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Who is going to win the election, now less than eight weeks away? That is the question we try to answer on May2015. We have built our own model, which uses the latest national and constituency polls to make a prediction, and we are tracking all other forecasts.

Today we are launching a new academic forecast, which will complement two other academic forecasts we track: Election Forecast and Elections Etc.

This new forecast, by the team behind Polling Observatory – that’s Rob Ford, William Jennings, Mark Pickup and Christian Wleizen – is for polling as of March 1 (the polls do not seem to have shifted materially since then). Polling Observatory will offer their March polling analysis in early April, and this forecast will update fortnightly from then until the election.

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Polling Observatory’s new election forecast

All current election forecasts predict the Tories will win the most seats in May. Today, our new Polling Observatory seat forecast will be the first to disagree. Our maiden forecast, which uses all national, Scottish and constituency polling up to March 1, predicts that Labour will win 20 more seats than the Tories in May.

An average of the five forecasts tracked on May2015 – which range from a pair of academic forecasts to the Guardian’s and the bookies’ – gives the Tories 283 seats and Labour 270. Our forecast predicts the opposite: Labour will win 285 seats and the Tories 265.

We are also predicting the SNP to win 49 seats; Labour are headed for the wipeout that polls have implied for months now. The SNP are set to win more than 30 of Labour’s 40 Scottish seats. Other forecasts are divided on whether the SNP will win around 40 or more than 50 seats. More significantly, most pundits and academics think they will only win around 30.

As with other forecasts, our model projects the Lib Dems to lose more than half of their seats. A Tory-Lib Dem deal would only muster 289 seats based on our forecast – 34 short of an effective majority. In contrast, a Labour-SNP pact would have 334 MPs: a double-digit majority.

Here’s our forecast in full. The figures in brackets show our upper and lower estimates for each party; our specific seat totals mask a lot of uncertainty.

Labour — 285 (260-313)

Tories — 265 (235-293)

SNP — 49 (34-56)

Lib Dem — 24 (17-33)

Ukip — 3 (1-5)

Others — 6 (4-9)

Largest party and possible coalitions

Our forecast suggests there is a 77 per cent chance of Labour being the largest party. That’s in stark contrast to Election Forecast, another academic forecast, which says they have just a 38 per cent chance.

But the probability of a Labour majority is essentially non-existent (less than 0.5 per cent). The likelihood of Labour and the Lib Dems having the numbers for a majority is also small (19 per cent), but the possibility of Labour and the SNP holding a majority of seats is very high (78 per cent).

The possibility of Labour and the SNP holding a majority of seats is 78 per cent.

A Tory majority is almost as distant a possibility as a Labour one. More importantly, their paths to a governing coalition would be even more winding.

Based on our forecast, partnering the Lib Dems will leave them 34 seats short. If they had an informal arrangement with the DUP and/or Ukip they would still only hold around 300 seats. If the Tories only win 265 seats, as our first projection suggests, it would be very difficult for them to sustain a government without some form of SNP support (like abstention).

Our polling estimates

What these sums illustrate is just how difficult the parliamentary arithmetic is likely to be in May, unless the polls move sharply in the next two months.

Our forecast is based on polling as of March 1. Have the polls changed materially in the past fortnight? At times it has seemed like they have, but there is very little difference between our estimates of voting intention and May2015’s latest 5-day average of national polls.

There is very little difference between our estimates and May2015’s latest poll averages.

Our current estimate puts Labour on 32.2 per cent; the Tories on 31.5 per cent; Ukip on 14.8 per cent; the Lib Dems on 8.4 per cent; and the Greens on 6.4 per cent. The Labour-Tory lead is very similar to May2015’s Poll of Polls. The biggest difference between our numbers and May2015‘s is that ours put the Lib Dems and Greens about 1 point higher, and the two main parties slightly lower.

Nowcast

Our results are based on a forecast of how the parties will poll on election day, which we explain in detail below. That forecast predicts Labour and the Tories to tie on votes on election day, with each winning 33.7 per cent. (That compares to the 2 point Tory vote lead predicted by Election Forecast and the 2.9 point Tory lead forecast by Elections Etc.)

