It was suggested often during last year’s Labour leadership contest that if the party had Jeremy Corbyn at the helm it couldn’t win a general election. The argument holds that Corbyn, as a leftwinger, couldn’t appeal to people who had previously voted for the Tories, and these were the people Labour needed to win over in order to make the sums work.

I considered writing about this at the time, but events overtook me and I left it alone as the argument faded. But it has recently been used by Corbyn’s opponent this year, Owen Smith.

“It’s not just a question, as Jeremy said on a few occasions, [that] we need to get a few people who have contemplated voting Tory to vote Labour. We need to get two million people who actually voted Tory at the last general election to vote Labour,” Smith said in Bristol.

This two million figure, I imagine, comes from the Conservative lead in the popular vote over Ed Miliband’s Labour at the 2015 general election, 11.3 million to 9.3 million.

Of course, total votes doesn’t translate neatly into total seats — on vote share the Tories are overrepresented by 91 seats, Labour 34 — but you can see the principle.

This also underlies the idea that each vote taken off the Conservatives counts double, as they’re Labour’s main national opponents.

Taking votes off the Tories is a plausible strategy. In an abstract way, the numbers work, but it raises some difficult questions. “Winning over Tory voters” is traditionally code for adopting right-wing policies and it’s not clear if Tory voters would ever switch to Labour in sufficient numbers, let alone what it would do to Labour as a “democratic socialist party.”

However, this has been presented as the only way that Labour can win, usually by people who would like Labour to shift to the right regardless. But it’s very clearly not the only way Labour can win.

An unstated but clear part of the argument is the idea that voters come from some finite pool — as they do, but not in the way these people suggest — and so votes must be taken from other parties. There are no substantial parties to Labour’s left, so you must look to the right.

This is nonsense, as this chart shows:

Plot showing Labour and Conservative popular vote between 1992 and 2015

Between the 1997 victory and 2010 defeat, Labour lost 4.9 million votes. These votes largely didn’t go to the Conservatives. In 2001 both lost many votes, and the Tory recovery in 2005 was small compared to the number of votes Labour lost again.

The imbalance between Labour’s losses and the fortunes of other parties can be seen in the following chart. While some Labour votes may go elsewhere, they don’t make up the full picture.

Plot showing the change in the Labour vote, others’ vote and total change compared with the previous election between 1997 and 2015

The answer is turnout. (Brace for percentages.)

The 1997 election had a very low turnout by historic standards, at 71.4% the lowest since 1935. But things got worse in 2001, which had the lowest turnout (59.4%) since 1918 (57.2%).

(As an aside, 1918 is an interesting election, numbers-wise. It was the first in which women could vote, but only if they met certain property qualifications and were at least 30 years old — an age picked to ensure they were in the minority. For men all property rules were scrapped and they could vote from age 21. But the recently ended war and 107 uncontested seats meant that relatively few people voted.)

Turnout has recovered somewhat since 2001 — to 66.2% in 2015 — but the past 20 years form a noticeable trough in the past century. So for the question: “Where did 4.9 million Labour voters go?” a large part of the answer is: “Home.”

The following chart shows the evaporation of Labour votes, and puts the party’s total in the context of turnout and the size of the electorate:

Plot showing the size of the electorate, total number of votes and total Labour vote between 1992 and 2015

People who make the “votes must come from the Tories” argument are restricting themselves to a section of the electorate that is to a certain extent already committed to voting. It is a truism in Britain that the elderly and the rich are more likely to vote, and they’re more likely to vote for the right.

But, as the chart above shows, a huge chunk of the electorate regularly does not vote at all. Since 2001 that chunk has been a full third of those registered.

I’d argue that a strategy based on a right-wing policy shift in order to poach Tory voters would further alienate many people who previously did not vote. That certainly appears to the be the story of the past two decades — after booting out the Tories in ’97 people abandoned Labour as the neoliberal character of the New Labour project became ever clearer. The refusal of the Ed Miliband-Ed Balls leadership to break cleanly from neoliberalism shoulders much of the blame for the 2015 election defeat.

Everyone who’s watched The West Wing can probably recall that “Democrats win when turnout is high.” I don’t fully support that claim because it’s too simplistic and I feel it reduces what should be a more philosophical political debate — about what kind of society we want and the most just and effective way to achieve it — to one about tactics.

But, before Corbyn, it had been a long time since Labour’s policies looked towards real social democracy, let alone socialism. Those kinds of policies would help enormously the mass of people in Britain, across the board. A sustained campaign to reconnect with communities and show that if we fight together in that direction we can improve everyone’s lives has, I think, a far greater chance of pulling in enough of those non-voters to secure victory. And hey, a few ex-Tory voters might see something in it for them too.

Scotland’s experience of the independence referendum, engaging very many people in a political question that they felt they had both a stake in and influence over, shows that is is possible to draw in people who previously did not participate. Turnout in Scotland shot up from 63.8% in 2010 to 71% in 2015, with the independence referendum held in September 2014 (with a 84.6% turnout).

Unfortunately for Labour much of that energy swung behind the Scottish Nationalists, for a variety of reasons that were long in the making.

But is does show that a campaign that really speaks to people — and listens to them! — can draw in many people who had previously shrugged off the whole affair.