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YouGov's multilevel regression and post-stratification (MRP) model is seen as one of the most reliable pre-election predictors of what results will look like in the UK. Their turnout predictions by age are as follows:

Table 14: Current vote (column) by age (row), row percentages.

According to the academic analysis linked on their election centre, this is determined from historical figures, primarily in 2015 and 2017.

"In contrast to traditional polling approaches, we do not rely on respondents’ self-reported likelihood of voting when working out probable voting patterns across different constituencies. Instead, we build a model based on data from past elections to predict whether different types of individual would be likely to vote in a new election. The result of this process is that we assume that the electorate for a new election would be demographically similar to the electorates of 2015 and 2017 (which were themselves similar, despite 2017 claims about a “youthquake”). This is the same strategy we used for the 2017 election model. It is not perfect, as it is possible that there will be changes to the demographic make-up of the electorate, but is also unlikely to yield large errors overall."

It seems to me like these turnout figures exaggerate the differences that exist between age groups. Let's compare them to the historical figures from the parliament website:

Parliament Voter Turnout by Age

While youth voter turnout looks pretty much in line with what you'd expect (assuming that 2017 was largely an anomaly) their estimates for older voters seem significantly higher than the historical data would imply. Has anything been published which would explain this difference?

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The differences seem to be statistical and a result of the difficulty of obtaining turnout data broken down by age.

The main way we have of understanding the electorate is an analysis of exit polls. But as these are a sample of voters, they cannot directly measure turnout. So turnout estimations are made using post-election surveys, with all the issue of low response rate (about 6% typically) and a tendency to get more responses from voters than non-voters (which is particularly an issue if you want to find out about the numbers of non-voters).

Therefore while the overall turnout is known very well, the breakdown of turnout by different groups is not. YouGov have a model for turnout by age that is intended to be combined with other indicators of the likelihood of voting, such as voting habits or economic class. It may simply be that this model is a better at predicting the final voting outcome than others.

It is also worth noting that in past elections, the polls have underestimated Conservative voting strength, and have (as Nate Silver says) engaged in "pretty dodgy" methods to boost the headline figure for the Conservatives up to where they often seem to be at the election (Nate suggests these resulted in the polls missing the 2017 hung Parliament). Nate Silver's analysis may be found here.

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TLDR: they estimate turnout rates using data from the British Election Study, which in some cases has validated vote records.

The answer to your question is yes, at least for the 2017 election. From their article in the International Journal of Forecasting:

For each application, we estimated the conditional probability of turnout p(T_i = 1|X_i) as a function of covariates using a face-to-face probability survey conducted after one or more prior election(s). ... For the UK general election model, we pooled the 2010 and 2015 BES post-election surveys, after verifying that the demographics of turnout in the two surveys were largely similar. ... For all three applications, the turnout model took the form of a multilevel binary logistic regression model. ... for the UK general election model, BES weights were used via a quasilikelihood approach. The variables used in each model (including interactions) are listed in Table A.2 in the Appendix.

They go on to describe their procedure in more detail. So, basically, they estimate turnout by age group (and other demographics) from the British Election Study. Note that recent waves of the BES have validated turnout variables, which are presumably better measures than mere self-reported turnout. This FAQ on the 2019 forecast says they still use recent waves of the BES:

Turnout is assessed on voters’ demographics and is also based on analysis from 2015 and 2017 British Election Study data.

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