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Who will win the 2015 general election? With only 18 days to go, we now think it is likely that Ed Miliband will become Prime Minister this summer. There are few scenarios in which David Cameron will survive a vote of confidence. And the Liberal Democrats may only have influence under a Tory-led government.

These are the conclusions of May2015’s latest election analysis, which is based on all the latest polls, our election forecast and the recent predictions of other forecasters.

In the past five years Labour have lost Scotland, their greatest heartland; failed to win over almost anyone who voted Tory in 2010; and shed votes to both the Greens and Ukip. And yet the election maths clearly favours Labour. All the outcomes currently implied by the polls or predicted by forecasters put them in a superior position.

Our forecast

Let’s start with what May2015 currently predicts will happen on May 7. Labour are predicted to win 273 seats and the Tories 271. Polling suggests the SNP will win as many as 55, and the Lib Dems as few as 25.

This forecast is based on far more polling than British forecasters have had to make do with in past elections. It takes into account 25 national polls conducted over the past fortnight by 10 different pollsters, as well as Michael Ashcroft’s individual constituency polls of more than 150 marginal seats.

We can have some faith in this forecast, which is strengthening every week.

Some of those polls were conducted last summer. But many are more recent. In the past three weeks alone Ashcroft has polled 28 seats. He has polled 48 in 2015. And we adjust his polls every day in line with shifts in national polls, so his polls from last summer, late 2014 or earlier this year have all been updated to today.

In other words, we can have some faith in this forecast, which is strengthening every week as more polls are published. It’s more robust than the typical ‘uniform swing’ estimates that pundits often resort to. And it closely resembles other forecasts, from the Guardian’s to an academic forecast we host on May2015.

Why are we confident in Miliband?

Labour are only set to win about as many seats as the Tories. So why do we think Miliband must be favoured to be the next PM? Because governments aren’t necessarily formed by the largest party; the next one will be formed by whomever can cobble together 323 seats (there are 650 seats in the House, but 5 Sinn Fein MPs and the Speaker do not sit, so 323 is an effective majority).

That’s why any analysis of this race has to start with one question: will there be an ‘anti-Tory’ majority? In other words, will the parties that have committed to voting against the Tories win at least 323 seats? Well, this looks as likely now as it did two weeks ago, when Cameron endured ITV’s 7-way leaders’ debate.

The ‘anti-Tory’ parties are set to win 337 seats, 14 more than they need to ‘lock Cameron out’.

According to our forecast, the ‘anti-Tory’ parties – Labour, the SNP, and smaller parties like the Greens, Plaid Cymru, SDLP and Respect – are going to win 337 MPs, 14 more than they need to ‘lock Cameron out’, as Alex Salmond put it to us last month.

14 seats isn’t very many. Surely if the polls just swung slightly towards the Tories – as many pundits still expect – our ‘anti-Tory’ bloc would quickly lose at least a dozen seats?

The problem for Cameron is this isn’t really what happens. He can move ahead in the polls, as Election Forecast are predicting, or outperform them because they are overlooking ‘shy Tories’, as Elections Etc believe, and still fail to hold power. At best he would hold power by the slenderest of majorities. But any such scenario is far from the likeliest outcome.

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Our two-week average of the polls gives the Tories 33.7 per cent and Labour 34.0 per cent.

Let’s imagine the Tories tick up to 35 per cent, as Elections Etc predict. And let’s say Labour dip down to 33, as both Etc and Election Forecast expect. (We’ve also moved the Lib Dems up from 8 to 10 per cent at the expense of Ukip and the Greens, as both of these academic models forecast.)

Doing so leaves the Tories just shy of 280 seats and the Lib Dems on 28. Labour are on 262. The Tories now have a 2-point lead, and yet they and the Lib Dems still only have 307 seats between them – 16 short of a majority.

This prediction doesn’t adjust our forecast for Scotland. The Lib Dems are, despite what our model says, likely to win Orkney & Shetland; could certainly win Berwickshire (where they trail the SNP by two points); and perhaps even hold Charles Kennedy’s seat or Jo Swinson’s. So let’s give them three extra seats. Now the Tories and Lib Dems – Coalition 2.0 – have 310 between them.

