Biproportional apportionment with data frames

Method to proportionally allocate seats among parties/lists and districts/regions/entities ('Doppelter Pukelsheim').

Usage

pukelsheim(
  votes_df,
  district_seats_df,
  quorum,
  new_seats_col = "seats",
  weight_votes = TRUE,
  winner_take_one = FALSE,
  ...
)

Arguments

votes_df

data.frame (long format) with 3 columns (actual colnames can differ):

1. party id/name (character)

2. district id/name (character)

3. votes (numeric)

district_seats_df

data.frame with 2 columns (actual colnames can differ):

1. district id/name (character)

2. number of seats for a district (numeric)

quorum

Optional list of functions which take the votes_matrix and return a logical vector that denotes for each party/row whether they reached the quorum (i.e. are eligible for seats). The easiest way to do this is via quorum_any() or quorum_all(), see examples. Alternatively you can pass a precalculated logical vector. No quorum is applied if this parameter is missing or NULL.

new_seats_col

name of the new column

weight_votes

By default (TRUE) it is assumed that each voter in a district has as many votes as there are seats in a district. Set to FALSE if votes_df shows the number of voters (e.g. because they can only vote for one party).

winner_take_one

Set to TRUE if the party that got the most votes in a district must get at least one seat ('Majorzbedingung') in this district. This only applies if the district winnig party is entitled to a seat in the upper apportionment. Default is FALSE.

...

ignored (available for backwards compatibility)

Value

A data.frame like votes_df with a new column denoting the number of seats per party and district. Party and district divisors stored in attributes (hidden from print, see get_divisors()). An ungrouped tibble is returned if votes_df is a tibble.

Details

Each party nominates a candidate list for every district. The voters vote for the parties of their district. The seat allocation is calculated in two steps:

1. In the so called upper apportionment the number of seats for each party (over all districts) is determined.

2. In the so called lower apportionment the seats are distributed to the regional party list respecting the results from the upper apportionment.

Parties failing to reach quorums cannot get seats. This function does not handle seat assignment to candidates.

If you want to use other apportion methods than Sainte-Laguë use biproporz().

See also

This function calls biproporz() after preparing the input data.

Examples

# Zug 2018
votes_df = unique(zug2018[c("list_id", "entity_id", "list_votes")])
district_seats_df = unique(zug2018[c("entity_id", "election_mandates")])

seats_df = pukelsheim(votes_df,
                      district_seats_df,
                      quorum_any(any_district = 0.05, total = 0.03),
                      winner_take_one = TRUE)

head(seats_df)
#>   list_id entity_id list_votes seats
#> 1       2      1701       8108     2
#> 2       1      1701       2993     0
#> 3       3      1701      19389     3
#> 4       4      1701      14814     2
#> 5       5      1701       4486     1
#> 6       6      1701      15695     3

# Finland 2019
finland19_result = pukelsheim(finland2019$votes_df,
                             finland2019$district_seats_df,
                             new_seats_col = "mandates",
                             weight_votes = FALSE)
tail(finland19_result[order(finland19_result$mandates),])
#>   party_name district_name  votes mandates
#> 4         PS           UUS  86691        5
#> 5        KOK           HEL  84141        5
#> 7       VIHR           UUS  73626        5
#> 2        SDP           UUS  97107        6
#> 6       KESK           OUL  78486        6
#> 1        KOK           UUS 114243        7