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 (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 3.7+.

How-to

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.

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.)