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Calculate seat apportionment for legislative bodies using different established methods, including biproportional apportionment.

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# proporz <img src="man/figures/logo.png" align="right" height="138" alt = "proporz logo"/>

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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:

```r
install.packages("proporz")
```

Alternatively, install the development version from Github:

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

## Apportionment methods overview

### Proportional Apportionment

[`proporz()`](https://polettif.github.io/proporz/reference/proporz.html) distributes 
seats proportionally for a vector of votes according to the following methods:

- **Divisor methods** ([Wikipedia](https://en.wikipedia.org/wiki/Divisor_method))
    - D'Hondt, Jefferson, Hagenbach-Bischoff
    - Sainte-Laguë, Webster
    - Adams
    - Dean
    - Huntington-Hill
- **Largest remainder method** ([Wikipedia](https://en.wikipedia.org/wiki/Largest_remainder_method))
    - Hare-Niemeyer, Hamilton, Vinton

``` r
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](https://en.wikipedia.org/wiki/Biproportional_apportionment))
is a method to proportionally allocate seats among parties and districts.
The method is implemented in [`biproporz()`](https://polettif.github.io/proporz/reference/biproporz.html).

We can use the provided [`uri2020`](https://polettif.github.io/proporz/reference/uri2020.html) 
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.

``` r
(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()`](https://polettif.github.io/proporz/reference/pukelsheim.html) 
for dataframes in long format as input data. It is a wrapper for `biproporz()`. [`zug2018`](https://polettif.github.io/proporz/reference/zug2018.html) 
shows an 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.

``` r
# 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**](https://polettif.github.io/proporz/articles/apportionment_scenarios.html) 
contains more examples. 
How to adapt `biproporz` for special use cases is demonstrated in the [**Modifying biproporz() vignette**](https://polettif.github.io/proporz/articles/modifying_biproporz.html).

## 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.

🌐 [Try it out on shinyapps.io](https://polettif.shinyapps.io/proporz/)

```r
# install.packages("shiny")
# install.packages("shinyMatrix")
proporz::run_app()
```
<img src="man/figures/shinyapp-example.gif" style = "width:75%;" alt = "shiny app gif">

## Function details

[**Full function reference**](https://polettif.github.io/proporz/reference/index.html)

#### Divisor methods

You can use divisor methods directly:

``` r
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:

``` r
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](https://www.math.uni-augsburg.de/htdocs/emeriti/pukelsheim/bazi/RBazi.html): Package using rJava to access the functions of [BAZI](https://www.math.uni-augsburg.de/htdocs/emeriti/pukelsheim/bazi/welcome.html).
- [seatdist](https://github.com/jmedzihorsky/seatdist): Package for seat apportionment and disproportionality measurement.
- [disprr](https://github.com/pierzgal/disprr): Simulate election results and examine disproportionality of apportionment methods.
- [apportR](https://github.com/jalapic/apportR): Package containing various apportionment methods, with particular relevance for the problem of apportioning seats in the House of Representatives.
- [apportion](https://github.com/christopherkenny/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](https://github.com/polettif/proporz/issues/new).

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