Tali Mendelberg is the John Work Garrett professor of politics at Princeton University and director of the Program on Inequality at the Mamdouha S. Bobst Center for Peace and Justice. Christopher Karpowitz is an associate professor of political science at Brigham Young University and co-director of BYU's Center for the Study of Elections and Democracy. The views expressed in this commentary are solely those of the authors.

(CNN) Women are mobilizing for change more visibly than ever. The women's march may have been the largest such event in history. Across the country, the numbers of females signing up for workshops on how to run for office has surged, raising the potential for moving the percentage of women in city and state legislative bodies past its current 25% .

In the private sector, too, there is growing awareness of the shortage of women in the corporate hierarchies.

Arianna Huffington is a prime example. As a board member of Uber, Huffington spoke at a staff meeting with her cohorts (who were all male until she joined the board last year) and explained that if one woman joins a board, it's more likely that another woman will want to join the same board.

One male response to this phenomenon? "Actually, what it shows is that it's much more likely to be more talking," responded the now-resigned David Bonderman.

What Huffington and Bonderman's exchange and other events in the news this week bring into sharp relief is that when women do break the glass ceiling, their journey to parity is just beginning. Women who join majority-male boards or committees often encounter barriers to their authority like men who, whether intentionally or not, monopolize the discussion or interrupt women's speaking turns.

It's " The Universal Phenomenon of Men Interrupting Women ," as The New York Times puts it. The typical pattern in these settings is that women struggle to be heard. Just this week we saw US Sen. Kamala Harris get interrupted not once, but twice, by her male-majority counterparts.

In Senate confirmation hearings, senators interrupt and challenge women's testimony more often than men's, even when they belong to the same party. In research included in his 2003 book " Real Democracy: The New England Town Meeting and How It Works ," Frank M. Bryan found that in New England town meetings, most men spoke; most women didn't. We have even studied school board meetings where we found that the average woman speaks far less than the average man.

Put differently, Uber's board and the United States Senate are part of the same phenomenon: They both vastly under-represent women, thereby silencing women's voices.

Of course, it is easy to cherry-pick vivid examples of women's disadvantage. But in our research, we have found these patterns are typical: Women are silenced when they are the minority.

Between 2007 and 2009, we ran a study to assess how women exercised authority in groups where they are a minority, which was discussed Wednesday on " The Daily Show with Trevor Noah" in connection to Bonderman's sexist remarks at the Uber board meeting. We hypothesized that if the male-female board ratio mattered, then women's disadvantage would grow as their numbers on the board shrunk. And so, at random, we assembled 94 groups composed of five members each, and randomly varied the number of women and men in the group. We then had the group discuss a public issue.

We collected several measures of authority: how much women spoke, how often they were interrupted, how often they articulated the views they had privately reported to us, how often other members articulated women's views, whether the group adopted these views in its decision, and whether women were later rated as influential by other members. For each measure of authority, we compared women to men in their group and to men in groups with a male minority.

We found the pattern familiar to many women in the workplace. Where women make up a minority, they speak less, receive more hostile interruptions, refrain from articulating their views, and are rarely rated as influential. The group is less likely to discuss and use these views in making decisions. These are winner-take-all groups, in their process and their outcomes. Sound familiar, Uber employees?

In other words, in meetings where women are scarce, they are actively disrespected. The group suffers, too, as its range of perspectives shrinks.

Even extremely successful women have battle scars from the masculine work culture. Madeleine Albright, the first female secretary of state, who has stared down many a foreign leader in tough negotiations, confessed , that "To this day, I sometimes feel a squirm of anxiety when I interrupt a discussion in a room with only men."

A few simple reforms can go a long way. In our research, we instructed some groups to use a consensus process. This means that every member must agree to the decision. We expected that this would cancel out the disadvantage of women's minority status in the group. And in fact, in these groups, the gender gap in authority shrank dramatically. Women spoke about as often as men. They were treated with respect. They shaped the discussion, and the group took their opinions into consideration.

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Of course, consensus is a tough sell in many settings. But there are feasible elements of consensus for any group. At the start of the meeting, the moderator states that the group wishes to hear from every individual at the table. Members are each invited to say what's on their mind. No interruptions are allowed. The moderator periodically repeats this process as the meeting goes on. This is a cost-free way to leverage the strengths of consensus.