The prediction of Silver is a simple average of the last polls of the ten main polling organisations. He uses the same data as I do, kindly gathered by the volunteers of Wikipedia, who also made the plot below.
The statistics normally used to estimate the outcome of elections assumes that there is a fixed value and the surveys are noise around this value. In this case you have to average (in a smart way) to remove the noise of the surveys and get a better estimate of the fixed value.
Wikipedia uses the same assumption to compute the curve of the running average of all polls and takes the average over the 10 most recent polls. The distance between the curves of the Conservatives and Labour in the Wikipedia graph above is about 8 %.
Comrade Trend
However, if the polls are moving it typically keeps on moving in the same direction. Germans call this Genosse Trend, Comrade Trend. If you are going up in the polls Comrade Trend is a great friend.This could be because it takes time until "everyone" has heard the news, only small part of the population is a news junky. You may also want to wait whether refuting information comes in some time later, whether a campaign changes its position or you may want to talk about the news with your family and friends.
It takes some time until people have found time to read the manifestos (Conservative | Labour). Hopefully many do, there is a real choice this time. Also the strengths and weaknesses of the campaigns mostly stay the same during the campaign. Each time Theresa May openly refuses to answer basic policy questions she loses voters, at least for people like me.
Comrade Trend seems like a good assumption to me. The polls in the UK move so fast that the difference in assumptions really matters this time. The smoothing method [[LOESS]] estimates the trend at a certain time to make the best estimate at that time. It fits a line to the data over a subperiod. Estimating a fixed value would correspond to assuming the line is horizontal over this subperiod. LOESS thus takes Comrade Trend into account. It gives the figure below.
The predictions for election day, this Thursday, were made by assuming a linear trend for the period since the 1st of May.
Election turnout
An important reason that it is hard for polling to predict the outcome of an election is that it is not known who will actually get off the couch and vote. The figure/tweet below shows for one of the polls how much difference various turnout assumptions makes. The spread in the polls is very large this election. That may well be because turnout is very important this time. Older people tend to favour the conservatives and faithfully show up. The question we will not know until election day is how much young people will show up.For the first time, our results model (using latest poll averages) projects a hung parliament *if* turnout is 78% across all ages. #GE2017 pic.twitter.com/Wv7PzEufLY
— Ian Jones (@ian_a_jones) 2 June 2017
Polling bias
Then there is the question whether polls are not just noisy estimate, but whether they are also biased relative to the election. Nate Silver writes:Exactly how strong the Conservative tendency to outperform their polls has been depends on where you measure from. Since 1992, Conservatives have beaten their final polling margin over Labour by an average of 4.5 percentage points, and have done so in all but one election. (That was 2010, when both Conservatives and Labour gained ground as Liberal Democrats’ support collapsed, but Labour slightly outperformed its polling margin against the Tories.) Go all the way back to 1945, however, and the average Conservative overperformance is just 1.8 percentage points and is not statistically significant.I prefer to look at all the data and would say that the bias is not statistically significant. It would be weird for the bias to have become worse, except maybe for really recent elections where parts of the population can no longer be reached with landline telephones. That you can find a period with a higher bias may well be cherry picking. As long as no one can provide a reason for a change in bias since 1992, picking a specific period after looking at the data is statistically suspect.
Outcome
According to Nate Silver UK polling tends to have a relatively high uncertainty and misses the election outcome typically by about 4 %. Estimating a trend is harder than estimating a mean, thus it could be that my 2 % prediction is even a bit more uncertain. Thus if my best estimate is right and the conservatives are only 2 % ahead the election is a toss up: the difference is less than the uncertainty.Let's see who turns out.
[UPDATE. If you put in my numbers for the conservatives and Labour and add 8 % for the Liberal Democrats, 4 % for UKIP and 3 % for the Greens (estimated from Wikipedia graph), the Electoral Calculus app computes the following seat distribution:
National Prediction: Conservative majority 4
| Party | 2015 Votes | 2015 Seats | Pred Votes | Gains | Losses | Net Change | Pred Seats |
|---|---|---|---|---|---|---|---|
| CON | 37.8% | 331 | 40.0% | 6 | 10 | -4 | 327 |
| LAB | 31.2% | 232 | 38.1% | 14 | 1 | +13 | 245 |
| LIB | 8.1% | 8 | 7.6% | 0 | 5 | -5 | 3 |
| UKIP | 12.9% | 1 | 3.8% | 0 | 1 | -1 | 0 |
| Green | 3.8% | 1 | 2.9% | 0 | 0 | +0 | 1 |
| SNP | 4.9% | 56 | 4.7% | 0 | 1 | -1 | 55 |
| PlaidC | 0.6% | 3 | 0.5% | 0 | 2 | -2 | 1 |
| Minor | 0.8% | 0 | 2.5% | 0 | 0 | +0 | 0 |
| N.Ire | 18 | 0 | 0 | +0 | 18 |
[UPDATE. Just before closing of the election let me publish my last updated graph here. Currently Tories are 4.2 % ahead. That is still within the uncertainty and while it is quite likely that the Conservatives will win, there is still a Trump chance that Labour will win. Let's see who shows up to vote.
]
[POST ELECTION UPDATE. One of the best polls was by YouGov. Good with respect to statistical methodology and accuracy in this election. Interestingly, they did not find a steep trend towards Labour, but had a stable 3% lead for the conservatives since 27 May. Thus Comrade Trend may be more the inertia of the other polling organisations than that of the public.]
Related reading
YouGov, the heavily criticized poll that got it right: UK election: The day after. "But the general picture is clear: the model was a huge success in an election which most politicians, pollsters and commentators got badly wrong."Nate Silver at 538: Are The U.K. Polls Skewed?
Response to Nate Silver, part one (because it’s early!) This post warns that the averaging method in Nate Silver's post is very basic and not comparable to the advanced methods he uses for US polls.
UK polling report: How the polls have changed since 2015
* The code used to generate my prediction plot is on Github.
