After the release of videos this month showing Sanna Marin, the prime minister of Finland, dancing and posing with friends at a private gathering, some in Finland suggested that Ms. Marin had created a security risk by drinking alcohol, and called for a police investigation. The head of the opposition party pushed the 36-year-old prime minister to take a drug test, which Ms. Marin agreed to do. The test came back negative.

It wasn’t the first time a female politician was shamed or criticized for dancing.

In 2019, the night before she was sworn into the House of Representatives, Alexandria Ocasio-Cortez, then 29, faced an unexpected attempt at a smear: An account on Twitter released footage of her dancing in college, and called her a “clueless nitwit.”

And this summer, after Tiara Mack, a 28-year-old state senator in Rhode Island, posted a TikTok video of herself in a bikini, twerking while doing a headstand in the sand, she received more than 275,000 views — and a barrage of criticism.

“I’ve received death threats. I’ve received emails and phone calls of people calling me the n-word,” she told the publication The 19th. “I’ve received fatphobic comments. Just everything under the sun.” TikTok briefly suspended her account and Tucker Carlson mocked her on his Fox News show.

So what is it about female politicians dancing that makes people mad? One reason may be that young women do not fit the mold of a typical politician, so they have to work extra hard to prove themselves, and that means constantly projecting an image of sobriety, responsibility and focus.

Additionally, these videos all show young women who are bold, confident and joyful, and who do not appear to be seeking anyone’s approval. In that, they buck traditional societal expectations and norms.

“If the standard view of a politician has always been a middle-aged white man in a blue suit, when you’re stepping further away from that picture, you need to prove your viability, you need to prove your credentials,” said Michele Swers, a professor of American government at Georgetown University who researches women in politics. For Ms. Marin, she said, “there’s more scrutiny and more criticism because she’s both young and female, and these things combine to be out of the norm, so a step like this gets more attention.”

Eeva Luhtakallio, a professor of sociology at the University of Helsinki who has studied gender representations in Finnish media dating to the 1950s, said that part of what critics seem to have an issue with in Ms. Marin’s dancing is that “she dresses sexy and moves sexy.”

Sarah Crook, the director of the Center for Research Into Gender and Culture in Society at Swansea University, in Wales, pointed out that generally, society struggles to accept dimensionality in women who are in the public eye.

“We have trouble accepting that women can be more than one thing,” Dr. Crook said. “That they can be sexy and a mother. They can be silly and serious. They can be authoritative and a great dancer.”

In her research, Dr. Luhtakallio has found that the image of women in politics in Finland evolved from exceptional to normalized over several decades. Even before Ms. Marin, Finland had already had several female prime ministers. Nevertheless, Dr. Luhtakallio said, the image of women in powerful political roles is not yet entrenched, and so people react strongly when a female politician contradicts expectations.

Dr. Crook said that women in many countries “are perceived to be guests in positions of authority rather than accepted occupiers of those positions, and so the bar that they’re set is much higher.” When it comes to establishing an image of a dependable leader, women are expected to perform seriousness much more consistently than their male counterparts, Dr. Crook said.

She pointed to a video of Boris Johnson, the British prime minister, dancing at his wedding. “It got sort of mildly joked about on Twitter,” she said. “It didn’t provoke an extremely gendered response, and that goes to show the double standard.”

Plenty of former world leaders, including George W. Bush, Theresa May of Britain and Donald J. Trump, have been mocked for their dancing. The differences between those examples and those of Ms. Ocasio-Cortez, Ms. Marin and Ms. Mack are the age of the dancers and their perceived skill.

“She’s a very good dancer,” Dr. Luhtakallio said of Ms. Marin. “It’s not these awkward moves that you see other politicians do.”

In comparing the responses to Ms. Marin’s dancing with, for example, Mr. Johnson’s, it seems that many people may find it acceptable for politicians to dance as long as they look like goofy, awkward, self-conscious parents at a wedding. But if they look good while dancing, and confident, their behavior clashes with the cultural image of how a leader should behave.

“When you have this really successful female politician, exhibiting this embodied form of joy that’s unrestrained, unconstricted, all her own, that makes people upset,” said Irene Mata, an associate professor of women’s and gender studies at Wellesley College. “There is this kind of, ‘How dare she not behave the way I think she should behave?’ It’s all these antiquated ideas of gender roles.”

She noted that Ms. Marin’s dancing and joy led some people to assume that she was taking drugs. “There’s a moral panic that pops up,” Dr. Mata said. “As if dancing is somehow indicative of moral character.”

Dr. Mata noted that the response becomes manyfold more vicious and punitive if the female politician in question is also a woman of color.

Ms. Mack’s twerking, she said “is even more policed because it’s about Blackness, it’s about Black women’s sexuality, which is something that white supremacy and patriarchy have been invested in constantly policing and vilifying.”

In their responses to critics, all three women nodded at the idea of joy. “If you think I deserve death threats for a day at the beach then my twerk was not for you to begin with #TwerkFor the audacity to have joy and peace,” Ms. Mack tweeted. After her video went viral, she began using the #TwerkFor tag to draw attention to issues that are important to her, like abortion rights, trans and intersex rights, and bodily autonomy.

A week after the release of the videos of Ms. Marin, the prime minister faced a second round of scrutiny for photos taken at a party at her official residence, in which two women are kissing while pulling their shirts up to reveal their torsos. She apologized afterward.

“I am human,” she said, according to Yleisradio Oy, Finland’s national public broadcasting company. “And sometimes, in the middle of these dark clouds, I miss joy, light and fun. And that involves all kinds of picture material, all kinds of video material, which I wouldn’t want to see myself. Which I know you wouldn’t want to see, and yet it’s being shown to all of us. It’s private. It is joy and it is life.”

Ms. Ocasio-Cortez answered her critics in 2019 by sharing a video of herself smiling and dancing in front of her new Congressional office.

Despite the criticism, all three women found supporters, too. Ms. Mack’s video has thousands of likes; Ms. Ocasio-Cortez received a wave of positive reactions online; and in Finland, women are posting videos of themselves on social media dancing, with the hashtag #SolidarityWithSanna. Hillary Clinton posted a photo of herself dancing in Cartagena, Colombia, while she was the U.S. secretary of state. “Keep dancing,” she wrote, and tagged Ms. Marin.

“I love the fact that we see her as a full human being,” Dr. Mata said of Ms. Marin’s dancing. “How brilliant of a message is that for our young women? You can be a world leader, you can navigate your country through a pandemic, and you can still have a life.”