Former Coalition human services minister and conservative stalwart Alan Tudge bid an emotional farewell to politics on Thursday and quietly left behind him an existential question for the Liberal Party.

Mr Tudge – whose resignation is effective next week – had become entwined with a public perception that the Liberal Party had condoned the mistreatment of women after his affair with an adviser ended in allegations and denial.

Mr Tudge’s seat of Aston is also one of the last Liberal enclaves in metropolitan Melbourne. Voters in the party’s one-time heartland delivered a stunning rebuke at last May’s federal election when the Liberals forfeited four seats, including to a new wave of women Independent MPs.

The departure of Mr Tudge, who as education minister launched a government website that carried a Mormon charity’s sex education videos, now presents a dilemma.

Can a party down to nine women MPs in the House overcome its factions and nominate a candidate to win back the voters who left the Liberals as religious conservatives came to dominate party branches and as its supporters and representatives began skewing overwhelmingly male?

The party’s viability as a political force in Australia’s most progressive state could hang in the balance.

Past time

Monash MP Russell Broadbent, who was first elected in 1990, is the longest-serving Liberal MP in the Parliament.

He became the voice of the party’s social conscience during John Howard’s leadership, and on Thursday called on the Liberals to choose a candidate that reflected the local community.

“The party has no choice but to preselect a woman of a non-Anglo background,” he told The New Daily.

“It’s called diversity.”

Aston, an electorate that takes in Melbourne’s outer eastern suburbs and whose electors include a large base of Indian voters, hangs on the slender two-party preferred margin of 2.8 per cent.

A national poll released last week reflects the Liberals’ dilemma: 56 per cent of voters favour the PM, but only 26 per cent back Mr Dutton.

In Victoria, where Mr Dutton, who is from the party’s national right faction, was nowhere to be seen during a recent state election campaign, this gap will be even starker.

On Friday, Mr Dutton said the byelection would be difficult for the Coalition.

“It is a tough seat for us to hold, there’s no question about that, and there are lots of families there, though, who are really feeling the pain of their mortgages,” he told the Nine Network’s Today program.

“It’ll be a hard-fought contest but we’ll get a date [for the byelection] from the speaker, no doubt, in the coming weeks.”

Mr Dutton said work had begun on selecting a candidate for Aston, but admitted the loss of Mr Tudge would bring a drop in the party’s vote.

“Byelections are always difficult and there are different issues, lots of local issues,” he said.

“Alan is a popular member and that always brings a vote with it which won’t be present in the byelection. But we’ll preselect a great candidate and that process has already started.”

Labor has confirmed it will run a candidate in Aston but Liberals are watching closely for another announcement.

“It will be a big fight,” a senior Liberal MP said, “but this seat will be [for] the Teals’.”

Hours after Mr Tudge’s exit, the Climate 200 crowd-funding project that backed successful federal candidates such as Monique Ryan (who toppled former treasurer Josh Frydenberg) and Zoe Daniel, was seeking expressions of interest.

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Mr Tudge’s announcement fuelled speculation that Mr Frydenberg could fight the byelection and make a return to Parliament.

Senior Liberals poured cold water on Mr Frydenberg’s prospects while several reports citing a source close the former MP denied he had been weighing his options.

Liberal heavyweights and moderates have thrown their support behind two high-profile professional women.

One is Ranjana Srivastava, a Harvard-educated oncologist who works for Monash Health and writes for The Guardian. The other is barrister and City of Melbourne councillor Roshena Campbell, a columnist for The Age newspaper.

Conservatives are understood to be backing a former adviser to Mr Tudge; members of the faction are in control of Aston’s local Liberal branches which will vote on the preselection.

Ranjana Srivastava (left) and Roshena Campbell have been named as possible Liberal contenders in Aston.

Entitlement culture

In the late ’90s women were a majority of the Liberals’ electoral base but they have moved left in growing numbers across several elections. They amounted to less than a third of Liberal voters last May.

And while more women were elected to the current Parliament than any other in Australian history, the number of Liberal women fell by four, to reach its lowest point in 30 years.

Senior Liberals including Deputy Leader Sussan Ley have urged the party to address its “women problem” but the party continues to resist quotas.

Similar questions are also emerging in a looming preselection contest in NSW to choose a replacement for former Senator Jim Molan, who died in January.

Former NSW minister and long-time federal politics aspirant Andrew Constance was named as the most likely Liberal prospect in an ABC report on Thursday.

But a suggestion that the Senate spot could be an ideal launching for a future run for a lower house seat has escalated debate among members about whether women were being excluded by the party’s culture.

The contest’s leading female candidate, Fiona Scott, is a Liberal moderate who shot to national attention after winning a crucial marginal western Sydney seat in 2013.

That was despite former Prime Minister Tony Abbott remarking on her “sex appeal” during the campaign, a comment that was widely criticised as undermining his own candidate.