## Voting tactically in the EU elections

This post is addressed at anyone who is voting in Great Britain in the forthcoming elections to the European Parliament and whose principal aim is to maximize the number of MEPs from Remain-supporting parties, where those are deemed to be the Liberal Democrats, the Greens, Change UK, Plaid Cymru and the Scottish National Party. If you have other priorities, then the general principles laid out here may be helpful, but the examples of how to apply them will not necessarily be appropriate to your particular concerns.

### What is the voting system?

The system used is called the d’Hondt system. The country is divided into a number of regions, and from each region several MEPs will be elected. You get one vote, and it is for a party rather than a single candidate. Once the votes are in, there are a couple of ways of thinking about how they translate into results. One that I like is to imagine that the parties have the option of assigning their votes to their candidates as they wish, and once the assignments have been made, the $n$ candidates with the most votes get seats, where $n$ is the number of MEPs representing the given region.

For example, if there are three parties for four places, and their vote shares are 50%, 30% and 20%, then the first party will give 25% to two candidates and both will be elected. If the second party tries a similar trick, it will only get one candidate through because the 20% that goes to the third party is greater than the 15% going to the two candidates from the second party. So the result is two candidates for the first party, one for the second and one for the third.

If the vote shares had been 60%, 25% and 15%, then the first party could afford to split three ways and the result would be three seats for the first party and one for the second.

The way this is sometimes presented is as follows. Let’s go back to the first case. We take the three percentages, and for each one we write down the results of dividing it by 1, 2, 3, etc. That gives us the (approximate) numbers

50%, 25%, 17%, 13%, 10%, …

30%, 15%, 10%, 8%, 6%, …

20%, 10%, 7%, 5%, 3%, …

Looking at those numbers, we see that the biggest four are 50%, 25% from the top row, 30% from the second row, and 20% from the third row. So the first party gets two seats, the second party one and the third party one.

### How does this affect how I should vote?

The answer to this question depends in peculiar ways on the polling in your region. Let’s take my region, Eastern England, as an example. This region gets seven MEPs, and the latest polls show these kinds of percentages.

Brexit Party 40%
Liberal Democrats 17%
Labour 15%
Greens 10%
Conservatives 9%
Change UK 4%
UKIP 2%

If the percentages stay as they are, then the threshold for an MEP is 10%. The Brexit Party gets four MEPs, and the Lib Dems, Labour and the Greens one each. But because the Brexit Party, the Greens and the Conservatives are all close to the 10% threshold, small swings can make a difference to which two out of the fourth Brexit Party candidate, the Green candidate, or the Conservative candidate gets left out. On the other hand, it would take a much bigger swing — of 3% or so — to give the second Lib Dem candidate a chance of being elected. So if your main concern is to maximize the number of Remain-supporting MEPs, you should support the Greens.

### Yes, but what if everybody were to do that?

In principle that is an annoying problem with the d’Hondt system. But don’t worry — it just isn’t going to happen. Systematic tactical voting is at best a marginal phenomenon, but fortunately in this region a marginal phenomenon may be all it takes to make sure that the Green candidate gets elected.

### Aren’t you being defeatist? What about trying to get two Lib Dems and one Green through?

This might conceivably be possible, but it would be difficult, and a risky strategy, since going for that could lead to just one Remain-supporting MEP. One possibility would be for Remain-leaning Labour voters to say to themselves “Well, we’re basically guaranteed an MEP, and I’d much prefer a Remain MEP to either the Conservatives or the Brexit Party, so I’ll vote Green or Lib Dem instead.” If that started showing up in polls, then one would be able to do a better risk assessment. But for now it looks better to make sure that the Green candidate gets through.

### I’m not from the Eastern region. Where can I find out how to vote in my region?

There is a website called remainvoter.com that has done the analysis. The reason I am writing this post is that I have seen online that a lot of people are highly sceptical about their conclusions, so I wanted to explain the theory behind them (as far as I can guess it) so that you don’t have to take what they say on trust and can do the calculations for yourself.

Just to check, I’ll look at another region and see whether I end up with a recommendation that agrees with that of remainvoter.com.

In the South West, there are six MEPs. A recent poll shows the following percentages.

Brexit Party 42%
Lib Dem 20%
Green Party 12%
Conservatives 9%
Labour 8%
Change UK 4%
UKIP 3%

Dividing the Brexit Party vote by 3 gives 14% and dividing the Lib Dem vote by 2 gives 10%. So as things stand there would be three Brexit Party MEPs, two Lib Dem MEPs and one Green Party MEP.