If we offered a ‘nowcast’, our projection would be even more favourable to Labour, although our results do not change much. The main parties fare slightly worse (Labour win three fewer seats and the Tories seven fewer), and the minor parties win more (the SNP win four more, Ukip win two more, and the Lib Dems win one extra).

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How we come up with our forecast

The Polling Observatory forecasting model has been a long time in the making, and builds on our effort in 2010, when we fared relatively well both in absolute terms and compared to other forecasters. (Our forecast before the start of the official campaign proved even more successful.)

Forecasting like this is inherently limited, as there are factors which impact elections but are difficult to quantify or model effectively. We know that things like candidate quality or local campaign intensity can influence results, but these things are hard to measure. Our forecast is therefore of the form, ‘given what we know about things we can measure, this is what we think is most likely to happen’.

Noise and signal

First, how do we estimate support for the parties and turn today’s polls into an election day forecast?

We try to be cautious about over-interpreting short-term fluctuations – since much of it is random noise or about methodological differences between pollsters – and focus on underlying trends.

‘Given what we know about things we can measure, this is what we think is most likely to happen.’

There have been big shifts in voting intention during this parliament: voters fled the Lib Dems in 2010; the Tories fell after the ‘Omnishambles’ budget in spring 2012; support for Labour has slowly declined since then; and Ukip have risen.

As of March 1, our estimates show the race is tied. Labour are on 32.2 per cent and the Conservatives on 31.5 per cent – but the confidence intervals (a measure of the level of error), are such that we cannot say Labour lead.

Lessons from the past

As we noted when we introduced our inaugural polling forecast last May (drawing on our previous research), the polls component of our forecast uses the historical relationship between polls and the election day vote from past elections to project forward from the current polling.

A key idea here is ‘regression to the mean’: that if a party is polling above its historical equilibrium, it will tend to underperform the polls on election day. If a party is below the equilibrium, it will tend to do better.

For this reason our initial forecast a year out suggested that both Conservatives and Labour would poll around 36 per cent. Of course, this election cycle has seen sustained support for UKIP – this is why the polls have not come into line with our original forecast.

Support for the SNP and the Greens is now also keeping down our forecasts for Labour and the Tories. Our forecast for vote share now stands at 33.7 per cent for both parties, with our estimates having edged down gradually in each new forecast.

The estimates are listed below with confidence intervals, to indicate the degree of uncertainty that still remains with two months to go.

Tories — 33.7% (31.9-35.5)

Labour — 33.7% (30.1-37.2)

Lib Dem — 8.8% (5.4-12.2)

From votes to seats

So how do we translate these polling day vote predictions into a specific seat forecast? We don’t just want an overall seat estimate, but probabilities of victory for each party in every seat.

First, we work the ‘swing’ since the 2010 election implied by our forecast. At a national level, if both parties polled 33.7 per cent that would represent a 4.0 per cent swing to Labour and 3.3 per cent swing away from the Tories, or a 3.7 per cent swing from the Tories to Labour.

First, we work the ‘swing’ since the 2010 election implied by our forecast.

In other words, every seat which the Tories won by less than 7.4 per cent in 2010 would go to Labour. There are 63 of these, which would easily make Labour the largest party, all other things being equal.

But we actually apply two uniform swings – a uniform swing across England & Wales, and one across Scotland. This has become fairly established practice. We also add in constituency polls, as provided by Lord Ashcroft and also included in May2015’s model.

Calculating uniform swings

We work out these swings by taking the most recent polls in Scotland and subtracting them from GB-wide polls. This gives us figures for England & Wales; pollsters do not regularly poll Northern Ireland. (May2015 also follows this two-step process.)

This means that our estimate of swing may lag the GB polls a little – as we require Scottish polls for the same period.

We assume that any change in the swing for Scotland and E&W between now and election day will be proportionately the same. So if the swing in Scotland changes by 1 percent (not percentage point), the swing in E&W will also change by 1 per cent.

Constituency polls

Lord Ashcroft has polled nearly 150 seats since last spring. Our model includes polls for 136. These are polls for almost all of the election’s marginal seats – we can rely on uniform swings to do fairly well at explaining how the other 500 or so seats will vote.

If we don’t have a constituency poll, we apply a random deviation from uniform swing in each seat. This random deviation is drawn from a distribution of possible outcomes, which are determined by the distribution of deviations from uniform swing between 2005 and 2010.

