Making social science accessible

06 Nov 2019

Politics and Society

Brexit Party
At the Brexit Party campaign launch, Nigel Farage claimed that UKIP had ‘disproportionately hurt the Labour party in the 2015 general election’ and that the Brexit Party would do the same again in 2019.

My colleagues on the British Election Study have shown that Farage is wrong: the Brexit Party – and UKIP before it – mainly draws voters away from the Conservatives, not Labour.

The Conservatives won a majority in 2015 despite UKIP, not because of them. Likewise, the Conservatives lost their majority in 2017 despite the UKIP collapse, not because of it.

That UKIP and the Brexit Party primarily draw their support from the Conservatives is not a new finding – Geoff Evans and Jon Mellon first pointed it out in 2015.

Why then, does this idea continue to persist?

One possibility is that politicians, journalists, canvassers, and ordinary citizens might talk to Labour-Leave voters and find that they are more likely defect to the Brexit Party than Conservative-Leave voters.

But this doesn’t mean that the Brexit Party is more of a threat to Labour, because both of these things can be true at the same time:

  • Labour-Leavers are more likely to defect to the Brexit Party than Conservative-Leavers.
  • More Conservative voters are likely to defect to the Brexit Party than Labour voters.

The reason that both of these things can be true at the same time is simply that there are lots more Conservative-Leave voters out there than Labour-Leave voters: the British Election Study data suggests the proportion of 2017 Labour voters who voted Leave was about 31% (and this doesn’t vary that much between constituencies), while about 73% of 2017 Conservatives voted Leave.

Failing to take this ‘base rate’ into account is a very common mistake that people make when reasoning about probability – and the question of whether the Brexit Party is a threat to the Conservatives or Labour is, at its core, a question about probability.

People are not making this mistake because they are stupid. As Professor Sir David Spiegelhalter – one of the top statisticians in the country – has said, people find probability unintuitive and difficult because it is unintuitive and difficult!

Fortunately, however, statisticians have learned that people find probability much easier to understand when you express things in terms of expected frequencies rather than as probabilities and percentages.

So, for the remainder of this blog I’m going to do just that, and try and explain why the Brexit Party is more of threat to the Conservatives than Labour, even if Labour-Leavers are more likely to defect to the Brexit Party.

Imagine a seat with 100 voters. This seat is an ultra-marginal and last election, 51 people voted Labour and 49 voted Conservative.

Then, let’s say about 35% of Labour voters in this seat voted Leave in the referendum, which means there are 18 Labour-Leavers. And let’s say 70% of Conservatives voted Leave, which means there are 34 Conservative-Leavers in our seat.

This means that, like the country as a whole, this seat voted 52 Leave to 48 Remain in the referendum.

To make the easier to follow, I’ve turned these numbers into a chart, which shows Leavers as solid circles and Remainers as shaded circles.

Brexit Party

Now let’s say the Brexit Party is better at recruiting Labour-Leavers than Conservative-Leavers. In my scenario, one in two Labour-Leavers defect to the Brexit Party but only one in three Conservative-Leavers do the same.

With 18 Labour-Leavers that means nine people defect to the Brexit Party from Labour, while from 34 Conservative-Leavers 11 defect. The end result is that Labour win the seat again, 42 votes to 38 – an increase in the size of their majority.

Brexit Party

At this stage I should point out that these numbers are very generous to the ‘Brexit Party is a threat to Labour’ argument.

At the 2019 European Parliament election, the British Election Study data suggest that Conservative-Leavers were more likely to defect to the Brexit Party than Labour-Leavers.

This has changed since Boris Johnson (who was very popular with Brexit Party voters) became Prime Minister.

More recent survey data suggests that Labour-Leavers might now be more likely to defect to the Brexit Party, but at a rate of about one in four, compared to one in five Conservative-Leavers – considerably less than the rate of defection in my example.

Now let’s imagine another seat, again an ultra-marginal. However, this one has a Conservative incumbent who won 51 votes compared to Labour’s 49.

To keep things simple I’ll keep the proportions voting Leave and Remain the same as last time. 35% of Labour voters voting Leave is 17 people, while 70% of Conservatives voting Leave is 36 people.

In total, this seat is slightly more Leave-y than my other seat, with 53 people supporting Leave and 47 supporting Remain.

Brexit Party

Again one in two Labour-Leavers defect to the Brexit Party, which means nine defectors, and one in three Conservative-Leavers defect, which is 12 people.

The end result of all this switching is that – despite the overall support for Leave being higher than my previous example – Labour wins the seat off the Conservatives, 40 votes to 39.

Of course, this isn’t to say that the Brexit Party wouldn’t pose a threat to Labour if they recruit enough Labour-Leave voters.

However, there are more than twice as many Conservative-Leave voters as there are Labour-Leave voters. So to pose a threat to Labour rather than the Conservatives, the Brexit Party would need to recruit Labour-Leavers at more than twice the rate they recruit Conservative-Leavers.

The current polls suggest the Brexit Party are a long way from achieving that. Conservative-Leavers and Labour-Leavers seem to be defecting at similar rates – the net result being that more than twice as many Conservatives are switching to the Brexit Party compared to Labour voters.

So to cut a long story short, if you’re a politician, journalist, canvasser, or just an ordinary citizen: you may well talk to Labour-Leavers and find that more of them are defecting to the Brexit Party than Conservative-Leavers.

But you need to remember that there are many more Conservative-Leavers out there, which is why the Brexit Party poses a threat to the Conservatives.

By Chris Prosser, Presidential Fellow at the University of Manchester and Co-Investigator of the British Election Study


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