Look around the world this week and you see women exercising power and influence everywhere. In the United States, House Speaker Nancy Pelosi is wrangling US President Donald Trump over his shutdown of federal government. In the UK, Prime Minister Theresa May doggedly pursues Brexit. Yvette Cooper, chair of the British Parliament’s Home Affairs Select Committee and described by some as the Labour opposition’s “alternative leader”, is bringing forward legislation to try to head off a “hard” Brexit.

In Germany, CDU leader and likely Angela Merkel successor Annegret Kramp-Karrenbauer co-authored a public letter to the British people urging them to remain in the European Union. And from New Zealand, Prime Minister Jacinda Ardern wrote a comment piece for the London Telegraph expressing solidarity whichever way Britain goes.

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And in Australia? Reportage involving senior women in politics is dominated by Morrison government cabinet minister Kelly O’Dwyer quitting her prime Melbourne seat of Higgins, fellow Liberal Senator Jane Hume ruling out running for it, and speculation about whether or not former Foreign Minister Julie Bishop will, like O’Dwyer, quit politics at the forthcoming federal election too. It is a sharp contrast. What is going on?

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The UK has already had two female prime ministers in May (since 2016) and Margaret Thatcher (1979-1990) – the latter, after Winston Churchill, the most significant British prime minister of the 20th century. This is not to say politics is easy for women in Britain – far from it. Political attacks on May are three-times as likely to be gender-based as those on Opposition Leader Jeremy Corbyn.

Claims Corbyn called May a “stupid woman” in parliament got traction because of the widely perceived implicit sexism of Corbyn-era Labour, which tends to be overshadowed by controversy over its more blatant antisemitism. Female MPs come under sustained social media attacks of the most violent and reprehensible kind, something Labour’s Yvette Cooper and Jess Phillips have campaigned against prominently again and again.

It is in this climate that Labour MP Jo Cox was murdered by white supremacist Thomas Mair during the Brexit referendum campaign in 2016.

But while politics is incredibly tough for women in Britain, they hang in and fight on, across the political spectrum. This is because in Britain women’s presence in politics has been normalised. There’s no sending them back to the kitchen. To an extent which should not be necessary, they are battle-hardened. Male opponents know they will not go away.

Equally in the US, women in politics will not be seen off. The pronounced misogyny of President Donald Trump stirred rather than cowed women who stormed the House of Representatives in the 2018 midterm elections, creating an all-time high in congresswomen’s numbers.

Democrat Nancy Pelosi prevailed against significant internal challenge and external opposition to be elected Speaker. From this position she is prominently calling Trump’s bluff and, since the government shutdown, bettering him in the rhetorical struggle for decent government.

In New Zealand, women in politics has long been business as usual. Ardern, elected in 2017, is the country’s third woman prime minister after Helen Clark (1999-2008) and Jenny Shipley (1997-1999). One could go on and on, citing the normalisation of women in politics in Sri Lanka, India, Israel, Iceland, Denmark, Pakistan, Indonesia, Canada, Germany and elsewhere.

Women have, often with the help of quotas, been accepted as regulars in political battle in all these places, sometimes rising to the political equivalent of generals and supreme commanders just like the men, many of whom might not like it but know it is an inescapable – and, in fact, reasonable - part of contemporary life.

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The military metaphor is unfortunate, but in this context useful to explain through analogy what is going on by contrast with women in the senior levels of the Morrison government.

May and Pelosi are playing the long game – operating strategically – in pursuit of specific political outcomes irrespective of the extra, gendered-tier of political attack to which they are subject. They do this in the confidence that women in their parties and parliaments are political “regulars”, in the business of politics for good.

In Australia, the presence of women in politics has been normalised other than in the Liberal and National parties. Labor’s Julia Gillard was prime minister from 2010 to 2013. If Labor’s sustained poll lead holds through to election day, Opposition deputy-leader Tanya Plibersek is likely to become deputy prime minister this year. The Greens have been, and before them the Australian Democrats were more often than not, led by women. Australia’s flagship far right-winger, Pauline Hanson, is a woman.

But to be a woman in the Liberal or National parties is still to be a political “irregular” – one of a group of resented interlopers, tiny in number, whom many male colleagues hope can be driven away.

Female LNP leavers manifest this – not just O’Dwyer and, likely, the prominently-snubbed Bishop when her decision finally crystallises – but those like Julia Banks who have left the Liberal Party and gone to the crossbench, and Liberal fellow travellers like Cathy McGowan and Kerryn Phelps who sit as independents alongside her.

It seems the position of women in the Liberal and National parties is too fragile, too brittle, for them to stand and fight like regulars. Rather, like guerillas on the wrong end of the power asymmetry women face within the Morrison government, they are withdrawing from the battlefield. It will be up to others to stand and fight another day.

That fight cannot be won without critical mass. Women in the Liberal and National parties need to embrace quotas and they need to do it now. They will never be numerous enough to achieve the status of “regulars” reached by women in most of the rest of the democratic world otherwise.