Locals seats forecast from national polls 2014

Last year I published details of a basic model for forecasting the number of local council seats won from national opinion polls here. The basic idea is to estimate change in seats since the last time they were fought (four years ago) as a function of change in the polls over that time.  Despite the massive increase in UKIP candidature last year and their remarkable achievement of a Projected National Share (PNS) of the vote of 23%, the model still performed relatively well. In part because the even distribution of their vote meant UKIP only won 147 seats. 

The following table shows the actual number of gains and losses in 2013, and both my model estimates and the Rallings and Thrasher forecast.

	Actual	Estimate	Range	Rallings & Thrasher
Con	-355	-205	-295 to -115	-310
Lab	+291	+260	+160 to +355	+350
LD	-124	-190	-85 to -300	-130

Having updated the model, the estimated gains and losses of seats in tomorrow's local elections are as shown in the table below.

	Estimate	Range	Rallings & Thrasher
Con	-130	-235 to -30	-220
Lab	+130	+30 to +220	+490
LD	-400	-570 to -230	-350

The Rallings and Thrasher forecasts come from their PSA briefing.  The pattern of who's expected to be up and who down is straightforward. The seats up this year were last fought on the same day as the 2010 general election; Labour have recovered since then while the governing parties have gone down in the polls. The Liberal Democrat drop is particularly dramatic.

The difference between my model and the Rallings and Thrasher forecast is that for the two main parties the changes are much more muted in my model, especially for Labour.  This maybe partly because they are also predicting UKIP +80, but that still leaves over 300 seat discrepancy to explain. (My model won't be capable of sensibly estimating UKIP seats till 2016: four years after they first fought a large majority of wards in local elections.)

It also doesn't look like the discrepancy is due to differences in estimates for the overall share of the vote. The Rallings and Thrasher forecast 2014 National Equivalent Vote (NEV, similar to PNS) is Con 30, Lab 33, LD 14, UKIP 16, Other 7.  If anything this shows smaller losses and gains since 2010 than do the opinion polls I'm using.  

The graph below shows both the polls and the PNS over time. The rise of UKIP last year led to bigger drops in the PNS for Labour and the Conservatives than might otherwise be expected.  Given the changes in the polls since 2013 and the concurrent Euro elections, the PNS for Con, Lab and UKIP could be close, with UKIP likely to do better than the 16% Rallings and Thrasher have forecast for them.

Returning to the seats forecasts, the differences between the two are most likely to be due to Rallings & Thrasher more careful ward level estimates. My model is a national level only one, estimating the overall share of seats won by each party. Their approach is more detailed and should work better. 

Acknowledgements: Thanks to David Cowling, John Curtice, and Michael Thrasher for help with the data.

Reasons for changing the forecasting model: a response to The Economist

The Economist magazine have published a great article on the difficulties of predicting the next election. It makes lots of good points well and kindly covers my 2015 general election forecasting model. But I was bemused by the line that reads, "Within months he had published a revised model: polls had not adhered to the original one."

I did revise my October 2013 model in February 2014, but not because the polls had not adhered to the original one. They have kindly published a correction. The rest of this post sets out why adherence of polls to the model has be adequate and explains the actual basis for the change in the model, before finally noting that adherence to the polls might weaken close to the European Parliament and local council elections.

As I wrote last week here, there has been very little change in the polls or the forecasts since October, especially relative the to prediction interval for the forecast. Given the polls, this would be true for any model of this kind at this stage in the election cycle. Without dramatic swings in the polls, we are too far from the election and there is too much variation in the historical record to be able to say that deviations from the central estimates of any such forecasting model are so big as to cast doubt on any particular model.

Only today, have I looked at how both models changed between the first published forecast on the website (25th Oct 2013) and last published forecast for the old model before switching to the new one (31st Jan 2014).  While the two models have substantially different predictions the change in the forecast share of the vote for both models over this period was the same: Con +1, Lab -1 and less than a percentage point change for LD. 

