“A man is not dead while his name is still spoken,” said Terry Pratchett, and by this measure the 19th-century Belgian mathematician Victor D’Hondt has surely achieved a form of immortality. His method for allocating seats in proportional voting systems is used in many countries around the world, as well as for European elections in the UK. So how exactly does this system work, and what implications does it have?
In the UK, Members of the European Parliament are elected by vast regional constituencies with millions of voters, each electing several MEPs. Voters cast just one vote each, either for a party list or for an independent candidate. Here in Cambridge we are part of the East of England constituency, which elects seven MEPs. Here’s how we voted at the last EU elections in 2014:
So based on this result, how were the seven MEPs allocated between the parties? On strict proportionality, UKIP would be entitled to 2.41 MEPs, the Conservatives to 1.99, Labour to 1.2, and so on. However, it would be impractical to send UKIP’s first two candidates, Patrick O’Flynn and Stuart Agnew, to Brussels along with 41% of their third candidate, Tim Aker. So some way must be found to assign whole numbers of seats to each party – and this is where the D’Hondt system comes in. We take the votes for each party, and divide them in turn by the numbers one to seven. For simplicity I’ve ignored the five smallest parties, who don’t affect the results:
This gives a nominal “score” for each candidate. The score for a party’s first candidate is simply the whole vote for that party; the second candidate’s score is half the party’s vote; the third candidate’s score is one third of the vote, and so on. The seats then go to the seven candidates with the highest scores – represented by the seven tallest bars on the chart.
Here, the first two seats go to the first candidates for UKIP and the Conservatives. The third seat goes to Labour’s first candidate, narrowly ahead of UKIP’s second candidate, who finishes fourth. The last three seats go to the second Conservative, then the third UKIP candidate, then the third Conservative. Overall, UKIP and the Conservatives get three seats each, with one for Labour.
While the system gives a reasonably proportional result, it does tend to favour larger parties. Here UKIP got three seats from a vote share of 2.41 sevenths, and the Conservatives did particularly well, getting three seats from slightly less than two-sevenths of the vote. Meanwhile the Greens and Lib Dems got enough votes for 0.6 and 0.5 MEPs respectively, but came away with nothing. To illustrate this further, let’s see how many MEPs would be elected based on the remarkable recent Opinium opinion poll, which put the Brexit party on 34%, ahead of Labour on 21%, the Lib Dems on 12%, and the Conservatives languishing in fourth place with 11%. Here’s what the chart looks like:
With seven seats to allocate, the Brexit party gets three, Labour take two, and there is one each for the Lib Dems and the Conservatives. But now look what would happen if the Lib Dems, Greens and Change UK run as a single “Remain” list:
On the same vote shares, the Brexit party still gets three, but Remain is now in second place with two, with just one each for Labour and the Conservatives. So it looks like the failure of the Remain parties to run as a single list is likely to end up costing them seats. We’ll find out when the votes are counted on Sunday 26 May.