • "borda_score": Borda scores for method-agnostic comparison, ranging in \([0,1]\), where the top candidate receives a score of 1 and the lowest-ranked candidate receives a score of 0, based on the total number of candidates.

Candidates are ordered by the sequence in which they were selected.

See also

Other voting methods: av(), sav(), seq_phragmen()