How the d’Hondt system works for the European Parliament elections

Verification of ballot papers at an election count - photo from Coventry City Council, used under the CC BY-NC-ND 2.0 license - see https://www.flickr.com/photos/coventrycc/26840047475/ for full license information

Verification of ballot papers at an election count. Photograph from Coventry City Council, used under the CC BY-NC-ND 2.0 license.

Electoral system for European Parliament elections

For European Parliament elections in Scotland, Wales and England a form of list proportional representation is used, called the d’Hondt system. (STV is used in Northern Ireland.)

Voters get a ballot paper with the names and logos of different parties and get to put one cross against one of those parties. There is no preferential (1, 2, 3 etc.) voting.

Candidate lists

Next to each party name on the European election ballot papers is also the list of their candidates to be a Member of the European Parliament (MEP), in order from number one downwards. If the party gets one seat selected, their top name is elected, if two then their top two names, and so on.

Voters, therefore, get to see which candidates will be elected but they can’t change the order of those candidates. For example, if someone really dislikes the top name on a party’s list but likes the second name then they are still forced to choose between voting for that party or not. They can’t say ‘I want to vote for party X but I don’t want the top name and instead want to prefer someone lower on that list’.

This makes the Euro elections a ‘closed list’. Some versions of list PR allow voters to pick their preferred candidate from a party’s list too; this is called an ‘open list’ election but isn’t the system used in England, Scotland and Wales.

This matters as, for example, Labour’s candidates for the European Parliament election include a mix of Remain and Leave supporters. Voters only get to decide whether or not to vote Labour; they can’t choose between Leavers and Remainers in Labour’s lists of names.

(Independents can also stand on their own. Think of them as special lists of just one name.)

Constituencies for the European Parliament election

Those candidate lists are not simply one list for all of England, Scotland and Wales. Rather, there are separate lists for Scotland, Wales and each of nine regions in England. Votes are counted within each of those eleven areas and used to decide how many MEPs each list wins in each of those areas.

The Brave New Not Too Ideological Dawn Party, for example, might run only in those nine England regions and get two MEPs in one region, one in another and none at all in the rest.

Turning votes into seats: d’Hondt

The conversion of votes into seats in each of those eleven areas is done using the d’Hondt system. The idea is that the number of votes a list (party) gets in that area should determine how many seats it gets. If you get half the votes, you should get half the seats, etc.

This is very different from first past the post where, as the 2015 general election in Scotland starkly demonstrated, you can get nearly all the seats with less than half the votes.

The complication is that there are not enough seats to go around to make all the allocation that proportional. For example, Wales has four MEPs. Should a party that gets 20% of the vote get one MEP (25% of the total) or zero seats (0%)? Instinctively, you may think that one seat is better than zero given how close 20% is to 25%. But for elections, precise rules are needed.

Which is where d’Hondt comes in. Named after the Belgian lawyer who invented the system in the 19th century (pause to marvel that the electoral system under which Ukip has done best in the UK is one from a Belgian…), d’Hondt uses the ‘highest average’ method.

It works like this:

  • See which party in the area has the largest number of voters. They get the first seat.
  • Divide that party’s vote by one more than the number of seats it has won (two, in this case).
  • Now look at all the party vote totals and whoever has the largest total gets the next seat.
  • Divide that party’s vote by one more than the number of seats.
  • Carry on doing this – give a seat to the largest, then divide it, then look again at who now has the largest – until all the seats are allocated.

For a numerical example with vote totals and all the calculations, see this one from the BBC.

I also quite like this rather different explanation from mathematician Helen J. Wilson:

Suppose you are in charge of allocating seats to parties. Once the votes have all been cast and counted, you are faced with a group of parties each of which has a certain number of votes.

You have a set of seats to allocate. The D’Hondt method is, in principle, very simple. You simply “sell” each seat to a party. Each seat “costs” the same number of votes; and each party buys as many seats as it can (and its leftover votes that are worth less than a seat, are discarded).

What is the practical implication of d’Hondt?

Because d’Hondt is used separately in each of Scotland, Wales and the nine English regions, and therefore to dole relatively small numbers of seats in each case (between four and ten), the results can end up quite a way off being proportional.

