POLYAS Election Glossary

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Hare-Niemeyer Method

The Hare-Niemeyer method (also known as the largest remainder method) is a mathematical method to allocate seats under a proportional representation system. It was used from 1987 to 2008 to allocate seats in the German Bundestag. 

The method is named after its developers: Thomas Hare (a British lawyer, 1806-1891) and Horst Niemeyer (a German mathematician, 1931-2007). The latter proposed it for use in the German federal elections of 1970. The resulting allocation of seats under this method is often similar to that under the d’Hondt’s highest averages method. However, the Hare-Niemeyer method is more beneficial for smaller parties and diminishes the supremacy of larger parties. 

The Hare-Niemeyer method in practice.

To allocate seats, it is first necessary to calculate what's called a 'quota'. The quota is the minimun number of votes required to gain a seat. There are a number of different ways to calculate a quota, but in this example we'll use the Hare-quota.

Hare-quota = total no. of votes / total no. of seats

To illustrate, using the above example of an election with 4 party lists, 176 total votes and 8 seats to be filled, we see that the quota is 22 (176 / 8).

Next, we divide the number of votes won by each party by the quota, which will give us a number to two decimal places for each party:

  • List 1 = 85/22 = 3.86
  • List 2 = 35/22 = 1.59
  • List 3 = 44/22 = 2.00
  • List 4 = 12/22 = 0.54

Each party list is then awarded the number of seats corresponding to the integer part of this calculation. So in this example, each party is automatically awarded 3, 1, 2 and 0 seats respectively. 

Notice that this only adds up to 6 seats, but we need to allocate a total of 8. In order to do this, we award 2 more seats to the parties with the two largest remainders as per the decimal values (lists 1 and 2, 0.86 and 0.59 respectively). So the final allocation of seats under the Hare-Niemeyer method is:

  • List 1 - 4
  • List 2 - 2
  • List 3 - 2
  • List 4 - 0

As we can see from this example, whilst the smallest party missed out on winning a seat, it came very close to winning one with its remainder value of 0.54. See this method of allocating seats under proportional representation compares with the Webster method and the d'Hondt method.


See also: D'Honst method, Webster method, Proportional Vote, Majority Vote

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