Politics can be a cruel business. Granted, the treatment of opponents has moved on since Roman times, when a defeated foe could expect to have a bucket of brown stuff tipped over his head, as seen in the marvellous Julius Caesar: the Making of a Dictator, now livening up Monday nights no end on BBC2.

These days, casting shadow over a one-time rival is a less smelly but still brutal affair. Ask Jacinda Ardern, New Zealand’s former prime minister. Among the policies of which she was most proud was her government’s rolling ban on buying cigarettes. In time, said supporters of the law, future generations of Kiwis would never know what it was to buy cigarettes legally and would reap the health benefits accordingly.

The policy seemed like that rare thing, a win-win. Other countries wondered why no one had thought of it sooner. Rishi Sunak was so impressed he made it UK Government policy.

Now Ms Ardern’s pioneering law is heading for the shredder. Christopher Luxon, leader of the National Party and the country’s new prime minister, announced the repeal this week. Prohibition, it is feared, will fuel a black market in cigarettes.

As if to add insult to liberal injury, the money raised from the continuing sale of tobacco will be spent on tax cuts. Also binned is a ban on future oil and gas exploration. The coalition government’s priority, said Mr Luxon, was to “fix the economy” after years of mounting debt under Ms Ardern’s Labour Party.

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So much for Ms Ardern’s legacy. Just when it seemed to be going so well for her, in comparison to the woman leader with whom she has so often been bracketed: Nicola Sturgeon.

It is uncanny the way the lives of the ex-First Minister and the former New Zealand premier have mirrored each other. Both took office at a young age, both were champions of progressive politics, both took prominent roles during the pandemic.

Lord help the mister who annoyed these political sisters. Ms Sturgeon was more up front in confronting her critics, with public slaughtering becoming the norm at First Minister’s Questions. Ms Ardern was sneakier, but a live microphone once picked up her calling an opponent an “arrogant p****”.

But nothing brought these two leaders together like their leaving of office. Ms Ardern was the first to go, famously telling the country in January that she did not have “enough in the tank” to fight the upcoming general election. A leader has to know when it is time to leave, she added.

Fast forward to Bute House one month later and it is Nicola Sturgeon’s turn at the mic for her swan song. Serving well means knowing when to make way for someone else, she said. Her need for a better work-life balance; doubts over whether she can give the job everything it demands - again, the similarity in thinking between the two women was remarkable.

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After that their paths diverged. Ms Ardern was not asked if she was stepping down as a result of a police investigation into her party’s finances. The former New Zealand premier was also spared the sight of a police forensics tent being erected in her garden, nor was she arrested and released without charge pending further inquiries.

Indeed, Ms Ardern has been enjoying the life Ms Sturgeon was expected to have on leaving office. Appointed a visiting fellow at Harvard Kennedy School, recently a speaker at the John F Kennedy Jr Forum where she was praised as “a global icon of strength and kindness”, the Ardern name is mentioned whenever there might be a vacancy in a plum international job.

Ms Sturgeon, meanwhile, had a few Fringe appearances. She got a sizeable fee for her autobiography, and she passed her driving test. That was the upside. She is still waiting to hear the outcome of the police inquiry. And her former boss and mentor has gone on the legal warpath.

It is not turning out to be the happiest of times either for her one-time counterpart. Ms Ardern’s party, albeit under a new leader, took a hammering in the elections, losing half its seats. A large part of the blame has been heaped on her head. The new conservative government is actively defining itself as the opposite of the Ardern administration. Hence the anti-tobacco law being trashed in such a public fashion.

At this point in their careers, both women might have expected to be thinking about their legacies. Ms Sturgeon certainly lost no time in doing so, citing in her leaving speech the Scottish Child Payment and the baby box among her achievements. Since then, however, the wheels have rather fallen off the Sturgeon legacy. Not among her supporters. Their devotion seems to grow stronger the more her record is attacked.

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What has happened to Ms Sturgeon, and to a lesser extent Ms Ardern, seems to confirm that old saw about all political careers ending in failure. Now, there could be many reasons why they should find themselves in the same position again. One could simply say they made mistakes, pursued the wrong policies, did not listen to the public, or were just plain old incompetent. Yet it is tempting to wonder if some careers are destined to go downhill quicker than others. Does being a woman, for example, mean you are judged more harshly than a man?

At the time of Ms Ardern’s quitting, the actor Sam Neill said his fellow Kiwi had been the target of bullies and misogynists. “She deserved so much better,” he said. Ms Ardern did not put it like that, but she did leave office appealing for more kindness in politics. We await Ms Sturgeon’s memoir to see what she thought motivated her critics.

Mrs Thatcher would never have seen herself as a victim of misogyny. Treachery, famously with a smile on its face, yes, but never done down because she was a woman. She would have thought that an insult. Yet she remains one of the most controversial figures in British politics. No male prime minister attracts that kind of heat, and that in turn colours her legacy.

Ultimately it is the public, not politicians, who have the last word on legacies. That is as it should be, even if it is a rough kind of justice that prevails.