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# A Python implementation of common apportionment methods
This is a collection of common apportionment methods. Apportionment has two main applications:
to assign a fixed number of [parliamentary seats to parties](https://en.wikipedia.org/wiki/Party-list_proportional_representation) (proportionally to their vote count), and to assign
[representatives in a senate to states](https://en.wikipedia.org/wiki/United_States_congressional_apportionment) (proportionally to their population count).
A recommendable overview of apportionment methods can be found in the book "Fair Representation" by Balinski and Young [2].
The following apportionment methods are implemented:
* the largest remainder method (or Hamilton method)
* the class of divisor methods including
- D'Hondt (or Jefferson)
- Sainte-Laguë (or Webster)
- Modified Sainte-Laguë (as used e.g. in Norway)
- Huntington-Hill
- Adams
* the quota method [1]
This module supports Python 3.7+.
## Installation
Using pip:
```bash
pip install apportionment
```
Latest development version from source:
```bash
git clone https://github.com/martinlackner/abcvoting/
python setup.py install
```
Requirements:
* Python 3.7+
* numpy
## A simple example
The following example calculates the seat distribution of Austrian representatives in the
European Parliament based on the D'Hondt method and the [2019 election results](https://www.bmi.gv.at/412/Europawahlen/Europawahl_2019). Parties that received less than 4% are excluded from obtaining seats and are thus excluded in the calculation.
```python
import apportionment.methods as app
parties = ['OEVP', 'SPOE', 'FPOE', 'GRUENE', 'NEOS']
votes = [1305956, 903151, 650114, 532193, 319024]
seats = 18
app.compute("dhondt", votes, seats, parties, verbose=True)
```
The output is
```
D'Hondt (Jefferson) method
OEVP: 7
SPOE: 5
FPOE: 3
GRUENE: 2
NEOS: 1
```
which is indeed the [official result](https://www.bmi.gv.at/412/Europawahlen/Europawahl_2019).
Another example can be found in [apportionment/examples/simple.py](apportionment/examples/simple.py).
We verify results from recent Austrian National Council elections in [apportionment/examples/austria.py](apportionment/examples/austria.py) and from recent elections of the Israeli Knesset in [apportionment/examples/israel.py](apportionment/examples/israel.py).
## References
[1] Balinski, M. L., & Young, H. P. (1975). The quota method of apportionment. The American Mathematical Monthly, 82(7), 701-730.
[2] Balinski, M. L., & Young, H. P. (1982). Fair Representation: Meeting the Ideal of One Man, One Vote. Yale University Press, 1982. (There is a second edition from 2001 by Brookings Institution Press.)