The moment it should have been obvious that Jeremy Corbyn was going to win the 2015 Labour leadership election was when Progress Magazine asked all four candidates why Labour had lost the last general election.

Andy Burnham, Yvette Cooper and Liz Kendall all responded with some manner of vague bafflegab. Corbyn, however, had an answer that was simple, memorable, and right: “Because we didn’t get enough votes.”

Two years on, Labour is just weeks away from another election in which it looks likely to once again end up with not enough votes to get the Tories out of No 10.

But perhaps there’s a solution. Labour could take its votes and add them to the votes of the parties of the centre and centre-left: the Greens, the Liberal Democrats and the Scottish National Party. Perhaps all of them, added together, would be enough to get the Conservatives out of office. You could call it a “progressive alliance.” The idea has attracted heavyweight support—Caroline Lucas, the leader of the Greens, and Jon Cruddas, Ed Miliband’s former policy chief, are among the heavyweights endorsing the scheme in a recent letter to the Observer.

It’s a beautiful idea—but there’s just one problem. It doesn’t work. There’s an immediate mathematical problem. Even if you were able to guarantee that not a single person currently backing Labour, the Greens, the SNP or the Liberal Democrats would be put off by the arrangement, more often than not, the combined forces of progressive parties haven’t even been enough to equal, let alone surpass, that of the Conservative Party in the bulk of the polls taken since Theresa May announced this snap election.

But even that assumption—that the votes of the four anti-Conservative parties can be traded freely—is fraught with peril. Contrary to what many in Labour seem to believe, people who vote for the SNP, the Greens, or the Liberal Democrats have not done so as a roundabout way of voting for the Labour Party. They are voting against the Labour party.

Equally, Labour voters in St Ives, Hazel Grove and Twickenham who voted for the Liberal Democrats from 1997 until 2015, when Ed Miliband’s party surged to a series of pyrrhic third places while the Conservatives won, were not seized by a sudden inability to tell whether or not Labour had a fighting chance of winning. Instead, thanks to the years of coalition, they no longer saw a point to lending their votes to the Liberal Democrats.

A YouGov poll on the durability of the progressive alliance found that around a third of Labour voters, asked whether they would vote for a Green over a Conservative, demurred. Some would prefer not to vote at all—others would opt for the Tory. Likewise, 15 per cent of Liberal Democrat voters would back a Conservative candidate over a Labour one—just 57 per cent of Liberal Democrats would, in fact, stick with “the progressive alliance” and back a Labour politician in lieu of a Liberal Democrat one.

Polls are polls. Surely, in the real world, faced with the actual choice of a Liberal Democrat or a Green over a Conservative, Labour voters would choose the progressive option—or vice versa?

Thankfully, the wonderful world of local politics means that we have plenty of real world examples of council by-elections—and indeed, full-blown council elections—when, for reasons of personnel as much as politics, a Green politician faces a Conservative alone, or a Liberal Democrat faces a Conservative alone, or Labour faces a Conservative alone. And what happens in each and every one of those contests is that while most of the “progressive” vote transfers to its natural home, a decent chunk of it doesn’t.

Those are just the mathematical problems. Here are the philosophical problems. Any progressive alliance is going to involve giving things up. A Labour politician is going to have to be less radical to lock in the votes of Liberal Democrat supporters who might otherwise back the Conservatives. A Green politician is going to have to tone down his/her environmental policies to get the votes of the rest of the progressive bloc. A Liberal one is going to have to sound less wooly on civil liberties. And the non-negotiable price for Labour in all of this would be the end of the current electoral system of first-past-the-post and movement towards a proportional system.

The unpalatable truth is that any “progressive alliance” would be restricted in opposition by the need to placate its least radical partner, in this case in the Liberal Democrats. It would then be hobbled in office by the need to keep its most radical partner—in this case, most likely the Greens—on side.

Then there’s the elephant in the room: that the only reason why anyone is getting excited about the progressive alliance is that they cannot see a plausible way for the Labour party in its current form to win power without assistance. But Labour’s problems of winning alone—that not enough people trust it with their money or want its leader in No 10—are also problems for Labour winning in coalition or a progressive alliance. Liberal Democrat voters who prefer May to Corbyn—around half of them—are not merely a kind word from Tim Farron away from changing their mind about the Labour leader.

A progressive alliance might be part of the solution if the Labour Party appealed to more people and was a more natural home for the sort of voters who might, at the moment, flirt with a vote for the Liberal Democrats or the Conservatives. It isn’t a substitute for the question of how it either makes its present leader more appealing or substitutes him for a better centre-forward.

Shortly after Labour’s third successive defeat, a young Tony Blair wrote that there was nothing that Labour should give up to enter a coalition that it should not give up to govern alone. As the left once again stares down the barrel of a third successive defeat, that remains the central problem with the progressive alliance. Why give something up to govern in partnership when you could do the same to govern alone?