The claim

“The Ukip fox is in the Westminster hen-house.”
Nigel Farage, 23 May 2014

 The background

Ukip leader Nigel Farage hailed Friday’s local election results as a resounding victory for the eurosceptic party – and most of the media followed suit.

At time of writing, out of the 4,000-odd council seats up for grabs, Ukip were up by 155, Labour were up 292, and the Conservatives and Lib Dems were down, by 201 and 292 seats respectively. This is all according to the BBC.

Mr Farage clearly thinks this increase in support will translate into success for his party at the 2015 general election.

He said of the three main parties that he will “see them in Westminster”, hinting that he will stand for parliament a in Kent constituency.

Could his optimism be misplaced?

The analysis

Commentators were quick to point out as the count dragged on that Ukip’s percentage share of the total vote had dropped significantly since the last local elections in 2012.

Last time around, 23 per cent of votes cast were for Ukip. At time of writing, the BBC says the Ukip share has slipped to 17 per cent.

The corporation has Labour on 31 per cent of the national vote, the Conservatives on 29 and the Lib Dems on 13.

The $6m question now is how that support is likely to translate into votes in the general election.

The main opposition party tends to do better than the party in power in local elections. But that doesn’t always mean the opposition goes on to win the next Westminster elections.

In fact, that has only happened about half the time since 1979, so we might as well flip a coin.

But Oxford academic Chris Prosser has come up with a mathematical model that looks more closely at the voting patterns and predicts the general election result from the preceding local election with a success rate closer to 90 per cent.

Fans of regression analysis can check out the basic modelling here – although it has now been updated to cope with the rise of a fourth party.

If we feed Friday’s projected shares of the national vote into Chris’s model, we get these predictions of voting in the 2015 general election:

Conservative: 35.9 per cent (plus or minus 1.3)
Labour: 30.9 per cent (± 3.4)
Lib Dem: 16 per cent (± 2.29)
UKIP 11.6 per cent (± 3.9)

Now you might think that means that the Conservatives get a clear majority in the House of Commons and Ukip ends up with more than 10 per cent of the seats, but our first past the post system makes things much more complicated.

It’s entirely possible for the party that comes second in terms of the percentage of national vote to get the most seats, if they tend to win in marginal seats where a smaller number of votes is decisive. It all depends on where your vote is concentrated.

So we need to run Chris’s numbers through the Electoral Calculus website to work out how these percentages translate into MPs. Here are the results:

The Conservatives end up with the most MPs but 20 short of an overall majority. The Lib Dems are reduced to 34 seats, and Ukip gets a grand total of zero seats, despite attracting a significant share of the national vote.

How accurate is this likely to be?

Chris’s task is more complicated this time than in 2012, when we were only really worrying about three parties.

The Ukip share is predicted by assuming that 63 per cent of people who voted for someone other than the Conservatives, Lib Dems or Labour will vote Ukip, as they did this week.

That’s not entirely satisfactory but we don’t know how the Ukip proportion of the “other” vote is going to change so there’s no other sensible way of doing it.

Chris also notes that the results of this election are very unusual compared to the previous local elections used to estimate the models (1973-2009).

The combined Tory and Labour vote share this year is lower than all but one of the previous local elections, an unusual situation that creates bigger margins of error.

But it’s interesting to note that another prediction model using a completely different method – analysing polling rather than local election results – comes up with a very similar forecast of how things will go in 2015.

Stephen Fisher, also at Oxford, predicts that the Conservatives, Labour, and Ukip will get almost identical shares of the national vote: (36 per cent, 31 and 11.5). His model is more pessimistic than Chris’s about the Lib Dems.

Again, if Ukip get 11.5 per cent of the votes they will get no seats at the next general election, according to Electoral Calculus.

In fact, such is the strange nature of the British electoral system, Ukip could get a considerably higher share of the national vote than the Lib Dems (say 17 per cent versus 13 per cent) and it would still fail to win a single parliamentary seat.

Chris tells us: “It might seem extreme (especially with Ukip getting more votes than the Lib Dems) but I think that is going to be pretty close to the mark come election day.

“Ukip’s support is too geographically spread for them to pick up many seats (though I wouldn’t be too surprised if they managed to pick up one with some clever targeting and hard campaigning, like the Greens in Brighton).

“I suspect that the day after the election there are going to be a lot of Ukip voters looking at the Ukip vote percentage and wondering where the hell their MPs are.”

The verdict

Let’s be clear: this is all educated guesswork. We are using historical precedent to predict how people are likely to vote in the future, and people can always surprise you.

There is always the chance of an impossible-to-predict “black swan” event next year, and this week’s results are in fact already very unusual compared to the historical norm, making accurate predictions harder than ever.

But Chris Prosser is joined by other academics in predicting that this week’s success won’t necessarily mean that the Ukip fox gets its nose through the doors of Westminster.