So not only was there was no reason to switch models on the basis of adherence to the polls, but the trajectory of the polls has been as close to that predicted by both models as could reasonably be expected.

What prompted the change of the model was explained at the time here, “The change in the methodology is due to a couple of the comments which prompted me to reconsider modelling reversion to the last election, which was an approach I had neglected too quickly.” The justification for the switch of model in the February working paper is better performance at predicting past election results: nothing to do with polls in this cycle. 

If and when I do change the model again (I have said I probably would) it will be an attempt to better reflect the most important aspects of the historical record. Forecasting the current election cycle does require some judgement calls which should depend on current circumstances. But the changes in the polls over the last year do not tell us much as to what kind of model to prefer.

All that said, as we approach the European Parliament and local council elections we are likely to see general election vote intention in the opinion polls change. The Conservatives dropped and UKIP rose in the polls in run up to last year’s local elections. Similarly in the month before the 2009 European and local elections, support for the government dropped while UKIP and other minor party support rose dramatically, not just in European Parliament vote intention but in general election polls too. The MPs’ expenses crisis doubtless contributed to the 2009 changes and this pattern was much more muted in 2004. In all of these cases there was some reversion back to pre-campaign levels afterwards.

This pattern does not always hold, certainly not for all local elections. But if this kind of phenomenon happens again this year then my forecasting model will behave strangely but revert back to normal in a couple of months time.

How the 2015 general election forecast probabilities have changed thus far and why

The graph below shows how my 2015 general election forecast probabilities have changed since October last year.*  The blue line shows the probability that the Conservatives will have the largest number of seats. The corresponding red line for Labour is just the mirror image. Also included in the graph is the probability of a hung parliament.

There hasn't been much change, and the most important thing to note is that there is a lot of uncertainty. The Conservatives have the edge but 59:41 is not a whole lot better than 50:50.

What little change there has been since October has to Labour's advantage. The estimated probability of Labour being the largest party has risen from 36% from 41%. There has also been an increase in the chances of a hung parliament from 40% to 48%.

These changes in forecast probabilities are a function of both forecast shares of the vote and the estimated uncertainty in those shares.  The uncertainty has declined a little since October, but is still huge. The changes in the probabilities are mostly driven by changes in the forecast shares which are shown in the graph below.

Again the main impression is of little change, both in the polls (pale lines) and the forecasts (dark lines). It is still the case that the model predicts a reversal of positions for the Conservatives and Labour and a recovery for the Liberal Democrats. 

While Labour has lost about three points in the polls since October, the two governing parties haven't made any progress at all. Labour losses have largely been matched by a rise in the UKIP share.

The Conservative's failure to improve their standing in the polls since October means their forecast general election share has dropped from 38% to 36% and that is the main reason why the forecast probability that they will win has dropped. 

Since the forecast Conservative lead over Labour in 2015 has also narrowed (to 5 percentage points), the probability of a hung parliament has increased.

Change in the polls relative to that predicted by the forecasting model can be thought of as a measure of party performance. It tells us whether the government is making the kind of recovery previous governments did at this stage and whether the opposition is managing to hold on to mid-term gains better or worse than previous oppositions.  While Labour are now in the polls exactly where the model and the October polls suggested they should be, the governing parties are each a couple of points behind. So the government has not since October achieved the recovery from mid-term blues that history suggests they ought to have done.  

But the difference between observed and predicted change over the last seven months has been small and dwarfed by the forecast uncertainty for both that period and for the year to come. So we are not much clearer about the likely outcome of the general election now than we were in October. The Conservatives still have the edge but there is still everything to play for.

*Methodological note: The graphs here use the revised method from the February 2014 working paper. I have gone back and reconstructed the series of forecasts from October 2013 to February 2014 with the February method rather than use the published forecasts. This is not to try to change history but just to compare like with like. The original October 2013 working paper is here. 

A long range forecast for the UKIP share of the vote at the 2015 general election

Previous posts at this blog introduce my long-range general election forecasting model, which is updated on Fridays at http://users.ox.ac.uk/~nuff0084/ge15forecast/.

