(Credit: Gallup. See full research here.)

Women may be 'leaning in' these days in higher numbers, but more Americans still say they'd prefer to have a male boss.

That's the most obvious takeaway from Gallup research data released earlier this week. In its annual Work and Education survey conducted in August, Gallup asked respondents to describe their ideal choice of boss if they were taking a new job, and 35 percent said they would prefer to work for a man. Meanwhile, 23 percent said they'd prefer a female supervisor, and 41 percent said they had no preference.

While the overall numbers lean male, more interesting is that the survey found two subgroups of respondents who were slightly more inclined to want a female boss. The first group consisted of those who already work for one. Thirty-two percent of people who currently work for female managers cited that as their preference, versus 31 percent of them who say they'd rather have a man.

The other group was Democrats. Thirty-three percent of survey takers who identified with that party said they'd prefer a female boss, while 32 percent said they'd rather report to a guy.

A subgroup that surprisingly didn't show a preference for women as managers? Women themselves. Forty percent of female respondents said they'd prefer a male boss, while just 27 percent of women said they'd like to work for a woman.

(Credit: Gallup. See full research here.)

Does this show that once someone works for a woman, they are more open to the idea? Gallup says it's possible. It could be that workers who initially prefer female bosses gravitate toward them, Gallup's Frank Newport and Joy Wilke write in the data's release, or it could be "that the experience of working for a female boss affects workers' preferences. If the latter is the case, and if the proportion of U.S. workers who have female bosses increases in the future, the current preference for a male boss in the overall population could dissipate."

I'd take that a bit further and connect those two thoughts. It's certainly possible that the more women get into leadership roles, the greater the likelihood that employees will actually seek them out as the people they want to work for. That, in turn, could then push more organizations to promote women into higher managerial roles.

Such a cycle might one day help to balance the ratios of people who prefer a male boss to a female one. But of course, an even better outcome will be when the vast majority of people care less about the gender of their managers, and care much more about their ability to lead and their integrity on the job.

Jena McGregor is a columnist for On Leadership.

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