Are you now, or have you ever been, a socialist? The Labour leadership candidates all pleaded guilty to quietly harbouring ideological convictions when asked what socialism meant to them, though they may well have anticipated some inquiry of a philosophical kind given that last night's hustings event at the Institute of Education in London was organised by the Fabian Society in partnership with a "broad front of the mind" (namely Progress, Compass, LabourList, Left Foot Forward and the Young Fabians).

Only David Miliband hinted that the question offered an old shibboleth, before showing that he was prepared to genuflect before it anyway in being "happy to sign up to" the assertion that "Labour is a democratic socialist party", a statement left in new Labour's new Clause Four in 1995.

This was clearly judged not quite the moment for Miliband the Elder to identify social democracy as the main live ideological strand of the socialist traditions, and to stake his claim that its political future now depends on a plural progressive fusion with the liberal tradition. Perhaps there will be other occasions and platforms for that argument, but a leadership hustings wasn't the place.

Miliband the Younger struck a Compassite note in arguing that socialism was about a critique of capitalism, or it was nothing: "being a socialist for me is about being willing to criticise capitalism and the injustices it creates". There is a significant difference of tone and rhetoric here, though "It is not about abolishing capitalism, but it is about changing it" was also essentially an argument for social-democratic reform, proposed as the viable means to meet socialist ends.

Andy Burnham quoted a popular socialist, saying that Billy Bragg's line "I've got a socialism of the heart" was the ethical socialist tradition rooted in the idea of community. For Burnham, socialism is about looking out for each other -- his best line of the night had been: "All of the things we criticise in the American health system are present in the way we fund care for older people in this country." But reciprocity has a hard edge in demanding a contribution, too: "Everybody looks out for each other, and everybody who is able to does their bit and makes a contribution."

Ed Balls wanted to make clear that he had been taking flak long before the contest for declaring himself "proud to be a democratic socialist" -- in the New Statesman, no less, during the New Labour high tide. The distinctive idea was collectivism in breaking down barriers.

But the substantive shift in "party ideology after New Labour" was not demonstrated by how they dealt with the S-word. That was a question Tony Blair could answer, too: hyphenating social-ism to argue it is essentially a "we're in this together" creed. (Indeed, Blair devoted a very short Fabian pamphlet to fleshing that thought out.)

What Blair the Social-ist had been unable to say, interviewed by Jeremy Paxman during the 2001 election, was that narrowing the gap between rich and poor mattered. Each of the "next-generation New Labour" candidates found ways to directly reference and reject his approach to what became known as "the David Beckham question", showing that Diane Abbott's claim that "there was a period when it seemed as though equality was a dirty word in the party" was now about the New Labour past and not the future.

Ed Miliband stated clearly: "It must be a central objective of policy to narrow the gap between rich and poor. It is so hard to do, that unless you make it a central objective, it isn't going to happen."

Ed Balls repudiated Mandelsonism, too, stating: "We aren't intensely relaxed about the filthy rich and it is important we say that." However, he wanted to stress the important commitments the previous government had made on redistribution and poverty, while attacking its "pandering" on inheritance tax in 2007 as a major political mistake.

"The gap does matter: it is not just about the floor, it is about inequality, too," said David Miliband, wanting to give equal priority to inequalities of wealth and power. As did Andy Burnham, who spoke about his background having informed his belief in a society where "health, wealth and life chances were more equal", presenting this as his defining mission and the cause of the party.

So Labour is clearly once again a pro-equality party. Yet, on the socialism question, it was Diane Abbott of the Campaign Group who suggested that a commitment to socialism need not be rooted in an intellectual framework.

"I am a socialist. What's it about? Well, I've never been a special adviser, I'm not an intellectual. For me, it's about: if you draw a line in the sand, what side are you on? If you come from a minority working-class background, you are acutely aware of what it is to feel marginalised in society. I've always chosen to stand with the voiceless and the powerless."

That hint of disdain for the usefulness of ideological speculation may be a rather more authentic Labourist tradition than any theory of socialism has ever been (the trade unions would never have founded the party if it had really wanted to be a socialist one).

The Fabian intellectual G D H Cole had written, somewhat approvingly, of Labour having a "socialism so undefined in its doctrinal basis as to make recruits readily among people of different types".

With the candidate of the left suggesting she was the least interested in the question of ideology, Cole's description of Labour as "a broad movement on behalf of the bottom dog" would seem to be the idea of socialism around which all five leadership candidates can easily converge.