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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