In particular, it is possible for quite a lot of votes to be ‘wasted’ by going to parties who do not quite reach the threshold for getting one seat. As a result, tactical voting to pump up the support of another party can make sense just as it does in first past the post. With d’Hondt there is, as it were, more than one post. The logic though that tactical voting can help one party past the post still applies. It’s just a bit more complicated to work out what tactical voting option might work best.

Or, to adapt Helen Wilson’s terminology from above, each seat may be sold for the same number of votes – and so parties who run up some votes but not enough to afford the price of even one seat end up with their votes wasted.

That means, for example, that Remain voters face the risk of their votes being split between different new or not so new parties – and so electing fewer Remain MEPs than if Remain voters vote tactically to maximise their impact.

Crucial also, though, is that point about the lists being closed lists. For parties putting up candidate lists containing people with a mix of views on Britain’s place in the European Union, such as Labour who have both those who want Britain to leave the EU and those who want it to remain on their candidate lists, voters are forced either to accept voting for a mixed group of candidates or to vote for another party/list instead.

26 responses to “How the d’Hondt system works for the European Parliament elections”

  1. Thinking of the forthcoming European elections (providing they take place), d’Hondt means that if the three pro-Remain parties (LibDems, Green and ChangeUK) run separately and take approx 8% of the vote each (probably a bit higher in London and the South East, a bit lower in the North and the Midlands) – as current opinion polls suggest – then at a push they may get one apiece in the South East, two (total) in London, but will cancel each other out in most other regions. A total of – let us say – six or seven seats. Run together and 24% would win them at least one seat (and often more) in most, if not all, regions (with the possible exception of the North East, where only three seats are up for grabs). Thus they would net approx 18 seats combined. And if they co-operate, they may even get an extra bounce from voters who see them putting country before party. One scenario will make Nigel Farage very happy; the other will not.

  2. The explanation of the d’Hondt system, and Jon Wheatley’s comment, makes it starkly clear why it is crucial for there to be close cooperation between Lib Dems, Change UK and the Green Party in England, and possibly between Lib Dems and SNP in Scotland, if we are to have the strongest voice for Remain in the Euro election. (I am less sure about the best arrangements for Wales and NI). It is not a matter of having a strong platform for working within the EU Parliament, but more of a launching pad for getting and winning a new referendum. We can also make a virtue of acting in the national interest, rather than along the narrow sectarian interests adopted by Labour and Conservatives.

    • Almost a month on from Dr John’s comment, and no alignment of the Remain parties has occurred. Such a shame, because this is the opportunity for Remain as a whole to make a huge statement. Yet, instead, it’s likely that the votes split between Lib Dems, Change and Green/SNP, will dilute that statement, and the elections will be a damp squib. I wish egos and ambition could have been set aside just once, for a last bid to stop the madness. History would have thanked them. Even Churchill “crossed the floor” from the Libs to the Tories, and he’s a “Great British Hero”… I wonder how different things would look if Chukka et al had have joined Vince Cable and his gang, rather than set up alone in a short lived blaze of glory and headline.

  3. Jon you are so correct. Hopefully the Remain parties can still come to some sort of Agreement so that we can truly fight Farage and his cronies.

  4. Surely there are 9 constituencies in England:
    East of England
    East Midlands
    West Midlands
    Yorkshire and Humberside
    North East

  5. Excellent explanation of the voting process and a powerful reminder that fractured voting can result in many wasted votes. The LibDems remain the stand out advocates for those seeking to defeat Brexit. But reality politics should prevail and the Change crowd and the Greens should be accommodated in a rainbow coalition (yes that awkward term) for the electoral tussle.

  6. The ‘south west’ includes Gibraltar. Do we know how people in Gibraltar vote? Surely not for UK parties? Or are most of them expat Tories? What impact do their votes have on the overall result?

    Given that the vast majority were Remain voters in the referendum, are Lib Dems able to capitalise on this for the European elections?

    • Not just Gibraltar but how might all the EU citizens (Poles, Romanians, French etc) in the UK vote? They couldn’t participate in the referendum but can vote in the European Parliament elections.

