Now many have raised eyebrows over a working group of senators that's aimed at drafting and moving ahead on their version of the bill. The reason is similar: All the group's 13 members are men.

In response, Republican aides have suggested critics are too focused on how the group works rather than its outcomes. An unnamed GOP aide told CNN “we have no interest in playing the games of identity politics, that's not what this is about,” saying the group would “work with any member of any background who wants to pass a health reform bill.”

After criticizing the all-male group, CNN's Erin Burnett read a fuller version of the statement, where the aide detailed policy differences between the committee, saying “to reduce this to gender, race or geography misses the more important point of the diverse segments of the conference the group represents on policies.” A voice mail left with Senate Majority Leader Mitch McConnell's press office and an email sent to a spokesman for Sen. Lamar Alexander, the Republican chairman of the Senate's Health, Education, Labor & Pensions (HELP) Committee, were not returned.

Yet one researcher who has studied the effect of diversity on group dynamics says such diversity of thought or approach to policy — though helpful — usually isn't enough to produce the best results. Katherine Phillips, a professor at Columbia University's business school, has studied how small group discussions benefit from what she calls “surface-level diversity” — the visible differences between team members — in coming up with broader and more innovative ideas.

“It’s almost like a trigger in the room, this salient identity,” she says. Having visibly different people together, such as women, means the senators might think " 'Well, huh, what would my daughter think about this? Or my mother?' even if that person doesn’t have a different opinion.”

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One of her research studies, for instance, put people in groups to try to solve a murder mystery. Some of the groups had all white members, while others included people of different races. There were a common set of facts, but each member also got his own clues that only he knew. To solve the murder, all the information would need to be shared.

She found that the groups with racial diversity did significantly better than the all-white groups. “Being with similar others leads us to think we all hold the same information and share the same perspective,” Phillips wrote in a Scientific American article in 2014. “This perspective, which stopped the all-white groups from effectively processing the information, is what hinders creativity and innovation.”

Similar research by others has found that when a black person presents a dissenting idea to a group of white people, the white recipients of the information saw it as a more innovative idea that prompted them to consider more alternatives than when a white person said the same thing. The visible differences between the people in the group provoked them to think differently, Phillips said, shaking up their thinking.

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Phillips's research has focused on race, but she believes the concept would also apply to gender, even if our ingrained expectations for how men and women should act in group settings might end up influence the results. “Assuming you have women in the room and they are senators, too, then absolutely, having them in the room could have an impact,” she said. “My research would suggest even if [the female senator] doesn’t say something different, that it would trigger the men in the room to consider that there may be alternative viewpoints to the issue they’re addressing.”

GOP aides argue that having people with different views on the conservative spectrum is diversity, but Phillips warns it's harder for it to have the same impact. “One of the things about 'diversity of thought' is it has to be expressed convincingly — it has to be heard. You cannot be guaranteed that it’s going to be salient to people,” she said. “Whereas racial diversity and gender diversity is vivid. You can see it. Being on the surface allows it to have an impact on people psychologically. It causes more cognitive diversity and deeper processing of information by the people who are in the room.” It can even make the back-and-forth between the men better, too, she says: “It can free up the men to dissent with each other and have real debate about what's going on.”

Marianne Cooper, a sociologist at the Clayman Institute for Gender Research at Stanford University, says that other research by Phillips shows that adding “newcomers” to the group — people not already part of an established group — might make people less confident in their results, “but the results are often superior,” Cooper said in an interview. “When we go into a diverse team group, we'll prepare more. We expect there to be a back and forth. When everyone in the room looks like you, you assume everyone has the knowledge.”

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Cooper also points to research that shows another drawback to having fewer women represented in the group. “When it comes to policy creation, there are literally studies on what women talk about on the floor in Congress,” she says. Women of both parties have been shown to advocate for breast cancer research, she says, and Republican women have been shown to bring up women's issues in floor speeches more often than Democratic men.

“They're much more likely to speak more openly about these issues,” Cooper said. “If women politicians in the political environment are more likely to speak out, and if they're not in this group of people creating policy, then we can expect their perspective is not as well represented. Personal stories really do matter in this debate.”

The debate over the women missing in the GOP's official working group comes at a time when the argument for having more women at the table has gained more traction than ever. Investors are urging companies to add more women at the top not simply because it looks bad if they don't, but because more diverse boards and management teams have been linked in research with outsized financial performance, better advice, stronger governance and lower risk.

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Companies are pushing for their advertising agencies to be more gender diverse not just for better optics, but to help them avoid embarrassing gaffes and better connect with their consumers. Even the NFL last year said it would interview at least one woman for each of its league-level executive positions, with Commissioner Roger Goodell saying last year “we believe we're better as an organization” when diverse talent is at the table.

So what do the five female GOP senators think who aren't part of the group think about it? That's not yet clear, but one of them — Sen. Susan Collins (Maine), a member of the Senate's HELP Committee — says she still intends to work on the measure. “The leaders have the right to choose whomever they wish,” she said Monday, according to the New York Times. “It doesn’t mean that I’m not going to work on health care.” She continued: “I spent five years in state government overseeing the Bureau of Insurance many years ago, and I think I can bring some experience to the debate that will be helpful.”

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