If we don’t have a constituency poll, we apply a random deviation from uniform swing in each seat.

In other words, we use the range of actual swings which occurred in 2005 and 2010 to inform the range of possible swings in 2015. Each simulation randomly draws one possible swing from this range for each seat. So the overall range of swings we project remains the same in each simulation, following the distribution seen in other elections, but the projected swing in each seat varies – each simulation picks a new swing for each seat from within the possible range.

If we have a constituency poll, we use it to update our expectation for the deviation from uniform swing for that constituency. In Ukip’s two seats – Clacton and Rochester & Strood – we treat each by-election as a constituency poll with a large sample.

Other parties

One challenge for our forecasting approach, which turns current polls into an election day forecast based on a party’s historical performance, is that we do not have past polling data for Ukip or the SNP.

But we do have historical data for all ‘Other’ parties. We can use this to come up with a polling day forecast for Ukip and the SNP. We need to determine the proportion of the ‘Others’ uniform swing (both in England & Wales and in Scotland) that will go to Ukip and the SNP.

We do this constituency-by-constituency. The default for the SNP is that 0.95 of the ‘Others’ uniform swing in Scotland goes to the SNP (that value is 0 in England & Wales). The default for Ukip is that 0.7 of the ‘Others’ uniform swing in England goes to Ukip (again, none of that swing goes to Ukip in Scotland).

Ukip

To calculate the distribution for the deviations from uniform swing for Ukip, we used the distribution of swings to Ukip in the 2014 European Parliament election.

This is not a perfect proxy for the general election, but it gives us a better idea as to the distribution of Ukip swings than the last general election – the overall rise in UKIP support between 2009 and 2014 in European elections (10.6 percentage points) is fairly similar to the rise in Ukip support we are currently seeing in election polls.

SNP

The current SNP surge also makes 2010 a poor choice for defining the distribution of SNP swings. Here we use the distribution of constituency voters in the 2011 Scottish Parliament election, when the SNP vote rose by 12.5 percentage points.

This is a rather smaller swing than is currently being predicted in Scottish polling, but was nonetheless a major surge in support and should therefore prove a more useful yardstick than the 2010 general election, when SNP support barely rose on 2005. Note also that we are not using this data to estimate the SNP swing but rather the distribution of the deviations from uniform swing (in order to get forecasts for each constituency).

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As before, if we have a constituency poll, we use it to update our expectation for the deviation from uniform swing in that constituency. (Note that the deviation of constituency polls from uniform swing is calibrated against our daily poll estimate at the time the fieldwork was carried out.)

We use the sum of votes for radical right parties in 2010 as our estimate of the 2010 Ukip vote.

Also note that for Ukip we use the sum of votes for radical right parties in 2010 as our estimate of the 2010 Ukip vote – as we expect that UKIP, as the dominant representative of the radical right, will win most of the support that previously went to the BNP, the National Front and the England Democrats. Even if this proves not to be the case, support for these smaller fringe right parties should still provide a useful proxy measure of Ukip potential in individual seats.

Plaid Cymru and the Greens

For the remaining ‘Other’ parties, we follow the same procedure as for Ukip and the SNP, with these parties receiving the proportion of the Scotland and England & Wales uniform swings that was not allocated to UKIP and SNP.

It was not necessary to include a deviation from uniform swing for these other parties; this is largely accounted for already.

Take Plaid Cymru. In Monmouth in 2010, Plaid won 2.7 per cent of the vote and Ukip 2.4 per cent, and so we allocate the ‘Other’ vote to each of them as 0.53 and 0.47 respectively. In each case, the remaining proportion of the other uniform swing is specified as going to the other ‘Other’ party. In England, we follow a similar procedure for Ukip and the Greens.

This procedure was repeated for each simulation, of which we ran an arbitrarily large number (we ran 15,000 simulations in total), so that for each simulation we have an estimate of the number of seats won by each party. By aggregating all these simulations, we get a range of possible outcomes.

We are then able to calculate the percentage of times each party wins each constituency across all simulations. We interpret these as the probability that each party will win each constituency.

Polling Observatory’s seat forecast will update regularly throughout April here on May2015.