Ranked third in the world by the United Nations on gender equality, Denmark was one of the first countries to give women the vote. Its prime minister is a woman, as is its minister of higher education and science.

But the current debate over gender imbalances in academia illustrates the challenge of addressing such disparities in a society that steadfastly refuses to allow preferential treatment for any group.

Only about a third of Danish researchers and fewer than one in five professors are women, according to a national task force that issued its report in May. In both cases, these levels are worse than the Nordic, European Union and Organisation of Economic Cooperation and Development averages. At the current rate of hiring, according to the report, Recommendation from the Task Force on More Women in Science, it could take 50 years to reach gender parity.

This state of affairs, said Sofie Carsten Nielsen, the minister of higher education and science, “is not good enough…It means that we miss talent.”

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The challenge is how to fix the problem without requiring that women be given priority in hiring.

In February, the University of Copenhagen, Denmark’s largest and oldest higher education institution, requiring every applicant pool for academic and administrative jobs to include at least one woman. That replaced a scheme under which departments that were increasing their proportion of female academic staff were allowed to add positions and received financial bonuses.

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But such policies are controversial – and may even be illegal, some critics have said.

“Even some women think it is a bad idea to do this,” acknowledged Camilla Gregersen, vice-chair of Dansk Magisterforening, Denmark’s academic union and professional association for university graduates, which endorses the goal of increasing the number of women in academic jobs.

“[But] sometimes you have to take steps to reach a goal,” Ms Gregersen said in her office in Copenhagen’s Frederiksberg neighbourhood. “It’s not the steps that are important; it’s the goal that’s important.”

Achieving gender parity in university jobs has been a surprisingly difficult process in otherwise egalitarian Denmark.

Women outnumber men among university undergraduates and comprise half of doctoral candidates.

“But as we get closer to the permanent senior positions, we find a much smaller proportion of women,” said Lisbeth Møller, director of human resources at Copenhagen.

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“At the universities, you have to accept uncertain employment for at least 10 years” before landing in a stable job, Ms Gregersen said. In many cases, this is the same 10 years in which women want to start families, she added.

There are other factors at play. One is the difficulty female academics have in finding mentors. Women are also less well represented in the sciences, where there is more funding, Ms Gregersen said.

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Danish law prohibits treating men and women unequally, even when rectifying gender imbalances is the aim.

Copenhagen’s previous policy of offering financial incentives to academic departments to increase the number of female academics ended in 2013, after five years in which it was roundly criticised. In an article in Denmark’s weekly judicial legal journal Ugeskrift for Retsvæsen, two University of Copenhagen academics said it contravened Danish and EU legislation.

Nevertheless, Ms Møller said, the university’s strategy helped to address gender disparity. Over the five-year period, the number of professorial posts held by women at Copenhagen rose from 15.3 per cent to 22.8 per cent.

Another initiative, the nationwide YDUN (for Younger Women Devoted to a University Career, with a nod to a Nordic goddess who could grant eternal youth), ran for one year in 2014. It distributed Dkr110 million (£10.5 million) in Danish Council for Independent Research funding to 17 female-led research projects. But the whiff of discrimination drew criticism in the Folketing, Denmark’s parliament, where some members said it insultingly implied that women needed special treatment.

In recommendations that carefully avoid singling out women – it refers only to “the under-represented gender” – Copenhagen’s new policy proposes to help male or female adjunct instructors and lecturers to hire research assistants or take other measures to reduce the impact of parental leave. It also requires the establishment of gender-balanced recruitment committees to encourage more candidates to apply for academic posts.

The goal is to increase Copenhagen’s ratio of female academics to about one in three over three years.

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“We should not discriminate against the men, either. I would not personally support hiring a woman and then a man and then a woman,” said Ms Gregersen. “It has to be the best person who gets the job.”