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proporz

Calculate seat apportionment for legislative bodies with various methods. These methods include divisor methods (e.g. D’Hondt, Webster or Adams), largest remainder methods and biproportional apportionment.

Mit diesem R-Package können mittels verschiedener Sitzzuteilungsverfahren Wählerstimmen in Abgeordnetensitze umgerechnet werden. Das Package beinhaltet Quoten-, Divisor- und biproportionale Verfahren (Doppelproporz oder “Doppelter Pukelsheim”).

Installation

Install the package from CRAN:

install.packages("proporz")

Alternatively, install the development version from Github:

# install.packages("remotes")
remotes::install_github("polettif/proporz")

Apportionment methods overview

Proportional Apportionment

proporz() distributes seats proportionally for a vector of votes according to the following methods:

• Divisor methods (Wikipedia)
  • D’Hondt, Jefferson, Hagenbach-Bischoff
  • Sainte-Laguë, Webster
  • Adams
  • Dean
  • Huntington-Hill
• Largest remainder method (Wikipedia)
  • Hare-Niemeyer, Hamilton, Vinton

library(proporz)
votes = c("Party A" = 651, "Party B" = 349, "Party C" = 50)

proporz(votes, n_seats = 10, method = "sainte-lague")
#> Party A Party B Party C 
#>       7       3       0

proporz(votes, 10, "huntington-hill", quorum = 0.05)
#> Party A Party B Party C 
#>       6       4       0

Biproportional Apportionment

Biproportional apportionment (Wikipedia) is a method to proportionally allocate seats among parties and districts.

We can use the provided uri2020 data set to illustrate biproportional apportionment with biproporz(). You need a ‘votes matrix’ as input which shows the number of votes for each party (rows) and district (columns). You also need to define the number of seats per district.

(votes_matrix <- uri2020$votes_matrix)
#>      Altdorf Bürglen Erstfeld Schattdorf
#> CVP    11471    2822     2309       4794
#> SPGB   11908    1606     1705       2600
#> FDP     9213    1567      946       2961
#> SVP     7756    2945     1573       3498

(district_seats <- uri2020$seats_vector)
#>    Altdorf    Bürglen   Erstfeld Schattdorf 
#>         15          7          6          9

biproporz(votes_matrix, district_seats)
#>      Altdorf Bürglen Erstfeld Schattdorf
#> CVP        5       2        2          3
#> SPGB       4       1        2          2
#> FDP        3       1        1          2
#> SVP        3       3        1          2

You can use pukelsheim() for dataframes in long format as input data. It is a wrapper for biproporz(). zug2018 shows an actual election result for the Canton of Zug in a dataframe. We use this data set to create input data for pukelsheim(). The other parameters are set to reflect the actual election system.

# In this data set, parties are called 'lists' and districts 'entities'.
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 = 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

The apportionment scenarios vignette contains more examples.

Shiny app

The package provides a basic Shiny app where you can calculate biproportional apportionment on an interactive dashboard. You need to have the packages shiny and shinyMatrix installed.

# install.packages("shiny")
# install.packages("shinyMatrix")
proporz::run_app()

Function details

Full function reference

Divisor methods

You can use divisor methods directly:

votes = c("Party A" = 690, "Party B" = 370, "Party C" = 210, "Party D" = 10)

# D'Hondt, Jefferson or Hagenbach-Bischoff method
divisor_floor(votes, 10)
#> Party A Party B Party C Party D 
#>       6       3       1       0

# Sainte-Laguë or Webster method
divisor_round(votes, 10)
#> Party A Party B Party C Party D 
#>       5       3       2       0

# Adams method
divisor_ceiling(votes, 10)
#> Party A Party B Party C Party D 
#>       4       3       2       1

# Dean method
divisor_harmonic(votes, 10)
#> Party A Party B Party C Party D 
#>       5       2       2       1

# Huntington-Hill method
divisor_geometric(votes, 10)
#> Party A Party B Party C Party D 
#>       5       3       1       1

Largest remainder method

The largest remainder method is also accessible directly:

votes = c("I" = 16200, "II" = 47000, "III" = 12700)

# Hamilton, Hare-Niemeyer or Vinton method
largest_remainder_method(votes, 20)
#>   I  II III 
#>   4  13   3

See also

There are other R packages available that provide apportionment functions, some with more focus on analysis. However, biproportional apportionment is missing from the pure R packages and RBazi needs rJava with an accompanying jar.

• RBazi: Package using rJava to access the functions of BAZI.
• seatdist package for seat apportionment and disproportionality measurement.
• disprr Examine Disproportionality of Apportionment Methods.
• apportR: Package containing various apportionment methods, with particular relevance for the problem of apportioning seats in the House of Representatives.
• apportion Convert populations into integer number of seats for legislative bodies, focusing on the United States.

Contributing

Please feel free to issue a pull request or open an issue.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.