Question: how can non-voters win the 2020 election for Jeremy Corbyn?

Short answer: they can’t.

This isn’t an anti-Corbyn point, by the way: they also can’t win a general election for Yvette Cooper, Andy Burnham or Liz Kendall. There is no route to a parliamentary majority for any of Labour's leadership candidates which doesn’t involve addressing the concerns of Conservative voters. Why not?

Well, there’s the obvious point that you can’t only raise your own turnout. Take, say, Barack Obama’s successful presidential bid in 2008: yes, he increased turnout among young graduates and ethnic minorities, contributing to his victories in traditionally Republican-leaning states like North Carolina and Florida. But he also increased turnout among Republican voters, losing by a bigger margin in Tenessee, Arkansas, Louisana, Oklahoma and West Virginia than John Kerry did in 2004.

The problem for British politicians attempting to emulate the Obama strategy is that Britain is less diverse than the United States. British constituencies are, for the most part, what sociologists call “socially crunchy” – so if you increase turnout among, say, ethnic minorities and young graduates, but turn off, say landlords and middle-managers, there are very few seats where you will feel the benefits but not the punishment. (In fact, most of the seats where this is the case Labour already hold.)

Then there’s the bigger problem. Non-voters aren’t actually all that different from voters. After the election, the Trades Union Congress commissioned Greenberg Quinlan Rosner Research to find out what had gone on. Here’s why non-voters and voters didn’t opt for Ed Miliband’s Labour party here:

As you can see, there is not a vast gulf between the two groups. (“Other” by the way, includes responses like “They weren’t leftwing enough”, "They sold the gold", "Iraq" and so forth.) Even if you assume the 35 per cent of “Don’t Knows” actually mean “I was waiting for a real Labour party”, and that a more radical Labour party would attract all of them, look at the worries that people who went on to back Labour despite them in 2015 had:

It’s hard to see how a more “traditional” Labour approach on public spending, welfare, and so on wouldn’t also lose voters from Labour’s existing 2015 bloc. But what about, say, the Greens and the SNP?

It is just possible that the 20 per cent "Other" in the SNP is all "Labour weren't leftwing enough" but it seems likely that at least some of it is "I want to leave the United Kingdom". But even if we take all of that 20 per cent, we're still talking Labour gais in Scotland of fewer than ten seats. Now let’s look at people in social grade DE, semi-skilled and unskilled manual workers, what you might categorise as Labour’s “traditional” core:

Look familiar? Now, here’s what Ukip voters and Tory voters made of Labour in 2015:

That’s not to say that the next Labour leader shouldn’t aim to increase turnout. It’s just to say that there is no evidence at all that policy prescriptions that turn off Conservative voters will have a more natural home among people who didn’t vote – quite the reverse. Whatever happens, if the next Labour leader wants to win the next election, they are going to have to win over people who thought "they would make it too easy for people to live on benefits", and that "they would spend too much and can't be trusted with the economy". The next Labour leader – whoever they are – is going to have to try to win over people who voted Tory in 2015. This is one of the few times in politics where there really is no alternative.