  7. Thanks, Mark. This, surely, is the key point that needs hammering.

    Voters only get to decide whether or not to vote Labour (or Conservative); they can’t choose between Leavers and Remainers in Labour’s lists of names.

    If you are Remain, a vote for Labour or Tory will be a wasted vote.

  8. This is an excellent exposition of the d`Hondt voting method used in the EU Elections in England,Wales and Scotland but STV in N Ireland-Why? and this method appears to hold more positive factors for all those who support a fairer and more proportionate voting system that clearly includes all Remainer Political Parties led by the Liberal Democrats: fighting againsit the imposition of Brexit.

    This EU Election- that none of the `Brexit’ wanted in place- is now evident to test by how much the Tories and Labour voting will be decimated by widespread media reports that the Tories are due to record their lowest support return since 1832 and that Labour are incapable of clarity on the Second Referendum may will lose out in their Leave Regions.

    The observation made by Sir Vince et al that there is more virtue for the `Remain’ Political Parties to share a common platform in the EU Elections but not across the board, is well taken and understood at the Liberal Democrat `Grassroots’.

    The `D`Hondt Voting EU voting sytem is more honest to individual voters generally since it was introduced but will not serve democratic justice in 2019, as voters cannot identify specific candidates, who support `Remain’ and `Leave’ clearly and judiciously on the ballot Paper and there is further confusion that Labour have not declared on support for the `Second Referendum’.

    We shall also see how keen EU Voters transfer support to the Local Elections in May 2nd!

  9. Thanks Mark for this excellent explanation of the d’Hondt system for the European Parliament elections, and thus the clear need for Remain parties to cooperate seamlessly if the UK participates.
    In the longer term, whether the UK remains in the EU or departs, the battle to use STV in our elections will need to go on. It’s not only fairer and more proportionate, as others have stated, but it also properly enables electors to take electoral power from the parties, both by ordering a party’s candidates according to their own preferences, and also by choosing their preferences from among all the parties’ lists.
    These possibilities would have had clear advantages, especially for the voters of the divided Labour and Tory parties, in this virtually single issue Euro-election in the UK. Analagous advantages apply to local and general elections, so long as the number of members to be elected is likewise not too small.

  10. Can anyone tell me the following – do voters have a single cross against a party or independent candidate? I’m interested in London. Thanks!

  11. Fortunately this is less of a problem for Leave voters. They only have two parties on the ballot paper and therefore less of a chance of diminishing the Leave vote.

    Given UKIP diminishing influence then Brexit Party should go well logically and mathematically.

  12. Is there a website where one can try online the results of the d’Hondt system for the European Parliament elections with various alternative percentages?

  13. I’m wanting to vote by proxy, but I am confused about the vote for candidates in the south east region. I know there are ten candidates for this region, but how do I register my vote?
    What will the form of nominees look like?

    • Hi Alan – if you read the bit in the post about the ballot papers above, that should explain matters – you get one vote for one party/independent list of candidates, i.e. you put one cross on the ballot paper.

  14. Again following on from Helen Wilson’s cost-per-seat analysis, one of the ways that the small parties could also act tactically would be to try to ensure that there are a lot of wasted votes amongst the three leave parties (brexit UKIP and Tory) i.e. the remain parties make sure that they have more than half the votes of any of the leave parties, so evening out the votes between your opponents may be just as effective

  15. So I am still confused as to whether I should vote Green or LibDem in Wandsworth London to Remain!

  16. I also very much like Helen Wilson’s explanation of the principle behind d’Hondt. But I think it might help if you included the paragraph after the two you quote, viz.

    Your job is to set the price of a seat so that, at the end of this process,
    •there are no seats left unsold; and
    •no party has enough votes left over to buy another seat.
    The technical method is simply a process whereby you initially set the price too high, and iteratively reduce it until you reach the right value.

  17. Quick question I’ve not been able to find an answer for…

    What happens in the D’Hondt method if an independent (ie list of one) gets enough votes for two seats?
    Do you just allocate an extra seat (eg if there were meant to be 8 seats, the party who “came 9th” get a seat too)? Or does it get more complicated than that?

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