Thus far I haven't published a forecast of the UKIP share of vote because the party hasn't been competing in general elections for long enough to build a proper statistical regression model of the relationship between their support in the polls and their votes at elections, as for the three main parties. But the forecast has nonetheless been suggesting a combined 'Others' share of the vote around 17% at the next election.

This estimate is naturally heavily dependent of the current fortunes of UKIP in the opinion polls.  So there is a case for estimating the UKIP share of the vote in 2015 using their current share of the combined Others share in the polls.  This will now be a regular feature of the published forecast.

As you can see from the current forecast below, UKIP are at 12% in the current UKpollingreport.co.uk polling average. This is 60% of the combined Others total of 20 percentage points.  Since the current forecast for all Others combined is 17.0%, the UKIP forecast share is 0.6*17 = 10.2%.

I still haven't decided how best to estimate prediction intervals for the Others and UKIP, but they are likely to be of a similar size to those for the main parties, i.e. plus or minus 8 percentage points.

Despite forecasting a substantial increase in the share of the vote for UKIP, the model is not forecasting any seats for UKIP in 2015. This is despite attributing all of the increase in the Others share to UKIP wherever it was the largest Other party in 2010.  This reflects the very flat distribution of the UKIP vote across constituencies in 2010.

Whether the UKIP vote will be similarly evenly spread in 2015, or whether they will be able to mount successful campaigns in selected seats remains to be seen.  It is certainly something that can't be predicted this far from the election with the statistical technology this forecasting model is based on.

Date of forecast: 04.04.2014
Days till the election: 398

Inputted current average poll shares 
Con : 33
Lab : 37
LD  : 10
Oth : 20
UKIP: 12 so UKIP share of combined Others vote is .6

Forecast Election Day Shares with 95% Prediction Intervals
Con : 36.9 plus or minus 8.4 i.e. between 29 and 45
Lab : 31.8 plus or minus 6.3 i.e. between 26 and 38
LD  : 14.3 plus or minus 9.9 i.e. between 4 and 24
Implied point estimate shares for:
   Others combined: 17.0
   UKIP           : 10.2 (based on share of combined Others vote.)

Forecast Election Day Seats
Con : 308
Lab : 283
LD  : 31
Con largest party, but short of a majority by 18

Forecast Election Day Seats with approximate 95% Prediction Intervals
Assuming LD share at 14.3 and Other share at 17 and allowing Con and Lab to vary as per intervals above.
Con between 218 and 413
Lab between 185 and 368
LD between 25 and 39

Approximate probabilities of key outcomes
Pr(Con largest party) = 60%
Pr(Lab largest party) = 40%
Pr(Con majority) = 35%
Pr(Lab majority) = 19%
Pr(Hung parliament) = 46%
Pr(Hung parliament with Con largest party) = 25%
Pr(Hung parliament with Lab largest party) = 21%

Revised long-range forecasting method for a 2015 British General Election

I have revised my 2015 forecasting methodology. There is a new working paper here. The old one from October 2013 is still here, and there are past blog posts here and here that provide more background. The current forecast is below and will be updated weekly here. 

The new method averages forecasts from two different forecasting models: the old model in which parties have a tendency to move towards their historical average level of support, and a new model in which parties tend to move towards the last election result. (Technically, these are two different regression-to-the-mean effects but with different means.) Both models perform equally well for previous elections and are relatively similar for the Conservatives and Labour, but they have dramatically different predictions for the Liberal Democrats. Allowing for reversion to a long-run level of support produces a low Lib Dem forecast, while a model based on reversion to the previous election result generates a high forecast for them. Without any strong methodological reason to prefer one over the other it is arguably best to average over them.

