Social change—from evolving attitudes toward gender and marijuana to the rise of Donald Trump to the emergence of the Black Lives Matter and #MeToo movements—is a constant. It is also mysterious, or so it can seem. For example, “How exactly did we get here?” might be asked by anyone who lived through decades of fierce prohibition and now buys pot at one of the more than 2,000 licensed dispensaries across the U.S.

A new study about the power of committed minorities to shift conventional thinking offers some surprising possible answers. Published this week in Science, the paper describes an online experiment in which researchers sought to determine what percentage of total population a minority needs to reach the critical mass necessary to reverse a majority viewpoint. The tipping point, they found, is just 25 percent. At and slightly above that level, contrarians were able to “convert” anywhere from 72 to 100 percent of the population of their respective groups. Prior to the efforts of the minority, the population had been in 100 percent agreement about their original position.

“This is not about a small elite with disproportionate resources,” says Arnout van de Rijt, a sociologist at Utrecht University in the Netherlands who studies social networks and collective action, and was not involved in the study. “It's not about the Koch brothers influencing American public opinion. Rather, this is about a minority trying to change the status quo, and succeeding by being unrelenting. By committing to a new behavior, they repeatedly expose others to that new behavior until they start to copy it.”

The experiment was designed and led by Damon Centola, associate professor in the Annenberg School of Communications at the University of Pennsylvania. It involved 194 people randomly assigned to 10 “independent online groups,” which varied in size from 20 to 30 people. In the first step group members were shown an image of a face and told to name it. They interacted with one another in rotating pairs until they all agreed on a name. In the second step Centola and his colleagues seeded each group with “a small number of confederates…who attempted to overturn the established convention (the agreed-on name) by advancing a novel alternative.”

For the second step, as Centola explains it, the researchers began with a 15 percent minority model and gradually increased it to 35 percent. Nothing changed at 15 percent, and the established norm remained in place all the way up to 24 percent.

The magic number, the tipping point, turned out to be 25 percent. Minority groups smaller than that converted, on average, just 6 percent of the population. Among other things, Centola says, that 25 percent figure refutes a century of economic theory. “The classic economic model—the main thing we are responding to with this study—basically says that once an equilibrium is established, in order to change it you need 51 percent. And what these results say is no, a small minority can be really effective, even when people resist the minority view.” The team’s computer modeling indicated a 25 percent minority would retain its power to reverse social convention for populations as large as 100,000.

But the proportion has to be just right: One of the groups in the study consisted of 20 members, with four contrarians. Another group had 20 members and five contrarians—and that one extra person made all the difference. “In the group with four, nothing happens,” Centola says, “and with five you get complete conversion to the alternative norm.” The five, neatly enough, represented 25 percent of the group population. “One of the most interesting empirical, practical insights from these results is that at 24 percent—just below the threshold—you don’t see very much effect,” adds Centola, whose first book, How Behavior Spreads: The Science of Complex Contagions, comes out this month. “If you are those people trying to create change, it can be really disheartening.” When a committed minority effort starts to falter there is what Centola calls “a convention to give up,” and people start to call it quits. And of course members have no way to know when their group is just short of critical mass. They can be very close and simply not realize it. “So I would say to Black Lives Matter, #MeToo and all of these social change movements that approaching that tipping point is slow going, and you can see backsliding. But once you get over it, you’ll see a really large-scale impact.”

Real-life factors that can work against committed minorities—even when they reach or exceed critical mass—include a lack of interaction with other members, as well as competing committed minorities and what’s called “active resistance”—which pretty well describes the way many people in 2018 respond to political ideas with which they disagree. But even with such obstacles, Centola says the tipping point predicted in his model remains well below 50 percent.

Certain settings lend themselves to the group dynamics Centola describes in his study, and that includes the workplace. “Businesses are really great for this kind of thing,” he says, “because people in firms spend most of their day trying to coordinate with other people, and they exhibit the conventions that other people exhibit because they want to show that they’re good workers and members of the firm. So you can see very strong effects of a minority group committed to changing the culture of the population.”

The other environment in which the 25 percent effect is particularly evident, Centola says, is online—where people have large numbers of interactions with lots of other people, many of them strangers. This raises some tricky questions: Can a bot stand in for a member of a committed minority? And can a committed minority be composed of bots and the real people the bots influence, so that bots are actually driving the change? According to Centola, “In a space where people can’t distinguish people from bots, yes. If you get a concerted, focused effort by a group of agents acting as a minority view, they can be really effective.”

Yale sociologist Emily Erikson, who also studies social networks but was not involved with the study, sees the new paper partly as a warning. “In some sense it’s saying extreme voices can quickly take over public discourse,” she says. “Perhaps if we’re aware of that fact, we can guard against it.”