The d'Hondt System

This is a voting system for allocating seats to parties using a party list system. It is designed to give small parties some representation while giving the majority of seats to the main contenders. It is the system used for EU elections, where the country is divided into a number of regions, each electing several MEPs. London elects 8 MEPs.

The Modified d'Hondt System

The d'Hondt system may be modified for use in elections where there are a number of constituency seats and a number of top-up seats from party lists. It is the system used for GLA elections, where there are 14 constituency seats (each consisting of either two or three neighbouring boroughs) and 11 top-up seats.

Both:

The full d'Hondt method may be considered to be a special case of the Modified version in which there are no constituency seats, so the explanations may be taken together. It works in the following curious fashion:

Here's an example, from the 2008 GLA election: In the constituencies the Conservatives won 8 seats, Labour 6 and nobody else won any.

There were 11 seats to allocate via the top-up lists and the voting percentages were (roughly):

Conservative 34.1%
Labour 27.1%
Lib Dem 11.2%
Green 8.3%
BNP 5.3%
(the total does not come to 100% because there were a number of other parties failing to reach the 5% threshold)

The allocation process then worked as follows:
O = Original vote share
S = Seats so far
V = Vote share counted for this allocation

Voting Con Lab L.D. Green BNP Seat
Round O S V O S V O S V O S V O S V alloc to
1 34.1 8 3.8 27.1 6 3.9 11.2 0 11.2 8.3 0 8.3 5.3 0 5.3 L.D.
2 34.1 8 3.8 27.1 6 3.9 11.2 1 5.6 8.3 0 8.3 5.3 0 5.3 Green
3 34.1 8 3.8 27.1 6 3.9 11.2 1 5.6 8.3 1 4.2 5.3 0 5.3 L.D.
4 34.1 8 3.8 27.1 6 3.9 11.2 2 3.7 8.3 1 4.2 5.3 0 5.3 BNP
5 34.1 8 3.8 27.1 6 3.9 11.2 2 3.7 8.3 1 4.2 5.3 1 2.7 Green
6 34.1 8 3.8 27.1 6 3.9 11.2 2 3.7 8.3 2 2.8 5.3 1 2.7 Lab
7 34.1 8 3.8 27.1 7 3.4 11.2 2 3.7 8.3 2 2.8 5.3 1 2.7 Con
8 34.1 9 3.4 27.1 7 3.4 11.2 2 3.7 8.3 2 2.8 5.3 1 2.7 L.D.
9 34.1 9 3.41 27.1 7 3.39 11.2 3 2.8 8.3 2 2.8 5.3 1 2.7 Con
10 34.1 10 3.1 27.1 7 3.4 11.2 3 2.8 8.3 2 2.8 5.3 1 2.7 Lab
11 34.1 10 3.1 27.1 8 3.0 11.2 3 2.8 8.3 2 2.8 5.3 1 2.7 Con


Notice how slowly the votes ('V') for Con and Lab go down as they get seats, compared to the other parties that had none to start with