In this scenario, the Tories and Lib Dems – Coalition 2.0 – have 310 seats between them.

They are 13 short of a majority, but they can just reach 323. First, they need 9 seats from Northern Ireland’s main unionist party, the DUP, who currently hold 8 and are hoping to re-take Peter Robinson’s once long-held seat of Belfast East. That would give this Tory-led pact 319 seats.

They are short by 4. The only party that can take them over the line are Ukip. Will Ukip win 4 seats? Election Forecast think they will only win in Clacton (their reasoning: Nigel Farage is trailing in Thanet and Mark Reckless has none of his advantages – charisma or demographics). But perhaps Ukip win as many as four, which would most likely be Clacton, Thanet, Rochester and Thurrock.

But we haven’t reached 323, because if Ukip win Thanet than the Tories haven’t (thanks @stephenkb). We are still one seat short. And even if we had reached 323, no laws can be passed if so much as a single one of those 323 MPs votes against the government. Can David Cameron really rely on Douglas Carswell? [1]

Or, more relevantly for this analysis, if one of these four parties – the Tories, Lib Dems, DUP or Ukip – doesn’t win just one of the seats we’ve given them, this unprecedented four-party pact will fall short.

For this to happen, pretty much every marginal race has to go in the Tories and Lib Dems favour.

More problematically, it’s not clear how Ukip and the Lib Dems could vote together. As the Lib Dems’ strategy director stressed to us this morning, Nick Clegg has ruled out any type of deal with Ukip, and it’s hard to imagine Ukip voting with the Tories on anything unless the UK is offered an expedited EU referendum – something which many senior Lib Dems cannot countenance.

Finally, for this to happen, pretty much every marginal race has to go in the Tories and Lib Dems favour. The Lib Dems have to hold off Labour in Sheffield Hallam and Bristol West, not to mention Bermondsey, Leeds North West and Birmingham Yardley. While the Tories have to win in nine seats – Pudsey, Milton Keynes South, Lincoln, Finchley, High Peak, Norwich North, Halesowen, Crewe and Brighton Kemptown – that are all narrowly set to vote Labour.

This is possible, but it can’t be considered likely.

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But could the Tories do even better than this? We’ve mapped out what a 35/33 win would look like (with the Lib Dems doing fairly well too) – the Tories win 279 seats – but what if the Tories won even more seats?

This is what Elections Etc predicts. Not because the data suggests the Tories will poll even more than 35 per cent, but because the Oxford academic behind it, Steve Fisher, believes first-time Tory MPs (i.e. those elected in 2010) will benefit from a 1-point ‘incumbency effect’, and this will be enough to hand around a dozen extra seats to the Tories.

Could the Tories do even better, and win more than 290 seats?

So Fisher gives the Tories 292 seats. This is equivalent to giving the Tories another nine English marginals – seats like Northampton North, Croydon Central, Cannock Chase, Harrow East, Nuneaton, Broxtowe, Sherwood, Waveney and Ealing Central – as well as a handful of Lib Dem seats in the south west, like St Ives, Torbay and Cornwall North.

We’ve now given the Tories nearly 20 seats in England that we currently predict will all vote Labour, some by as many as 5 points. This is about as good as it can get for the Tories. (It is the upper end of Polling Observatory’s forecast.) We have given them the exact same percentage of the GB-wide vote that they won in 2010 – 36.97 – even though we know they have lost about a sixth of it to Ukip.

But even under this scenario Cameron will struggle to survive, despite having beaten Labour in the polls by 4 points. For the Tories to have done so well, they have had to take seats from the Lib Dems. (This is a critical point: if the Lib Dems do better than we predict, any extra seats are more likely to come from the Tories than Labour or the SNP.) So Coalition 2.0 is now still 9 seats short of 323 (292 + 22 = 314).

They could reach 323 with DUP support, provided the DUP win East Belfast, where a recent poll put them only narrowly ahead. But again, this Tory-led bloc is incredibly fragile. If a Tory MP gets stuck in traffic on the way to the Queen’s Speech, Cameron wouldn’t command the confidence of the House.

How could this analysis be wrong?