This is a bit close for comfort, but the second Lib Dem candidate is in a more precarious position than the Green Party candidate, given that the Conservative candidate is on 9%. So it would make sense for a bit of Green Party support to transfer to the Lib Dems in order to be sure that the three Remain-supporting candidates that look like being elected in the south west really are.

Interestingly, remainvoter.com recommend supporting the Greens on the grounds that one Lib Dem MEP is bound to be elected. I’m not sure I understand this, since it seems very unlikely that the Lib Dems and the Greens won’t get at least two seats between them, so they might as well aim for three. Perhaps someone can enlighten me on this point. It could be that remainvoter.com is looking at different polls from the ones I’m looking at.

I’m slightly perturbed by that so I’ll pick another region and try the same exercise. Perhaps London would be a good one. Here we have the following percentages (plus a couple of smaller ones that won’t affect anything).

Liberal Democrats 24% (12%, 8%)
Brexit Party 21% (10.5%, 7%)
Labour 19% (9.5%, 6.3%)
Green Party 14% (7%)
Conservatives 10%
Change UK 6%

London has eight MEPs. Here I find it convenient to use the algorithm of dividing by 1,2,3 etc., which explains the percentages I’ve added in brackets. Taking the eight largest numbers we see that the current threshold to get an MEP is at 9.5%, so the Lib Dems get two, the Brexit party two, Labour two and the Greens and Conservatives one each.

Here it doesn’t look obvious how to vote tactically. Clearly not Green, since the Greens are squarely in the middle of the range between the threshold and twice the threshold. Probably not Lib Dem either (unless things change quite a bit) since they’re unlikely to go up as far as 28.5%. But getting Change UK up to 9.5% also looks pretty hard to me. Perhaps the least difficult of these difficult options is for the Green Party to donate about 3% of the vote and the Lib Dems another 2% to Change UK, which would allow them to overtake Labour. But I don’t see it happening.

And now to check my answer, so to speak. And it does indeed agree with the remainvoter.com recommendation. This looks to me like a case where if tactical voting were to be widely adopted, then it might just work to get another MEP, but if it were that widely adopted, one might have to start worrying about not overshooting and accidentally losing one of the other Remain MEPs. But that’s not likely to happen, and in fact I’d predict that in London Change UK will not get an MEP because not enough people will follow remainvoter.com’s recommendation.

### This all seems horribly complicated. What should I do?

If you don’t want to bother to think about it, then just go to remainvoter.com and follow their recommendation. If you do want to think, then follow these simple (for a typical reader of this blog anyway) instructions.

1. Google polls for your region. (For example, you can scroll down to near the bottom of this page to find one set of polls.)

2. Find out how many MEPs your region gets. Let that number be $n$.

3. For each percentage, divide it by 1, 2, 3 etc. until you reach a number that clearly won’t be in the top $n$.

4. See what percentage, out of all those numbers, is the $n$th largest.

5. Vote for a Remain party that is associated with a number that is close to the threshold if there is also a Brexit-supporting (or Brexit-fence-sitting) party with a number close to the threshold.

One can refine point 5 as follows, to cover the case when more than one Remain-supporting party has a number near the threshold. Suppose, for the sake of example, that the Brexit party is polling at 32%, the Lib Dems at 22%, the Greens at 11%, Labour at 18% and the Conservatives at 12%, and others 5%, in a region that gets five MEPs. Then carrying out step 3, we get

Brexit 32, 16, 10.6
Lib Dems 22, 11
Greens 11
Conservatives 12
Labour 18, 9

So as things stand the Brexit Party gets two MEPs, the Lib Dems one, Labour one and the Conservatives one. If you’re a Remain supporter who wants to vote tactically, then you’ll want to push one of the Lib Dems and the Greens over 12% to defeat the Conservative candidate. To do that, you’ll need either to increase the Green vote from 11% to 12% or to increase the Lib Dem vote from 22% to 24%. The latter is probably harder, so you should probably support the Greens.

### A final word

I’m not writing this as an expert, so don’t assume that everything I’ve written is correct, especially given that I came to a different conclusion from remainvoter.com in the South West. If you think I’ve slipped up, then please let me know in the comments, and if I agree with you I’ll make changes. But bear in mind the premise with which I started. Of course there may well be reasons for not voting tactically, such as caring about issues other than Brexit. But this post is about what to do if Brexit is your overriding concern. And one obvious last point: PLEASE ACTUALLY BOTHER TO VOTE! Just the percentage of people voting for Remain-supporting parties will have an impact, even if Farage gets more MEPs.

