I’ve just started publishing a 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 October 2013
Days till the election: 559

Inputted current average poll shares
Con: 33%
Lab: 38%
LD: 11%

Forecast Election Day Shares (with 95% Prediction Intervals)
Con: 40.2% (±11.8, i.e. 28% – 52%)
Lab: 31.8% (±6.6, i.e. 25% – 38%)
LD: 11.8% (±14.5, i.e. 0% – 26%)

Forecast Election Day Seats (with approximate 95% Prediction Intervals)
Con: 337 (219 – 471)
Lab: 265 (140 – 376)
LD: 21 (14 – 30)

Central forecast: Con majority of 24

Probabilities of key outcomes
Con majority: 57%
Lab majority: 15%
Hung Parliament: 28%
Con largest party: 88%
Lab largest party: 12%