Compared with using the old model alone, the new combined method raises the predicted election-day share by 4 percentage points for the Liberal Democrats, lowers the Conservative forecast by 2 points, with little change for Labour.  The net effect on the probabilities is to reduce the probability of the Conservatives being the largest party in parliament from 60% to 56% and increase the probability of a hung parliament from 32% to 44% (because of the higher Lib Dem share and lower Tory lead). 

Compared with October 2013, when I first started publishing a forecast, using the new method the chances of a Tory lead in seats has dropped by 8 percentage points and chances of a hung parliament have increased by the same amount (full details in the paper). The positions of the parties in the polls have barely changed over this period. The change in the forecast reflects the greater proximity to the election. Since there has been no Conservative recovery over the last four months, the expected eventual recovery is now smaller than previously forecast. By this measure, Labour have done well to maintain their lead since the middle of last year. 

The change in the forecast does not mean that the old forecast was wrong or invalid. The new forecast is based in part on the old model and the bounds of the new prediction mostly overlap with the bounds from the October forecast. It is more appropriate to think of the changes as updates in light of more information. The historical relationship between polls and votes still suggests the Conservatives are more likely than not to emerge ahead of Labour in votes at the election. Although because of the bias in the electoral system, the outcome in seats is too close to call.

Thanks to all those who (politely) commented on the previous paper or blog post. The change in the methodology is due to a couple of the comments which prompted me to reconsider modelling reversion to the last election, which was an approach I had neglected too quickly. I think the method is better for it so I’m very grateful. 

Most comments on the old model focused either on UKIP or the effect of coalition government on the chances of a Liberal Democrat recovery. The latter is something I agree is practically impossible to model properly in this framework because this is the first time since 1945 that the Liberals have been in government. The rise of UKIP is a major development and although it is not formally modelled the forecast of the combined Other share of the vote mostly reflects UKIP’s high standing in the polls. So UKIP have not been ignored and they are expected to do unprecedentedly well in 2015. 

I will continue to consider modifications to the methodology, so comments are still very welcome. I think the main thing that is missing from the model at the moment is an adjustment for first-term incumbency, which should help the Conservatives, but that will take some time to estimate. Much as I’m sympathetic to some of the comments about things that might mean this time is different, there is not much I can do about them in this framework which relies on understanding how polls translated into votes are previous elections. However, the prediction intervals on the forecast are wide because of all of the idiosyncrasies of previous elections. Whether those for this election are really much different will not be known until after the election. 

Current forecast from the new methodology:

Date of forecast: 10.2.2014
Days till the election: 451

Inputted current average poll shares 
Con : 32
Lab : 39
LD  : 9

Forecast Election Day Shares with 95% Prediction Intervals
Con : 36.8 plus or minus 8.8 i.e. between 28 and 46
Lab : 32.5 plus or minus 6.6 i.e. between 26 and 39
LD  : 14 plus or minus 10.8 i.e. between 3 and 25

Implied point estimate for Others combined: 16.7

Forecast Election Day Seats
Con : 304
Lab : 289
LD  : 30
Con largest party, but short of a majority by 22

Forecast Election Day Seats with approximate 95% Prediction Intervals
Assuming LD share at 14 and Other share at 16.7 and allowing Con and Lab to vary as per intervals above.
Con between 211 and 413
Lab between 186 and 375
LD between 23 and 38

Approximate probabilities of key outcomes
Pr(Con largest party) = 56%
Pr(Lab largest party) = 44%
Pr(Con majority) = 33%
Pr(Lab majority) = 23%
Pr(Hung parliament) = 44%
Pr(Hung parliament with Con largest party) = 23%
Pr(Hung parliament with Lab largest party) = 21%

Initial responses to comments so far on the long-range election forecasting post

Thanks for all the various comments on my initial post about long-range forecasting from historical polls and votes relationship http://electionsetc.blogspot.co.uk/2013/10/a-long-range-forecast-for-2015-british.html. 

Here are some initial responses to comments and questions that have been made on Twitte and on the blog. I've grouped them according to theme and pasted them unedited. I haven't copied everything but I have tried to take examples of all points/queries. Sorry if I've inadvertently left something out but I haven't deliberately done so.

