Is that even possible?

Yes. If neither side can convince Governor-General Peter Cosgrove it can command the confidence of the House of Representatives, then a fresh election could become the only means of breaking the deadlock.

Bill Shorten reckons the Prime Minister is weighing the idea: "There is a very real chance that Malcolm Turnbull is considering calling a snap election in the mistaken belief this will sort out his own problems."

Has this ever hapenned before?

Not in Australia, no. 

We've only had two hung federal parliaments in the past 100 years, in 1940 and 2010. On the first occasion, Robert Menzies was able to cobble together a minority government, although the independents later switched sides and gave government to John Curtin. Julia Gillard did better, taking her minority government full-term – with a little "help" from Kevin Rudd – despite its reputation for chaos.

This time could be different. With Turnbull and Shorten ruling out deals – and given the ideological gulf between the crossbenchers – there is potential for true deadlock.

How likely is a re-run?

While it is one option on this messy table at this stage it remains a mercifully unlikely outcome.

The chief reason being it's in no-one's interest. Turnbull wouldn't want to risk falling even further – he's made enough strategic miscalculations and has probably lost his appetite for high-stakes gambles.

Shorten might fear that now Australians have stared into the abyss of another hung parliament they will retreat back into the government's arms and give Turnbull his second chance. Why risk the gains he's made?

Besides, if Shorten cannot form a minority government he knows that his surest path to power is to force Turnbull to govern over a chaotic parliament and watch his government self-destruct.

The crossbenchers have no interest in a re-run. Why would they want the stress and expense of another campaign? Particularly given a hung parliament gives them power and influence they wouldn't otherwise have.

They may choose not to enter into any formal agreements but they're unlikely to foment too much instability by supporting no-confidence votes.

How would a re-run work?

The PM has the upper hand. Constitutional conventions give him some benefits of incumbency. Even if he can't form a majority government he's allowed to remain in office until parliament convenes – sometime next month – to determine who holds its confidence.

He could technically call another election before that, but that would be considered a serious breach of convention and Cosgrove would be well within his rights to refuse him. Needless to say, that would be a bad look.

According to constitutional law expert Anne Twomey it's a generally accepted principle that a new parliament "must at least be given a reasonable chance to function".  When it did resume, Turnbull would be entitled to stay in office unless there was a successful vote of no confidence against him.

If that happened and Shorten too was unable to command the House's confidence Cosgrove could dissolve it.

It's all highly unlikely. But if it did occur it would be a lower house election only - the new Senate would stay put. And there would be the regular five-week campaign.

Who would win?

Who knows. It could go either way. Or maybe we'd replicate Spain, which just last month sought to break a parliamentary deadlock with a second election: and the people delivered another deadlock. There is perhaps no more compelling argument for working with the parliament we've got. – SYDNEY MORNING HERALD