Illustration: John Shakespeare Interviewers have pressed the two rivals at every opportunity since, demanding to know when they will meet, stoking anticipation of an eventual showdown. Both have resisted the idea. When interviewer Neil Mitchell goaded Turnbull on Thursday, the Prime Minister replied: "I look forward to having a chat with him when I catch up with him next." So what an anti-climax to learn that the pair have already spoken this week. By the time Turnbull brushed aside Mitchell's question, they'd already had a conversation. No, it wasn't the grand reconciliation. But it wasn't an angry exchange, either. It was a brief, businesslike chat to discuss their positions ahead of the weekend Party Futures Conference. As it happens, Turnbull and Abbott agreed on the key principle at stake.

Though their factions are in conflict over it, the current and former leaders converged on it – specifically, that all ordinary members of the Liberal Party should be allowed to have a vote in choosing their candidates for Parliament. A plebiscite, in other words. Turnbull phoned to let Abbott know in advance that he'd be publicly supporting the principle, even though it was the one championed by Abbott's faction. Curiously, neither man has wanted to advertise their conversation. It wasn't a drastic change of position for Turnbull. He has supported the idea of plebiscites for years. "Our pre-selections for our members are, in every state except NSW, plebiscites, so our members all get a direct say and I'd certainly like to see plebiscites in NSW as well," Turnbull said on Q&A in 2013. And it's not a radical concept. The remarkable fact is that the NSW Liberal party has remained so antidemocratic for so long. The Left faction's lock on power in NSW has almost entirely shut out ordinary members. When the former major general Jim Molan tried to run as a Liberal Senate candidate in NSW at the last election, he was stunned to find that a business lobbyist, Michael Photios, ran the state as a personal fiefdom.

The man who had commanded some half-million soldiers as chief of coalition operations in Iraq threw himself into the campaign for reform: "As someone who has accompanied five countries down the road to democracy, and seen people die for the right to vote, and taken life to protect the right to vote," says Molan in rallying Liberal branches, "I find it astonishing that our party doesn't give our members the same right." In Britain, ordinary members get to vote on party representatives all the way up to national leader. In NSW, John Howard formally proposed plebiscites in 2014. Mike Baird supported the idea too. In the era when the No.1 accusation against the political class is that it's disconnected from ordinary people, the plebiscite is an irresistible idea. The principle is so powerful that the anti-reform camp has taken to scaremongering. They claim that the democratic reformers are a Trojan horse for Abbott-loving, far-right weirdos who will branch-stack the party into oblivion. They call them "the Taliban", as my colleague Sean Nicholls reported. A reformer laughs at this picture: "As if we have a shortage of weirdos and strange things going on now." The NSW division is dying, he says, with record low membership and a financial crisis that obliged the Prime Minister to donate $1.75 million of his own funds. The party was being used to serve the business interests of some powerful people, he said, even as it was collapsing. Calling the reformers the "Taliban", he said, was an embarrassing own-goal – Jim Molan's career was spent fighting fundamentalist terrorist movements. John Ruddick is a businessman who is well-known as an advocate for democratisation of the NSW Liberals, so well-known that he was ultimately forced out of the party for his trouble.

Ruddick says that if the two key reform motions due for a vote on Sunday, known as the Warringah motions, succeed, "the NSW Liberal Party will catapult from the least democratic state division of any party in Australia to the national leader in democratic excellence". And if they don't succeed? Says Ruddick: "Cory Bernardi is like the phantom menace circling the party" referring to the former Liberal senator who defected to start his rival Australian Conservatives Party. "He has been reaching out to NSW conservatives in recent months and has been warmly received. My guess is around half of the party membership is in danger of defecting to Bernardi and will gladly do so if democratic reforms are not introduced. This convention is the last roll of the dice to prevent a historic split in the party." Turnbull would not be unhappy to see the reform motions die, because it would preserve his group's control of the NSW party, but he cannot say so openly. He will address the meeting on Saturday and endorse the plebiscite principle, but he won't be there to cast a vote when it comes up on Sunday. The reformers think they have the numbers, with perhaps 60 per cent of the 1400 members who've registered to come along, but acknowledge that it could be a close run thing.

So rather than bring Abbott and Turnbull into an epic showdown, this weekend's conference has actually brought them together. But for those who crave conflict, fear not. There will be no reconciliation of their greater ambitions. The rivalry that roils the Australian government will continue. Turnbull merely wants to hold his job; Abbott wants him destroyed. But what of Nick Greiner's warning that the government will lose office? He's correct, no doubt, but Abbott thinks it's irrelevant – he is sure that they are going to lose anyway. The logic is this. The Coalition is permanently behind in the polls because its primary vote is too low, in the mid 30 per cent range. It will remain there so long as Pauline Hanson's One Nation is polling the 7 to 11 per cent that it has enjoyed since the last election. She has taken disenchanted Liberal voters away and they are not coming back. But wouldn't most come back ultimately, through the preferential voting system? It's possible but it's highly unpredictable. It's impossible to predict the sort of preference-swapping deals that Hanson might make with other parties. This is the structural vote trap Turnbull finds himself in. So how can the Coalition raise its primary share of the vote to winning levels? One option is the one represented by Abbott. He and his acolytes argue that, if he is restored as leader, he will appeal to Hanson's voters with an authentically right-wing appeal, with policies such as his proposals to cut the immigration intake and have the federal government build coal-fired power plants. The other option is the one represented by Turnbull. By moving to the "sensible centre" on policies such as schools funding and health care as he did at the May budget, he will win votes at the centre of the spectrum, votes that otherwise would go to Labor. The problem with this scenario is that, so far, there's no sign that it's actually working. The polls have remained unmoved.

Bill Shorten is taking no chances, however. On Friday the Labor leader signalled that, while Turnbull might have moved to the left to try to seize the "sensible centre", Labor will move yet further left. Taking a cue from Jeremy Corbyn's revival of British Labour, Shorten promised to make the tackling of inequality the "defining mission" of a future Labor government. He promised to return to the "too-hard basket in tax reform", for instance. The centre, in other words, is moving leftwards. This will further stretch Turnbull on the left even as he tries to defend on the right. In the past week we've seen Turnbull make no fewer than three big announcements on national security. One was complete with a theatrical backdrop of armed commandos in balaclavas. If the budget zig to the centre failed to yield any extra votes, this is a concerted zag to the right to see if that works any better. With an election still more than a year away, why should Turnbull be so desperately chasing votes week to week? Because he himself announced the polls as his judge and jury. Remember that he said 30 losing Newspolls in a row constituted a death sentence; he has lost 15 already. And Abbott is limbering up to be his executioner. Loading

How's that for democratic reform? Peter Hartcher is political editor.