The response to the first set is an apology for something I should have sorted out and will try to resolve. The rest are attempts at explanation, clarification and hopefully helpful responses. Apart from the first three the topics are in no particular order.

Incompatible probabilities:

• Pr(Lab majority) = 15% & Pr(Lab largest party) = 12% are not compatible.
• How can Lab have a bigger chance of a majority than being the largest party?

Fair cop. These figures are logically incompatible. Clearly I need to revise the method to ensure these are fully consistent, and I will do. For computational reasons the method does not currently estimate a full uncertainty distribution over all possible seat outcomes which is necessary for guaranteed strictly consistent estimates. If you read the paper you'll see that, at present, the probabilities for Con majority, Lab majority and difference between Con and Lab are generated from three different assumed normal distributions from the prediction intervals (for Con seats, Lab seats and the difference respectively). These are not strictly defined to be fully compatible. Much of the time this shouldn't matter but did on in this situation and I should have at least flagged this up and discussed it or solved the problem before publishing. Sorry.

It might take a bit of time to resolve the problem but unlikely to make much different to the main story - that the probabilities for Labour largest or Labour majority are small.  Most likely direction of change with a different method is that the probability of Lab largest party will be revised up, but I would be surprised if it became more than 25%. 

All the probabilities come from approximate methods so best just look at them as rough estimates. 

Conflict of interest?

• Someone got paid from CCHQ?

No - I'm not paid by any political party and have never made a political bet. No conflict of interest issues here at all.

What about UKIP?

• Seems odd that there's no mention of UKIP. Not convinced this is best use of regression ever.
• Does this include #UKIP causing Conservatives in marginal seats losing to Labour?
• No Ukip MPs?
• No serious prediction can be made without factoring in Ukip They will take Labour as well as Conservative votes
• This model is flawed as it takes no account of UKIP's rise in popularity (even allowing for a possible tail off at the GE).

UKIP are factored in indirectly but as a young party we can't model their historical experience of polls and election results in the same way as for the main parties. UKIP current standing is reflected in the input share of the vote, which has the Others on 18. Predicted Other share in 2015 is 16.2, which you could say is likely to be mostly UKIP. Apart from Nationalists, the seats prediction assumes that the largest other party in any constituency will get the full amount of the predicted 2010-15 change in Other share. Despite this, UKIP are still not predicted to win any seats - they are just too far behind.

The model doesn't allow for UKIP to benefit disproportionately from any one party. I can see this is a concern but note that Rob Ford, Matthew Goodwin, myself and others have been pointing out that UKIP take votes from Labour as well as the Tories, so the differential impact on Tories may be much more muted than many assume. 

Prediction is implausible?

• Forgive my scepticism. No-one has polled over 40% in an election for 12 yrs, and the Tories haven't for 21.
• those Con + Lab vote shares would be mirror of Blair vs Hague in 2001 
• All 3 points seem logical and v probable.. but direction of travel seems too drastic to take seriously.

I agree that the prediction is remarkable, but think it is worth seeing what the data say. The patterns in previous cycles are surprisingly consistent. Paper discusses idea of weighting more recent elections more but that doesn't improve out-of-sample prediction substantially. I don't think it is a good idea to try to find the single previous election that seems to best characterise what you think is going on and rely on that. Better to pool information from a set of previous elections.

This time is different because of the coalition

• History of Tory incumbency barely relevant because Coalition are incumbents not Tories.
• Surely many historical precedents are not valid because we are in a unique situation - there will be no incumbent government defending its position. All parties will be campaigning on the basis of change.
• Nor does it allow for the fact that a significant number of unhappy Lib-Dem voters will be registering their dis-satisfaction with the Coalition & voting Labour. As Mike Smithson says, this will be a unique election. Such generalised models based on previous voting patterns are, therefore, unlikely to be correct.

