The response from women on Twitter was, well, not so happy. “Frown. You just had a big night of proving you're a dope,” tech journalist Kara Swisher wrote. “Way to condescend to a potential future world leader,” wrote another. Plenty of women did respond with smiles -- in photos and GIFS that ranged from creepy toothy clowns to "Broad City's" Ilana Glazer and Abbi Jacobson turning up the corners of their mouths with their fingers.

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Then on Wednesday, Samantha Bee, the "Daily Show" alum and host of “Full Frontal with Samantha Bee,” replied with a tweet of herself frowning and added her own hashtag, saying “Ladies, it’s very important that you #SmileForJoe.”

Some replied with pictures of their dogs.

Others added their daughters.

Or a photo of the Joker.

In a series of tweets Wednesday, Scarborough responded on Twitter, saying "we've called @BernieSanders grumpy for a year. @HillaryClinton is tough as hell. She doesn't need this fake outrage." In yet another tweet, he wrote, "we've hammered all candidates on their style and substance. We try to hold all candidates to the same standard." In reply to a woman who said he crossed a line, Scarborough wrote that "I don't look at HRC as a woman anymore than I did Thatcher. I look at her as a tough candidate who can handle it."

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But the outrage appeared to be real. And the gender biases we ascribe to women leaders certainly are. Being told to "smile" may be the ultimate nails-on-the-chalkboard comment for women, yet it's also illustrative of an impossible predicament female leaders face in their jobs.

Study after study has confirmed what's known as the "double bind" problem female leaders confront, in which they're expected to act like our stereotypical idea of a leader -- bold, serious, tough, assertive. Yet they're often held back when those don't conform with the gender norms we associate with women, such as being selfless and agreeable. It's a big reason that underpins why women don't as frequently negotiate on their own behalf, ask for a promotion or speak up in meetings.

As Deborah Gruenfeld, a professor of leadership and organizational behavior at Stanford University, described the dilemma in Sheryl Sandberg's book "Lean In": "We believe not only that women are nurturing, but that they should be nurturing above all else. When a woman does anything that signals she might not be nice first and foremost, it creates a negative impression and makes us uncomfortable."

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Not that it really matters, but Clinton did smile in her speech. She practically beamed at the beginning of it, as she thanked her supporters, and she grinned when she hit on popular themes, such as equal pay for equal work or when the crowd chanted her name.

In fact, she smiled a whole lot more than GOP front-runner Donald Trump did in his speech Tuesday night. He lets out a half smile or two, such as when he takes the stage, but doesn't even crack a grin when he says he's having a good time. Finally, there's a big smile at the end, when the crowd laughs at his joke about the discomfort of hosting corporate executives at Doral while the TV was playing negative ads about him.

Trump, it's worth noting, had a very big night on Tuesday, too, winning Illinois, Florida and North Carolina.

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