### 13 Responses to “Voting tactically in the EU elections”

1. Joseph Says:

I think the following shows that that the poll you’ve used for the South West gives different results to the ones you’ve stated.

Brexit Party 42 (21, 14, 10.5)
Lib Dem 20 (10, 6.7, 5)
Green 12 (6, 4, 3)
Conservative 9 (4.5, 3, 2.3)
Labour 8 (4, 2.7, 2)
Change UK 4 (2, 1.3, 1)
UKIP 3 (1.5, 1, 0.8)

So this gives the Brexit Party four MEPs, the Lib Dems one MEP and the Greens one MEP. For the Lib Dems to get a second they would need an increase of >1% to come from the Greens which could then leave the Greens vulnerable to the Conservatives. Of course this looks quite close so perhaps voting for either Lib Dem or Green has it’s advantages.

• gowers Says:

My guess is that this is indeed remainvoter.com’s reasoning — going for an extra Lib Dem seat looks too risky.

2. lockywolf Says:

Why would anyone be willing to pursue such a strange goal?

• gowers Says:

I don’t find it strange myself, but that’s because (i) I’m not wedded to party politics and (ii) Brexit is my overriding concern at these elections.

3. Confused Says:

What are the numbers in brackets? E.g.

Liberal Democrats 24% (12%, 8%)

• gowers Says:

They are what you get when you divide the original percentage by 2, 3, 4, etc. They are there to help calculate who gets the MEPs, as explained at the end of the section “What is the voting system?” (where I didn’t put them in brackets).

4. Louise Bell Says:

I agree with all this and I think the reason your result is different in SW is RV are using grades averages of all polls obv smaller and older polls have less weighting than newer bigger polls. This is probably a more responsible approach than looking at just one poll in isolation. And unfortunately in this case has given a different result.

• gowers Says:

You raise an important point that I should have emphasized more, which is that remainvoter.com have put a lot more effort into crunching the numbers than I have, and I think they take into account more subtle effects such as the likelihood of someone switching from one party to another. So in a case like the South West, where it isn’t completely obvious what the right conclusion is, their recommendation is likely to be better than my back-of-envelope calculation.

5. James Says:

Is maximising the number of Remain-supporting MEPs an important objective? Will the balance of the UK representation in the European Parliament have much effect on whether/how Brexit goes ahead? (And afterwards, if Brexit does go ahead, it doesn’t much matter which MEPs we elected.)

Instead it might be better to treat this as a glorified opinion poll. (I.e. the effect you mention in your final sentence may actually be the dominant one.) Looking ahead, it’s more important to have as strong a showing as possible for a single party that could have a serious effect at a general election if one is held soon. That should push Remain-supporting voters strongly towards voting Liberal Democrat. If the LibDems were to outscore both Labour and the Conservatives, that would have some impact. (I can’t see a scenario in which Change UK supplant the LibDems, and a general election scenario where they split the vote in a widespread way would be terrible.)

So, for example, switching away from LibDem to Change UK for “tactical” reasons seems like a bad idea.

• gowers Says:

As far as the glorified opinion poll is concerned, I think that the figure that people will pay attention to is the total number of votes for Remain parties versus the total number for Brexit parties. Since switching one’s vote tactically from one Remain party to another doesn’t affect that, one might as well also try to increase the number of MEPs (ideally at the expense of Farage’s Brexit party).

Whether that’s more important than the Lib Dems doing well and therefore becoming the undisputed Remain party, which could well be the best way for Remain to do well at the next general election, is a delicate question. I can certainly see the case for trying to make sure Change UK do badly so that they are killed off and don’t cost the Lib Dems seats in Westminster. (I say that as someone who is very grateful for everything that the current Change UK MPs have done to fight against Brexit.)

6. pait Says:

The problem is that the uncertainty in vote intention polls is overwhelming. Differences of a few percentage points are barely significant.

I think it might be better to simply choose the best candidates, which in this election must be the Liberals and the Green ones.

7. gowers Says:

I have just contacted @remainvoter.com and had a further explanation of a point that had been bothering me. On their site, they suggest that in Scotland you should vote for the Lib Dems, and they predict that that will lead to an additional seat for the SNP. Apparently that’s because they are taking into account more complex effects such as that additional Lib Dem votes from undecided voters are more likely to come from Labour, and reducing the Labour vote helps the SNP.

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