Maybe there are good reasons to believe that things are not likely to be so different. Research on coalition government electoral performance cross-nationally by myself and others suggests that the Tories are most likely to held responsible for government actions as the largest party in the coalition. So for want of a better reason to do differently I have effectively produced the forecast in the same way as if the Conservatives were in a single party government.  Equally I haven't taken any account of minority governments in the past. Too sporadic to model statistically.  The paper discusses how the coalition affect on Lib Dem and Labour support is factored in because it is already reflected in the polls.

Are past polls a good guide to the future?

• Interesting data, but why assume that past polls are a good guide?
• My preference wld be for "fundamentals" forecasts at this stage (economy, maybe PM approval)

I'm not assuming history of polls is definitely a good guide. I'm partly trying to work out how good a guide it is and the confidence intervals reflect estimates of how poor a guide current polls are. There is a meta level question as to whether the past is a good guide to future levels of uncertainty. The out-of-sample prediction section in the paper suggests that it has helped a bit in the past and so it may do again in the future. It may not work out but in trying to say something about the future I think it is better than not considering past experience.

The question of whether there are better bases for forecasting is a good one. My impression is that the "fundamentals" might be good to also consider later on, but at this stage you would be effectively predicting the future trajectory of the economy over quite a long time period; arguably more difficult.

Is this the best forecast we can do?

• is your view that this model provides the most accurate available forecast, or just that these factors produce it?

I'm not aware of any others this far out apart from assuming that current polls are the best guide we have and projecting them forward assuming no change between now and the election. Part of the point of the paper is to consider the most likely direction and magnitude of change between now and the election. Past experience suggests that the method I'm talking improves prediction by about 30% over just assuming the polls will stay steady. (See paper.)

Regional and constituency factors

• How's that going to happen without any Tory seats in a city north of Birmingham?
• Also doubt past precedent is helpful either & believe Tories are losing the North as they lost Scotland
• You results suggest a Tory lead of less than 10% resulting in comfortable majority. Which seems unlikely
• boundaries used to favour Tories now favour Labour.

The seats prediction is off the back of 2010 constituency results and so respects the geographical performance of the parties then.  Uniform swing and similar haven't been perfect in the past but they have been sufficiently good so as to think that the seats prediction part is a small problem relative to prediction of the GB share of the vote. Bias in the system is clearly visible in simulations with other results.

Switching between parties

• Secondly what is going to happen to the 2010 LD>CON switchers. In your model they seem to evaporate.
• Third point the detail from almost all polls shows that very little of current LAB support comes from CON converts.
• To what degree does the model take into account the point frequently made by Mike Smithson, that the loss of half the Lib Dem vote from 2010 has mostly gone to Labour, and there appears to be little sign that it will either go back to the Lib Dems, and very little sign that it will migrate to the Conservatives?
  

Model doesn't look at all at individual level switching, just overall levels of change. The predictions say nothing about who switches which way, just the net effect. Switching up to now is reflected in current poll levels which influence the forecast but just based on current levels of support, not origins or voting histories.  

Taking previous election result into account

• Historical tendencies? Well you forgot the historical tendency that incumbent parties have only once increased their share of the vote since the 50s.. 40% for the Tories from a 2010 starting point of of 35%? What a crock of shite!
• You are not taking into account that the GE to Mid-term fall this parliament is less than historical data

The model doesn't directly take the prior election result into account. It should influence things indirectly but affecting the levels of support in the polls in the mid term. I will explore further whether it adds value beyond current polls. What is being suggested in the first comment is actually a model of forecasting without any polls at all. It seems odd to ignore the most current information. I'm just arguing that we should look at with the perspective of how polls in the past have corresponded with future election results.

A long-range forecast for a 2015 British General Election based on current polls and historical polls and votes

I've just started publishing forecast from a polls based method for forecasting the next general election here. I'm hoping to update the forecast weekly. 

