The gender gap in Australian politics is not just confined to the lack of female representation in the Liberal party, it is also looming as a broader battleline in the upcoming federal election.

In a month when the Liberal party has been experiencing its #themtoo moment with claims of bullying, protest resignations and colour-coordinated signs of defiance, gender is becoming a key point of difference between the protagonists.

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With the new prime bloke Scott Morrison stubbornly refusing to utter the “q”-word, this week’s Essential Report shows a strong majority of voters supportive of quotas to increase the number of Liberal women in parliament.

The conservatives who now run the Coalition might shake their heads at the idea of such interventionist social engineering, but the idea of positive action appears to be another marriage equality moment where the electorate is now way ahead of their representatives.

What screams out in these figures is the high number of Coalition voters who would like to see the Liberal party step up rather than sit back and pretend it’s all about selection on merit.

They look at the two major parties and see one side of the parliament with close to gender parity, reflecting Australia, and on the other a group of middle aged men in suits and a handful of disenchanted women looking for a way to get out of the building.

There is no magic wand to fix this malaise; it’s taken Labor 20 years of quotas to create a culture where talented women feel comfortable and supported in stepping up and leading. The process has been contested at times, marred at others with cynical factional plays and trades in the political careers of spouses.

But where it’s landed is clear for all to see – a diverse team of talented women from all walks of life. And it’s not just about more women, it has also been a recipe for a higher calibre of bloke, now forced to compete for fewer spots.

Somewhere along the way the political culture shifts, and the way issues are approached does too, and the party begins to look like a team with the ideas to take the nation forward.

Does it make a difference? As this breakdown of votes shows, the female vote is proving decisive in Labor’s persistent lead in the polls. In fact, if it weren’t for these votes, the contest would be line-ball.

The big gender gap in the Liberal vote could be symptom or a cause of its current malaise. Are more men supporting the Liberal party because they are a party of middle-aged blokes, or is the control of middle aged blokes just making the party less attractive to women voters?

Either way, the impact on gender on the electoral pendulum is real and it is huge advantage to the ALP, which has diligently begun releasing policies to entrench that advantage. Policies, it should be noted, like topping up super payments for women on parental leave that are evidence of a deeper understanding of the lived experience of working women. Wherever would that have come from?

The march towards gender equality is never inevitable as a separate table illustrates. Indeed, a majority of men are ready to embrace the notion that the whole thing has gone far enough, that when it comes to gender equality we are already there.

While there is broad support for the notion of equal pay for equal work, big gender splits emerge around the question of how far there is to go on the journey to equality. With a 20 point gap between men on women opening up on propositions we have reached a suitable landing point.

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There is also a contradictory response to the final statement that might provide a clue to the most effective way of bringing the public on the rest of this journey. Yes, there has been significant progress but there is still a long way to go. Simply framing the story positively narrows the gender gap and entrenches the majority.

In politics stories matter, and in a era where there are so many disturbing stories about how far society needs to go for women to feel truly safe and equal, maybe Labor’s success with quotas is one of those positive prompts.

Because here’s the thing the Liberals can’t deny: the quotas have worked, the Labor party looks more like Australia and that gives them an electoral advantage.

Hard-headed politics, if nothing else, suggests its time for the Liberals to yield.

• Peter Lewis is the executive director of Essential and a Guardian Australia columnist