The reason we are confident in the picture we’re painting is because the big regional contests in this election – between Labour and the SNP in Scotland, and the Tories and Lib Dems in the south west – have little overall impact on whether Cameron can survive. If the SNP fade, Labour are the most likely to benefit. And if the Lib Dems strengthen, the Tories probably lose out.

The maths would change if the Lib Dems can save, say, half their Scottish seats, while Labour win very few. Or the Lib Dems recover in Labour-facing English and Welsh seats beyond Sheffield Hallam and Bristol West – in places like Norwich South, Cardiff Central and Hornsey & Wood Green.

Could the Lib Dems save their Scottish seats? Could Ukip win likely Labour seats?

But none of this looks likely. On Friday Ashcroft confirmed what Scotland-wide polls have already suggested: the Lib Dems are a fair way behind in almost all of their Scottish seats. And May2015 predicts they will lose Cardiff Central and those Guardian-reading English seats by at least 9 points.

Alternatively, Ukip could win a bushel of likely Labour seats: places like Great Grimsby, Cannock Chase, Heywood & Middleton, Dudley North, Walsall North, Plymouth Moor View, and Rother Valley. But it seems much more likely that Ukip win extra seats in Tory-held constituencies like Castle Point, Great Yarmouth and Boston & Skegness.

Or instead, the Tories could just win even more of the English marginals that they are forecast to lose. We’ve already handed them nearly 20. To win even more they need to prevail in places where polls suggest they trail by at least 5 points.

So will Ed Miliband be PM?

These outcomes are all at the edge of a range of possibilities. At the other end of possibilities, it is Labour who do much better than we are predicting.

Imagine that Labour win the popular vote 35/33. Now they would be the party with more than 280 seats, with the Tories about 20 seats behind and in the low 260s. In this scenario, it is Labour who do better in the Tory-held English marginals, winning seats like Peterborough, Swindon South and Rossendale & Darwen.

Compare the strength of the pacts Labour could form in this scenario with the incredibly fragile one we had to cobble together for Cameron.

Labour could add the SNP’s 55 seats to their 282 (recall that if the SNP win slightly fewer, it is most likely Labour who benefit), as well as the Lib Dems’ 26 – for Labour would be the largest party and the Lib Dems are willing to work with both sides – and 9 minor MPs.

Compare the strength of the pacts Labour could form with Cameron’s options.

That gives Labour 372 seats – a majority of 98. Without the SNP they would have 317, 5 short of a majority if the SNP voted against them, but 22 more than enough if the SNP were to abstain on most bills (without the SNP’s 55 MPs the effective majority in the House would become 295). If the SNP chose to be a ‘silent partner’ in exchange for devo-max, as some pundits think likely, Labour could govern in this way without them.

If, however, the SNP choose to be active partners in government, the Liberal Democrats could be marginalised. Some in the party may want to form a coalition with Labour, but Labour would not be able to pass anything without either SNP or Tory support.

The Lib Dems could not, even in this optimistic scenario, ever get Labour over the line, whereas they might be the critical group that gets the Tories to 323. Labour would be choosing to water down its manifesto, and enrage many of its activists, to accommodate a party that wouldn’t help it pass any laws.

But Labour would still be in complete control relative to the Tories, whose four-party pact would, in this case, barely make it to 300 seats.

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This outcome is at the edge of a range of possibilities. Our point is to show how different the two sets of possibilities we’ve demonstrated are. In one, Cameron may just about form a government. In another, Labour have a greater majority than Blair in 2005 or the Coalition in 2010.

Only Labour have a clear path to 323 seats.

In the middle of these alternatives, the parties win about as many seats as each other, but only Labour have a clear path to 323 seats. As soon as the SNP committed to voting the Tories down, Cameron’s survival became very difficult.

We would not be embarrassed by this analysis if Cameron managed to hang on – the Tories spent the twentieth century holding onto power against expectations – but everything we know at the moment leads to only one conclusion: Miliband is likely to displace him.

[1] May2015 also actually incorrectly counts the Speaker as a Tory, when he stands as an independent. In theory he could be dethroned by the next government and then represent his original party from the backbenches, but no Speaker has ever done this. It’s more likely he would resign and be replaced by a Tory, so we have generously counted him as a Tory for this analysis.