As I say on the website: "The methodology is described in a working paper. The approach is broadly to predict the next election based on current opinion polls and the track record of polls in previous electoral cycles allowing for change in opinion in the run up to the election. The method allows for three main phenomena: historical tendencies for the Conservatives to over perform and Labour to under perform their vote intention figures in the polls when it comes to election day; governments being more likely to recover and oppositions fall back in the run up to an election; and a tendency for parties to move back towards their long-run average level of support. All three suggest a Conservative recovery and a Labour set back from autumn 2013. The statistical regression methodology generates estimates of uncertainty and so prediction intervals (range of likely outcomes) and probabilities for key events are also provided below. The forecast represents a way to think about the implications of current opinion polls for the outcome of the next general election in light of the historical relationship between polls and election results. It is the product of a statistical analysis of the data and not my personal opinion about what will happen."

The first forecast is replicated below. There are two striking features. The first is that the Conservatives are forecast to do much better than they are currently polling, mainly because they are in government but also partly because they are historically at a relatively low point (from which regression to the mean effects suggests they should recover) and as a party they have tended to outperform polls at elections. Labour are predicted to do correspondingly worse and so the forecast for the top two is almost symmetrically opposite from the current polls: 40:32 instead of 33:38.

The second of the two most striking features is that the prediction intervals for shares of the vote are enormous.  For the main parties it is clear that there is more uncertainty in the Conservative vote but even the forecast Labour vote could be out by as much as 6.6 points: a huge political difference.  At first glance these prediction intervals may seem to encompass all foreseeable outcomes and more. For the Liberal Democrats the interval from nothing (a hard boundary that had to be invoked!) to 26% seems ridiculously large. While these may seem hilarious at first sight, remember that not all points within the intervals are equally likely to occur. Also as 95% forecast confidence intervals they reflect the historical variation in the votes for these parties and there should be only a 5% chance of a result outside the interval. So they are bound to be very broad to be credible. Even so, the lower bound for the Conservative forecast, at 28%, tells us that it is very unlikely the Conservatives will do much worse than they currently stand in the polls, which is informative. Similarly, the Labour prediction interval suggests it is extremely unlikely that Ed Miliband will do as well as Tony Blair in 1997 or 2001 but it would not be surprising (given polling in previous elections) if he did worse than Gordon Brown or Michael Foot. 

The forecast election-day seats are as you would expect them given the forecast shares. They are a probabilistic estimates of the kind used in election night forecasting. A classic uniform change prediction would produce slightly different figures but not by much, especially given the large prediction intervals for seats that follow from the large prediction intervals for votes.

The estimated probabilities for key outcomes are perhaps the most helpful feature of the forecast so far from an election. These show that the Tories have an 88% chance of being the largest party but only 57% chance of an overall majority. These are rather one sided at this stage in the cycle given there is plenty of scope for change in party support before the election. Even immediately before the election there is considerable uncertainty given the historic record of the polls as shown in Table 1 of the working paper.

Having some estimate for the probability of a hung parliament (currently 28%) is helpful to understand the operation of the electoral system. A Liberal Democrat recovery to May 2010 levels would increase the chances of a hung parliament to over 50%.

Date of forecast: 25.10.2013

Days till the election: 559

Inputted current average poll shares 

Con : 33

Lab : 38

LD  : 11

Forecast Election Day Shares and 95% Prediction Intervals

Con : 40.2 plus or minus 11.8 i.e. between 28 and 52

Lab : 31.8 plus or minus 6.6 i.e. between 25 and 38

LD  : 11.8 plus or minus 14.5 i.e. between 0 and 26

Forecast Election Day Seats

Con : 337

Lab : 265

LD  : 21

Con majority of 24

Forecast Election Day Seat approx. 95% Prediction Intervals

Assuming LD share at 11.8 and allowing Con and Lab to vary as per interval above.

Con between 219 and 471

Lab between 140 and 376

LD between 14 and 30

Probabilities of key outcomes

Pr(Con majority) = 57%

Pr(Lab majority) = 15%

Pr(Hung parliament) = 28%

Pr(Con largest party) = 88%

Pr(Lab largest party) = 12%