The plight of Jeremy Corbyn’s Labour opponents can be summed up like this. While they have, understandably, railed against the left’s “no compromise with the electorate” tendency, they’ve failed to acknowledge that they cannot retake the Labour leadership without first winning over the membership.

They lacked ideas, unable to realise that Corbynism emerged amid the intellectual exhaustion of all other wings of the Labour party. It triumphed because the old social democrats had abandoned consistent social democracy, and the only faction willing to still champion it was the party’s left flank. No answers have been offered as to why there is an international crisis of European social democracy, of which Britain is just one example. In other words, they became backward looking, defined by what they were against rather than what they were for, and politically incurious: traits they once characterised as defining their leftwing opponents.

In the aftermath of Labour’s catastrophic defeat, these remain the tests for any leadership candidate seeking a decisive rupture with what came before. On the candidates’ side is the knowledge that the members are traumatised, and, despite their frequent demonisation as an extremist and dangerous rabble, they are largely non-ideological, sharing a general revulsion at injustices and a desire for sufficiently radical solutions to tackle them.

Opinium finds that just 12% of the electorate rejected Labour because of its policies. This informs Keir Starmer’s campaign. His presence in Corbyn’s shadow cabinet won him admirers among the rank and file, not least because most of the members lean towards remain. His slick launch video, showcasing his involvement in popular struggles against Thatcherism and legal work on behalf of the oppressed and against the powerful, went down well. Early polling by YouGov – suggesting that he has a commanding lead – is likely to be accurate.

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Indeed, Starmer’s team has been approaching certain figures who have served the Corbyn project in some capacity, whether in the leadership office or even in Momentum taking on the impressively clever Simon Fletcher – who ran Corbyn’s first leadership election – as strategic advisor. Publicly, Starmer talks of maintaining Labour’s radicalism, and his team privately extols his commitment to public investment. But here are the questions Starmer and other candidates must answer. Will tax rises on the top 5% and corporation tax be maintained? What of scrapping tuition fees? What of public ownership, not just of rail, but of other utilities? What of the Green New Deal? Any Labour leader will face a campaign to purge Corbynism from Labour. Would Starmer withstand such pressure? He has now accepted that the election result ends the debate on Brexit, and that it must now happen; but how does he answer the likes of Caroline Flint, who lost her Don Valley seat and does not believe he can win back leave-voting areas? These questions need compelling answers.

Lisa Nandy’s advantages are that she resisted Labour’s shift towards a referendum, and that she is a woman and a solid media performer. And her fixation with towns is all the more important after the party’s devastating losses in the north and Midlands. But she too faces questions on her policy prospectus and on her passionate cry: “How dare we tell working-class people what’s good for them.” Listening after a devastating defeat is clearly crucial. But surely the point of politics is to offer a plan that will improve people’s lives – though, to be effective, it should be married to their lived experiences, and explained in a way that isn’t patronising or elitist.

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Jess Phillips’s campaign extols her background and promises a policy offer focusing on social care, childcare and the climate crisiswith a theme of priorities and “doing the right thing”. But with backers firmly on the Blairite wing, it would prove a decisive turnaround in the membership’s attitudes for them to accept an inevitable decisive shift to the right. Emily Thornberry’s sassy charisma and loyalty to Corbyn during the 2016 coup won her many admirers, and she was once Len McCluskey’s favoured successor. Today she faces the same questions as Starmer, and is unlikely to make the ballot. As is Clive Lewis, who won’t get the MPs and unions needed to pass the threshold. He is using the campaign to flag-wave for his passionate priorities: like a so-called progressive alliance, democratising the party and challenging what he sees as an intolerant machine politics. He deserves a bright political future.

The left’s flagbearer, Rebecca Long-Bailey, had a slow start for ironic reasons: her fear of being boxed in as “continuity Corbyn” made her reluctant to hire figures associated with the project, and there are few experienced leftwingers ready to serve who are not. And while her first Guardian article read like it was written by committee, her tub-thumping launch piece in Tribune energised the left’s base. Bright and details-focused, a working-class woman from a leave community, her impressive first interview on the BBC’s Today programme was cheerful and full of willingness to accept Labour’s major errors: on Brexit, on antisemitism, on not having a coherent vision, not having the public’s trust, not rebutting a vicious media onslaught. But her pitch must go beyond being “Corbyn without the baggage” or a one-more-heave approach: her team needs a detailed, coherent strategy for why a compelling socialist vision can win in 2024 that decisively breaks with what came before. Some fear a return to the worst machine politics of the Corbyn era: to convince doubters, her team should emphasise a pluralistic, let-a-thousand-flowers-bloom style. Indeed, elements from the current leadership who are wedded to such machine politics tried to encourage Labour chair Ian Lavery to stand and are now promoting Barry Gardiner as a candidate, fearing they cannot control Long-Bailey. It is entirely self-destructive.

All candidates have pressing questions to answer, and they must be addressed to a membership desperate to end Tory rule while offering an unquestioningly inspiring alternative. A break with the past, yes, but a genuine one – not a return to the discredited compromise of 2015, or irrelevant nostalgia for 1997.

•Owen Jones is a Guardian columnist