Proportional Representation in Regional Constituencies. How does it work?

For Westminster elections, parties each put up one candidate for each constituency. The one with the most votes wins the single seat available (even if that’s with far fewer than 50% of the votes).

For the European Parliament, each party puts up a team of candidates for the multi-seat constituencies. How many of their team get elected depends on their proportion of the vote. Parties have to list their candidates in ranking order: if they win one seat, the top candidate gets it, if they win two seats, the top two, and so on. Voters can then see which individuals are likely to be elected.

Given that it is done regionally, not nationally, with only a few seats in each region, small parties are unlikely to win seats. The share-out is reasonably proportional among the larger parties, but small margins can make the difference between them.

The calculation is based on a method worked out by a 19th Century Belgian mathematician called D’Hondt, and is widely used in proportional representation electoral systems.

It works by allocating the first seat to the party with the most votes, then dividing its vote by two before making a new calculation for allocating the next seat. (This tests whether or not the winning party got more than double the number of votes of the second party. If it did, it gets the next seat, otherwise the second party does, with its score then divided by two, and so on.  Similarly, once a party gains a third seat, its score is divided by three to see whether or not it got more than three times the score of the next party.)

Let’s take an example. Take a six member region (as is the case in, for example, in Yorkshire & Humber). Suppose these are the results (expressed as percentages for easy calculation).


The first of the six seats is allocated to Party A as it got the most votes. The figures are then looked at again with Party A’s total being divided by two (to make 14.5%).

Now, the largest figure is for Party B, which takes the second seat. Its score is then divided by two to make 14%.

The highest figure now is for Party A again, which takes the third seat, as it now has the largest total, ahead of Party C. (This reflects the fact that Party A got more than double the number of votes of Party C, so gets a second seat before party C gets one. If Party A had only had 28%, then its share divided by 2 would be 14, below party B, so the latter would have got the 3rd seat ahead of A.)

Having obtained a second seat, Party A’s original figure of 29 is now divided by three to make 9.66%.

Now the highest score is Party C which gets its first seat and its original figure of 14.1% is divided by 2 to make 7.05%.

Now, Party B has the highest figure, so takes its second seat, with its score of 28% now divided by 3 to make 9.33%.

This leaves Party A with the highest score to take the sixth and last seat (its third) by a fine margin against Party B. The final allocation of seats is therefore:

What is striking about this is that none of the small parties get enough votes to gain a seat. Despite having 28% of the vote between them,a vote for them is a “wasted vote” in terms of seats. (And this would have been true even if it had been a seven seat constituency.)

Also striking is that if the top two parties are close, which is quite conceivable, then a very small margin can determine which one gets the last seat (and therefore the most seats). Multiplied across several regions, that could change the result nationwide and the perceptions of who won.

In this technical explanation, I will not get political, but it is of course obvious that the top two parties in the European election could well be the Labour Party and the Brexit Party battling it out for first place and therefore the most seats, with the Tories in third, and the LibDems, Greens and ChangeUK failing to win a seat in a region of this size or smaller (that is, most UK regions).

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14 Comments

  1. This suggests that tactical voting will be difficult. Instead of focussing on getting largest no. of pro EU seats we should focus on maximising the % of votes cast for remain parties as a base for establishing a strong remain mood in the UK and a basis for winning an eventual PV.

    • Alas this still doesn’t tell me who I should vote for! Because I won’t know which remain party is likely to score the highest in my region. Remain parties should form an alliance and present only candidates from one party in each region. They should work out between themselves which party should be favourite in each region. And if it happens that LibDems would get a higher number of votes than any of the others in every region, so be it! they should be the only party to present candidates. Being greedy for seats will result in fewer seats for everyone of the remain parties.

    • It isn’t just about the Uk though (uppermost in our thoughts as it is). By splitting the vote – not just here but in many European countries – the small parties may get nothing & larger, very unpleasant parties may benefit.

