Why a split anti-Brexit vote may not be as good for the Conservatives as we assume.

First published in October 2019.

Imagine Britain being a straight line, with 100 seats lined up in order of share of the vote for Leave, as in the picture. Yellow for Remain, purple for Leave.

Let’s further assume that Leave voters vote either Tory (blue) or Brexit Party (turquoise), and Remain voters vote either Labour (red) or Lib Dems (orange).

The difference is that the Conservatives rack up 2/3 of the Leave vote, while Labour and the Lib Dems get approximately half each. So, we get:

In this scenario, Conservatives get 34%, Brexit Party 16%, Lib Dems 26% and Labour 24% (50-50 Leave-Remain split, for simplicity – SNP and Plaid Cymru vote goes to other Remain parties).

If we compute who wins in each seat, we get the Tory majority people are expecting from a split opposition: 63-37.

HOWEVER, what if the distribution of the Remain vote is different, but the share for each remains the same?

Let’s assume, for instance, that Labour and the Lib Dems are not equally strong in all seats, but they have their own territorial strength instead, like so:

If the Lib Dems and Labour distribute their vote more efficiently among each other by being stronger where the other one is weaker, holding the shares of the votes constant (Conservatives 34%, Brexit Party 16%, Lib Dems 26% and Labour 24%), we get that the Conservatives don’t get a majority:

Now, obviously, there is no reason to assume that Remain voters are better at tactical voting than Leave voters (and we are not going to do that!). HOWEVER, it may be that Labour and the Lib Dems have ‘naturally’ more distinct electorates than the Conservatives and the Brexit Party.

Luckily, there is a way to test this.

Let’s take the European Election results of 2019, and regress the Labour vote on the Lib Dems vote for each local authority. What we get is that they are negatively correlated: the Lib Dems are stronger where Labour is weaker and vice versa.

Conversely, if we regress the Conservatives vote on the Brexit Party vote, we get that they are positively correlated: the Brexit Party is stronger where the Conservatives are stronger, and weaker where the Conservatives are weaker.

So, reality is closer to the world where – from a spatial point of view – Labour and the Lib Dems redistribute effectively, while the Conservatives and the Brexit Party do not, producing no Tory majority EVEN IF, from the point of view of relative share, the Leave parties should have an in-built advantage.

Now, obviously, it doesn’t mean that Remain parties couldn’t ALSO redistribute more efficiently their share as well as their territorial distribution.

If we hold party functions constant and move from a 26-24 split in the Remain vote to a 28.5-21.5 one, the Conservatives lose 3 more seats:


Leave parties have an in-built advantage due to the ratio of Conservatives-to-Brexit Party share. But Remain parties may have an in-built advantage due to territorial differentiation of their vote (if you add in the SNP and Plaid Cymru, it is even starker, given that these are ultra-territorial).

The way those two biases interact with each other will decide the results of the next election.🔷


  • I did it in base R because I haven’t got much time. The graphs look horrific but then again, I have a life.
  • I made the Lib Dems the larger Remain party purely to wind all the right people up.

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[This piece was first published as a Twitter thread and turned into the above article on 3 October 2019, with the author’s consent, with the purpose of reaching a larger audience. It has been minorly edited and corrected. | The author of the tweets writes in a personal capacity.]

(Cover: Gif.)