What is the D’Hondt Method? An Explainer
Posted by Paul, 2017-03-06
Many jurisdictions that use proportional representation as an electoral system use the D’Hondt method as a way to assign seats to parties. It’s used in Argentina, Belgium, Chile, Denmark, Ecuador, Scotland, the London Assembly, some countries in European Parliamentary elections as well as in dozens of other countries, cities and assorted sub-national entries.
Named after Belgian lawyer Victor D'Hondt who developed the system in 1878, a similar system was earlier devised by Thomas Jefferson, who found some time between inventing the swivel chair and pedometers to develop a method to assign seats to states for the House of Representatives.
You may also be glad to find out that I was debating between calling this post The Thrill of D’Hondt, but ultimately decided against it.
How the D’Hondt method work? The main idea behind it is that it assigns seats (one at a time) to parties using a method of highest averages.
It might be best to work through an example. Let’s say we have three parties: Blue, Red and Green, and they are competing to win 5 seats. The results of the voting are as follows:
Blue: 100,000 votes Red: 90,000 votes Green 40,000 votes
Now, we haven’t actually assigned any seats yet. So first, we need to take each party’s votes and divide that number by the number of seats we’ve already assigned to that party (0 for each right now) and then add 1 (0 plus 1 equalling, as has been the tradition, 1).
Blue: 100,000 / 1 = 100,000 Red: 90,000 / 1 = 90,000 Green 40,000 / 1 = 40,000
We can award the first seat to the Blue Party as it has the largest quotient (or result of performing the division, in case you haven’t reviewed your arithmetic terms in a while). Now, we have to repeat the process, dividing the number of votes received by each party by the number of seats assigned to that party so far, plus one.
Blue: 100,000 / 2 = 50,000 Red: 90,000 / 1 = 90,000 Green 40,000 / 1 = 40,000
The second seat gets awarded to the Red Party. So far we’ve awarded two of the five seats, so let’s go ahead and award the remaining three:
Blue: 100,000 / 2 = 50,000 Red: 90,000 / 2 = 45,000 Green 40,000 / 1 = 40,000
(Blue wins a second seat.)
Blue: 100,000 / 3 = 33,333 Red: 90,000 / 2 = 45,000 Green 40,000 / 1 = 40,000
(Red wins a second seat.)
Blue: 100,000 / 3 = 33,333 Red: 90,000 / 3 = 30,000 Green 40,000 / 1 = 40,000
(Green wins its first seat.)
For this fake election, the D’Hondt method has assigned 2 seats to the Blue Party, 2 seats to the Red Party and 1 seat to the Green Party. If the number of jurisdictions were larger than 5, then you’d just repeat this process until you were done assigning seats. As the number of seats gets larger, the proportion of seats assigned quickly lines up with the proportion of votes won.
Using this in a party list system, then, the first 2 candidates on the Blue Party list would be elected, as would two from the Red Party list, along with 1 from the Green Party list.
There are also some variations of the D’Hondt formula, such as using it to assign ‘top-up’ seats in mixed-member systems, such as in the London Assembly, or combining it with quotas in a system known as Hagenbach-Bischoff.
Proportional representation can also choose to use a variety of other methods, which will be described in future posts.
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