The EU referendum: how did Westminster constituencies vote?

tl;dr version: 421 out of 574 English and Welsh Westminster
constituencies probably voted to Leave

Update: more recent estimates are available here [spreadsheet; technical details]. These estimates include Scotland, and respect local authority boundaries better.

Yesterday morning Catherine West, the Labour MP for Hornsey and Wood Green, tweeted that she would vote against Brexit in Parliament.

Ms West motivated her decision by claiming that 75% of her constituents voted to remain in the EU.

There’s a problem with this claim. The results of the referendum were not announced according to Westminster constituencies, but by local authority area. There is no referendum result for Hornsey and Wood Green.

There is a referendum result for the London Borough of Haringey, which contains Hornsey and Wood Green — but then Haringey also contains the constituency of Tottenham. The 75% figure therefore represents some unknown admixture of purely notional results for these two separate constituencies.

This figure of 75% would be a good estimate of how Hornsey and Wood Green had voted if we were prepared to assume that opinion in local authorities is at each and every place the same. That’s an unrealistic assumption, but it would at least allow us to calculate opinion in each area fairly easily. If 100% of people in parliamentary constituency X live in local authority Y, we can simply give X the result recorded in Y. Where half of the people in a parliamentary constituency live in one area, and half in another, we can simply average the results, and so on.

The problem with this way of proceeding is that it’s just not realistic to assume all parts of a local authority area see things the same way. Hornsey and Wood Green is very different to Tottenham.

  • In Hornsey and Wood Green, around half of the population have a university degree of equivalent (level 4) qualification; in Tottenham the figure is closer to a quarter;
  • In Hornsey and Wood Green, twenty percent of people are engaged in higher managerial, administrative, or professional occupations; the figure in Tottenham is half that.

Given these differences, and given the fact that education was a very important predictor of how people would vote in the referendum, it’s very likely that opinion in Tottenham is different from opinion in Hornsey and Wood Green. If anything, Catherine West’s estimate probably understates the Remain vote in her constituency.

How then can we produce defensible estimates of how parliamentary constituencies would have voted? My strategy is to assume that the same demographic relationships which govern the vote at local authority level also govern the relationship at the level of parliamentary constituencies. If we can build a model which ‘explains’ how local authority areas voted as a function of the average age in the area, the proportion of residents with degrees, and so on, then we can use that model to make predictions about how parliamentary constituencies would have voted.

You might be worried about this approach. You might think that demographics isn’t destiny. That’s probably not true at the individual level, but at the aggregate level, demographics help explain an awful lot of the variation in how different areas voted. If you add information on which region a local authority (or parliamentary constituency) is in, you do even better.

(For those who care about these kinds of things: adjusted R-squared on an OLS model with demographic predictors plus region dummy on data from 348 English and Welsh local authorities = 0.90).

If that doesn’t convince you, let me try a different tack. There are twenty-six constituencies whose boundaries match those of a local authority area. We know the result in these constituencies — it’s just the same as the result in the local authority area. Any model-based estimates should be very close to the actual result.

Model-based estimates v actual results for "perfect matches"

That’s what the graph above shows. In dark grey, you see the estimates, and their associated 95% prediction intervals. In red, you can see the actual results. These results are close to the estimates, and in all but one case (Burnley), the results are inside the prediction intervals. On average, the absolute difference between estimate and result is just over two percentage points.

What use are these estimates? Well, they provide us with a way of checking whether Catherine West’s original estimate was a good one. Here’s a chart showing the dozen constituencies in England and Wales with the lowest estimated vote share for Leave.

(I haven’t included Scotland in these sets of figures for two reasons. First, there are good reasons to believe that the relationships between demographic characteristics and the Remain vote in Scotland are slightly different to the relationships in England and Wales. Second, Glasgow and Edinburgh have already done us a favour by breaking their results down by parliamentary constituency: see here and here).

The dozen constituencies with the lowest estimated vote share for Leave

As you can see from the graph, Hornsey and Wood Green is in third place — although the prediction intervals for the bottom dozen are all overlapping. But the estimate for Hornsey and Wood Green suggests that the proportion of Catherine West’s constituents that support Remain is larger than Ms West thinks, at around 78 percent, but in any case between 71 and 85 percent.

More generally, this exercise allows us to make the following claims:

  • 421 out of 574 English and Welsh constituencies probably voted to Leave
  • Of these, 270 English and Welsh constituencies almost definitely voted to Leave
  • 152 constituencies probably voted to Remain.
  • Of these, half (76) almost definitely voted to Remain.

MPs make decisions based on many factors. Constituency opinion is one of these. The results of last Thursday already made it clear that a majority of voters in the UK want to leave the European Union. In this blog post, I’ve tried to demonstrate a claim that almost certainly follows on from that — that a majority of constituencies also favoured Leaving.

Technical note: if you want to download these figures, you can find a Google Docs spreadsheet here. Email me (c dot hanretty at uea dot ac dot uk) if you want the code and data files that generated these estimates. Finally, if you have any better ideas about how to map local authority results on to Westminster boundaries I'm all ears!