Maybe you, like me, woke up somewhat astonished to discover that the UK had gone and Brexited itself last Friday. Whilst the world is still trying to work out what that means, I’ve been particularly intrigued by a petition that has close to 4 million signatures on it, asking that the referendum be redone with better turn out guidelines. What’s intriguing is not so much that 77,000 signatures were removed from it, but rather that you can download all the petition information as a JSON file, and then analyse the data to see what the petition really means.

Why bother looking at the data? Well 15 million people voted in the UK to stay in the EU. In a way it’s not surprising that 4 million of them feel strongly enough to sign a petition. I’m interested in finding out where these signatures come from geographically, and how they compare to the referendum data. I’m looking at just English data, rather than the UK altogether, given that Scotland and Northern Ireland showed significant differences in how they voted compared to England.

A few technical notes. The English election data is based upon districts, whilst the petition data divides signatories by wards. Sometimes wards belong to multiple districts, and where this occurs each signature is divided between the multiple districts to which it belongs. I’m using the petition data from June 27 at 11PM roughly for this post.

Let’s begin by looking at the raw number of petition signatures by district in England. Plotted on a map, they look something like this:

There’s a lot of variety across the country in terms of absolute numbers of signatures, but who are the biggest voters, and who are the smallest? Here are the top 10 and bottom 10 voting districts.

Votes Constituency
 1055 Isles of Scilly
 1161 Boston
 1673 Barrow-in-Furness
 1766 Tamworth
 1855 Bolsover
 1903 Hartlepool
 1936 Corby
 2053 West Somerset
 2130 Burnley
 2170 Forest Heath
..... .....
37114 Barnet
37510 Southwark
37668 Manchester
37854 Brighton and Hove
38066 Hackney
44959 Lambeth
45092 Leeds
47349 Bristol, City of
48605 Wandsworth
52120 Birmingham

No surprises that the Isles of Scilly have such a small number, their electorate only contains 1,799 voters. Though if these petition numbers are to be believed, a lot of them must have signed (more indeed than first voted to remain, the vote to remain won in the Isles of Scilly 803 to 621). It’s also not surprising that the largest numbers of signatures come from major metropolitan regions.

But absolute numbers don’t reveal the whole picture. What I’ve been calling the Bregret Index, or Bregretfulness of a district is the amount of petition signatures as a function of the district’s population. I used the referendum data to find the size of each electorate and have plotted the Bregretfulness of each district, as a percentage of its size.

Interestingly, a lot of the vibrant yellow areas in the previous graph have faded. It’s now very clear that metropolitan areas are much more likely to sign the petition. This is echoed in the data of the 10 least and most bregretful districts. Maybe someone with more knowledge of England could interpret these a bit better than me. I’m intrigued nonetheless by the Isles of Scilly appearing again, though given its small population its not worth reading too much into this.

Bregret (%) District
2.7         Hartlepool
2.7         Ashfield
2.8         Redcar and Cleveland
2.9         Boston
3.0         Cannock Chase
3.0         Blackpool
3.0         North East Lincolnshire
3.0         Doncaster
3.1         Rotherham
3.1         Mansfield
.....       .....
21.6        Hammersmith and Fulham
21.8        Richmond upon Thames
22.1        Wandsworth
22.9        Haringey
23.3        Hackney
24.6        Camden
25.1        Islington
29.5        Kensington and Chelsea
58.7        Isles of Scilly
212.9       City of London

Most interesting is the City of London, where these numbers suggest that over twice as many people signed the petition as there are electors. There are probably some fake clicks here, but more likely the City of London’s weird electoral rules have made the analysis fail here. Possibly both.

In this picture, there is some unhappiness, some Bregret in every district. Which is normal after a referendum. But what we want to see is whether the data suggests that people have had a change of heart, and would have voted differently. The real thing to find out here then is where have people signing the petition come from compared to where people voted in the referendum.

If the signatures represent evenly the English population who voted for remain, then they should act as a good predictor for the referendum results. I’ve measured a “Bregret Difference” as the difference between how well the signatures’ geographic dispersal predicts the referendum result. If the Bregret Difference is positive, then the district feels very Bregretful and the petition suggests it should have voted more to remain in the referendum, whilst if it’s negative, the district doesn’t feel very Bregretful, and is more content with the Brexit decision. Like this, it’s possible to see if the rural areas that carried the Brexit vote have had a change of heart. This measure is different from the percentage of people signing the petition in the precedent graph, it is a measure of how much sentiment could have changed within a district before and after the referendum.

Looking quickly, you can see that the petition signatures are coming disproportionately from metropolitan areas. This is not too surprising, young people are more likely to live in metropolitan areas, are probably more likely to sign a petition online, and they are  less likely to have voted on referendum day. All of these skew the Bregret difference away from rural areas. In case you are wondering about how Bregretful your district is, here are the top and bottom ten most Bregretful districts:

Bregret (%)  District
 -55.9       Hambleton
 -52.6       Redcar and Cleveland
 -52.2       Barrow-in-Furness
 -49.2       Ashfield
 -47.7       Tamworth
 -45.9       Cannock Chase
 -45.0       North Lincolnshire
 -44.9       Hartlepool
 -44.8       Nuneaton and Bedworth
 -44.4       Rotherham
.....        .....
  66.6       Wandsworth
  74.2       Haringey
  79.4       Hammersmith and Fulham
  85.3       Hackney
  91.1       Tower Hamlets
  92.4       Islington
 103.2       Camden
 164.8       Kensington and Chelsea
 433.6       Isles of Scilly
1462.7       City of London

The Bregret values are quite high at the bottom here. This is because predicted election score comes from the rough assumption that the petition signatures are evenly divided amongst the electorate that voted remain. This is likely not the case, for mostly demographic reasons. One could look at these inconsistencies and use them to attack the integrity of the petition, but that isn’t straightforward to do.

Rather what can be inferred here is that, from this petition, there hasn’t been a significant change in mindset concerning the British departure from the EU in the rural regions, at least not enough to encourage the population there to sign an online petition en masse. The analysis also isn’t sensitive to a uniform movement across the country of people changing from Leave to Remain (or vice versa). But after all this is an online petition, we aren’t expecting scientific accuracy, but it is fun to poke data. If I could conclude anything, the only real winners here have been portmanteaux.

A lot of credit needs to be given for helping me make this post:

• The UK-GeoJSON project for the data files I used to make the maps
• Matplotlib, IPython, Jupyter notebooks, I love you.
• Shapely, for making plotting easy
• Descartes, for making Shapely and GeoJSON work together