This is a collection of common apportionment methods. Apportionment has two main applications: to assign a fixed number of parliamentary seats to parties (proportionally to their vote count), and to assign representatives in a senate to states (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 2.7+ and 3.5+.
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. Parties that received less than 4% are excluded from obtaining seats and are thus excluded in the calculation.
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.
Another example can be found in apportionment/examples/simple.py. We verify results from recent Austrian National Council elections in apportionment/examples/austria.py and from recent elections of the Israeli Knesset in apportionment/examples/israel.py.
[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.)