POLYAS Election Glossary

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D'Hondt highest averages or Jefferson method for proportional seat allocation

D'Hondt Highest Averages Method

Developed by Belgian jurist and mathematician Victor d'Hondt, the d'Hondt highest averages method is used in proportional representation party list elections to allocate seats within an elected body after votes have been counted. The d'Hondt method is also known as the Jefferson-method in the Anglo-Saxon world, and the Hagenbach-Bischoff-method in Switzerland. 

The above table illustrates how the d'Hondt method works. Here we can see that 8 seats in total need to be filled, with each list representing a different political party - so 'List 1' can be read as 'Party 1' and so on. The vote-count in the election yielded the following results:

  • Party 1 - 85 votes
  • Party 2 - 35 votes
  • Party 3 - 44 votes
  • Party 4 - 12 votes 

Applying the d'Hondt method, we allocate the first seat to the party with the highest number of votes - in this case, party 1 wins the first seat with 85 votes. In order to allocate the second seat, we must first apply the following formula to the total number of votes of party 1:

New no. of votes = Previous no. of votes / (1 + no. of seats already allocated to the party)

So, in our example: 

New no. of votes for party 1 = 85 / (1+1) = 42.5

We now repeat the process using this new figure of 42.5 replacing 85 as party 1's 'number of votes'. This time we see that party 3 has the highest number of votes with 44, so they get the second seat. We now alter party 3's number of votes using the above formula and repeat this process until all 8 seats have been filled.

The d’Hondt method for seat allocation is somewhat controversial because it can disadvantage smaller parties. However, alternative vote-count methods exist which aim to reduce this disadvantage including the Hare-Niemeyer method and the Webster (or Sainte-Laguë/Schepers) method.

See also: Hare-Niemeyer method, Webster method, Proportional Vote, Ballot paper

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