    • I agree with you Hugh-let’s improve the mood in this country towards remaining in the EU – most of what we have been told over the years about the EU has been negative…e.g. straight bananas….but holiday pay entitlement for part time workers -like other positive policies/laws – are overlooked and not reported! Having the right to holiday pay was significant to my being able to have a holiday as a part-time worker – because as we know most part-time workers are expectd to achieve what a full-time worker does!

    • Yes to the first, but the second? Depends on your point of view. This is not a referendum, it’s an election. If we can convert Con/UKIP/BP seats to Labour, that’s a victory. A PV would look totally different again, with many people voting differently when not tied to a seat allocation and parliamentary bloc that defines EU policy for years to come.

  2. I would always have voted Labour but this time it’s different. The party leadership want Brexit and rather than being unequivocal about a People’s Vote they now say that this is a very last resort. While my vote may well be a ‘wasted’ one in Richards opinion, in that it won’t help generate an anti-Brexit seat, it will at least be counted as a pro-Remain vote.

    Sorry Richard, I admire you but I don’t admire your parties leadership.

  3. If I’ve understood this correctly, and remembering that there are eight seats in London, you could argue that a vote for one of Lib Dem, Change and Green could stop the Conservatives getting a second seat by allowing the weakest of the three to get their first instead. I couldn’t find any polling for London but ran it through for the latest percentages for the country (I suspect far more pro Brexit than London) and got Brexit Party 2 seats, Labour 2 seats, Conservative 2 seats, Lib Dem 1 seat and Change 1 seat.
    Extra votes for Change would have got them their first seat and might possibly have been more useful than trying to get the Lib Dems their second! Difficult to say. Anyway Labour isn’t a remain party is it? Is it?

  4. Sorry, I should have said ‘Brexit Party 2 seats, Labour 2 seats, Conservative 2 seats, Lib Dem 1 seat and Green 1 seat’ not Change.

  5. Succinctly explained Richard. Agree with Hugh that an unorganized tactical vote for a pro-EU party dilutes (and likely as described negates) such a vote, so we must ALL get behind ONE single group.
    Sadly, that must be largest of those remain parties, the Lib-Dems

  6. Also goes to show how a vote for the Brexit Party will be a wasted vote – given the history of their party members is of an MEP who fails to turn up for votes and debates, and fiddled their expenses. Funny how the Brexit Party are anti-EU, yet want job as MEPs so they can be paid a salary and pension by the EU.

  7. This is based on the assumption that people will vote Labour, but I know that many Remainers are so disgusted with the Labour left leadership, that they will vote for a pro-Remain party such as LibDem. If this happens, is it then possible that LibDem could have the largest number of votes? I also think it could be a low turnout as people are so fed up. The determined Brexiteers however will almost certainly turn out to vote.

  8. Weird algorithm. If it were truly proportional there’d be 4 parties in — 2 As, 2 Bs, 1C and 1D. Looks like the modern academic disease (cleveritis) has infected the law.

  9. Until otherwise, I shall continue to vote for MEPs that represent my values in Europe (i.e., Labour) rather than treat this as a proxy referendum. Bear in mind, though, that single-issue foghorns and their backers have no scruples in bending stats (“17.4 mill voted to leave on No Deal, oh yes they did, and 82% – including me, apparently – voted for Brexit in the last GE”). The ones who’ve spotted this oppo to clean up at everyone else’s expense will certainly mantra the number that suits them best.
    I’ve long reckoned that the Out Means Out types represent, at best, 35% of the population but, with the implosion of UKIP and Tories not even trying, the whole lot will go Nigel’s way. As the above example shows, this will likely result in 35% returning half, or even a bit more, of the UK’s MEPs.
    Prepare for much repeated shouting that “We’ve had our 2nd referendum, and it was a clear majority for WTO” despite virtually none of these Brexit MEPs, never mind their voters, having much of a clue what that means.

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