by Ed Howker and Georgina Lee

It’s day two of the official election campaign.

FactCheck and Channel 4 News’ Target Voter team can reveal that the Conservatives have already spent thousands on Facebook ads that have been displayed over a million times — but contain a basic error, which the party admitted after we pointed it out.

Let’s take a look.

The adverts

Facebook users in some of the most marginal seats in the country might have seen something like this pop up on their timelines this week.

The adverts claim to show the number of votes needed in the local constituency to “elect a Conservative MP that will Back Boris to Get Brexit Done.”

The problem is that in 14 of the very closest seats, the Conservatives seem to have got their numbers wrong.

Let’s look at Newcastle-under-Lyme, one of the tightest marginals in the country. The Conservatives have run adverts here that claim just 15 votes are needed to win.

It looks like they’ve reached the figure by halving the difference between the Labour and Conservative candidates at the last general election — who were separated by just 30 votes.

But by that logic, 15 extra Conservative and 15 fewer Labour voters would see both secure exactly 21,109 votes. In other words, it would create a tie — not a Conservative victory.

Drawing lots

The Electoral Commission says that if two candidates get the same number of votes, they need to draw lots to decide the winner.

That’s what happened in the local elections this year when there was a tie to elect a member of Hambleton District Council in North Yorkshire.

The returning officer had to randomly choose between blank envelopes containing the name of each candidate.

How widespread are the ads?

The Conservatives have made the same error this week in 13 other Labour-held marginals around the country.

Facebook data reveals they spent up to £20,000 on the ads and that they have been displayed to users between 1.3 and 1.6 million times.

What do the Conservatives say?

We put our calculations to the Conservatives, using the example of Bolsover, where the party targeted an advert saying it would “only take 2,644 votes to get Brexit done.”

A spokesperson for the party said: “We recognise, as FactCheck point out, it will take 2,645 voters in Bolsover to switch from Labour to the Conservatives, to elect a Conservative MP to help get Brexit done. Leaving aside that the figure is one vote more than 2,644, it is significantly closer between Labour and the Conservatives in Bolsover than many people realise. That is true of all the seats mentioned.”

The underlying calculation is flawed

You might be thinking: okay, they got their maths wrong by one vote. But the problems with the calculation run deeper, as Dr Chris Prosser from the British Election Study explains.

The number of votes stated as enough to elect a Conservative MP “would only be true if that number of voters switched to the Conservatives and no other voters did anything different from the previous election.”

“Of course though, in reality voters will switch parties in all sorts of directions, not just between Labour and the Conservatives. This makes predicting exactly what is going to happen very difficult.”

Dr Prosser points out that the Conservatives’ methodology could lead them to under- or over-estimate the number of votes required to secure a Conservative victory in each seat.

For example, looking at Bolsover — one of the seats targeted by these adverts — “you could have done the same maths before the 2017 election using the 2015 election results, and you would have said there were only 5,889 votes in it. But in 2017 the Conservatives won 8,101 more votes than they did in 2015 and still didn’t win the seat.”

Conversely, “if you were the Liberal Democrats in Bath in 2015 you could have said there were 5,889 votes in it between them and the Conservatives. In that election the Conservatives only increased the number of votes they got by share by 3,065 but they still won the seat.”

Ultimately, Dr Prosser says the Conservatives’ method is “overly simplistic.”

FactCheck verdict

The Conservatives have targeted dozens of adverts at some of the tightest Labour-Conservative marginal seats in the country purporting to show the number of votes required to elect a Conservative MP.

But by their logic, in fourteen seats, the number of votes stated would result in a tie between the Labour and Conservative candidates — not a Conservative victory.

FactCheck put this to the party, who accept that their calculation was incorrect.

The incorrect adverts have been displayed on Facebook over a million times.

More fundamentally, the underlying calculation is flawed. It ignores the fact that voters may switch to other parties and could lead to an over- or under-estimate of the number of votes needed to get a Conservative MP in the seat.

Over the course of the campaign, Channel 4 News’ Target Voter team will be looking at political ads by all the main parties and its supporters.

But Facebook only gives us some information. Facebook give you, the user, a lot more. If you see a sponsored political ad, we want to know why.

And you can tell us by clicking the “Why am I seeing this ad?” button and sending us a screen grab to targetvoter@itn.co.uk.