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Create quorum parameter list for biproportional apportionment

Source: R/quorum.R
quorum_functions.Rd

quorum_any() and quorum_all() are used for the quorum parameter in upper_apportionment() (and thus biproporz()/pukelsheim()) and describe how quorums should be applied prior to seat distributions.

Usage

quorum_all(
  votes_any_district,
  votes_total,
  any_district_voters,
  total_voters,
  total = NULL,
  any_district = NULL
)

quorum_any(
  votes_any_district,
  votes_total,
  any_district_voters,
  total_voters,
  total = NULL,
  any_district = NULL
)

Arguments

votes_any_district

Vote threshold a party must reach in at least one district. Used as share of total votes within a district if less than 1, otherwise as number of votes. Must be > 0 if provided. Uses reached_quorum_any_district().

votes_total

Vote threshold a party must reach for all votes cast. Used as share of total votes if less than 1, otherwise as number of votes. Note that votes are not weighted with weight_votes_matrix() across districts, the usual and theoretically sound application for a total quorum is total_voters. Must be > 0 if provided. Uses reached_quorum_total().

any_district_voters

Weighted vote (voters) threshold a party must reach in at least one district. Used as share of total weighted votes (voters) within a district if less than 1, otherwise as number of voters. Must be > 0 if provided. Uses reached_quorum_any_district() with a weighted votes matrix.

total_voters

Vote threshold a party must reach for all weighted votes (voters). Used as share of total weighted votes (voters) if less than 1, otherwise as number of voters. Must be > 0 if provided. Uses reached_quorum_total() with a weighted votes matrix.

total

Replaced by total_voters (recommended) or votes_total

any_district

Replaced by votes_any_district (recommended) or any_district_voters

Value

List of parameters that describe which quorum methods and threshold values should be used. The list is handled in upper_apportionment() by eval_quorum().

Details

There is a difference in how the two functions work. With quorum_any, at least one quorum must be reached. With quorum_all all quorums must be reached. If you only use one parameter, quorum_any() and quorum_all() are identical.

Examples

votes_matrix = matrix(c(5020, 550, 800, 100, 1040, 550, 0, 10), ncol = 2)
dimnames(votes_matrix) <- list(c("A", "B", "C", "D"), c("Z1", "Z2"))
seats = c(Z1 = 50, Z2 = 20)

# use as parameter in biproporz or pukelsheim (general use case)
biproporz(votes_matrix, seats,
          quorum = quorum_any(votes_any_district = 0.1, total_voters = 20))
#>   Z1 Z2
#> A 40 12
#> B  5  8
#> C  5  0
#> D  0  0

biproporz(votes_matrix, seats,
          quorum = quorum_all(votes_any_district = 0.1, total_voters = 20))
#>   Z1 Z2
#> A 44 12
#> B  6  8
#> C  0  0
#> D  0  0

biproporz(votes_matrix, seats, quorum = quorum_any(votes_any_district = 0.1))
#>   Z1 Z2
#> A 40 12
#> B  5  8
#> C  5  0
#> D  0  0

biproporz(votes_matrix, seats, quorum = quorum_any(total_voters = 0.05))
#>   Z1 Z2
#> A 40 12
#> B  5  8
#> C  5  0
#> D  0  0

# the quorum parameter also accepts named vectors (e.g. calculated elsewhere)
biproporz(votes_matrix, seats,
          quorum = c(A = FALSE, B = TRUE, C = TRUE, D = TRUE))
#>   Z1 Z2
#> A  0  0
#> B 27 20
#> C 20  0
#> D  3  0

# quorum specifications are checked with eval_quorum
eval_quorum(quorum_any(votes_any_district = 0.2), votes_matrix)
#>     A     B     C     D 
#>  TRUE  TRUE FALSE FALSE