A protest rally in Singapore calls for the release of Amos Yee, a teen-ager who was arrested for social-media comments he posted after the death of the country’s leader. PHOTOGRAPH BY WALLACE WOON /EPA VIA LANDOV

Mark Zuckerberg, the C.E.O. of Facebook, has been touring China and India, and, naturally, he is documenting his travels online. On Monday, he posted a photo of himself and his colleagues jogging in the ancient Chinese city of Xi’an; on Tuesday, he followed up with a visit to the Taj Mahal. This is not, despite appearances, a pleasure trip. There are few remaining people in the U.S. and Europe who aren’t on Facebook. In Asia, by contrast, fewer than forty per cent of people even have access to the Internet, but that number is increasing, and Facebook hopes to take advantage; though the site is blocked in China, the company surely hopes its efforts will help that to change. (Internet penetration is even lower—but also growing—in Africa, where Facebook this year opened its first office, in Johannesburg.)

Of course, Zuckerberg, in his public comments during the trip to China and India, has focussed less on the potential usefulness of these countries to his business than on the potential usefulness of Facebook to their citizens. In a speech in Mandarin at Beijing’s Tsinghua University, he said, “Every person wants to connect with his friends and family. When we can share and connect, life gets better. When we connect and share, we build closer relationships with the people we love.” He took this argument further still: “We build stronger businesses because we can communicate better with customers. We build a stronger society because people know more.”

This rhetoric isn’t unfounded. As Nicholas Schmidle observed in a recent profile of a Syrian refugee who used fellow migrants’ posts on Facebook to learn how to get to Europe, social media has greatly expanded refugees’ access to information. But a report published Wednesday by the organization Freedom House highlights another development: even as it gets easier for people to get on Facebook and other social-media sites, it's also seemingly becoming more dangerous for them to voice their opinions in these venues. (Google, Facebook, Yahoo, and Twitter helped fund the report, but it does not necessarily reflect their views.)

I covered Freedom House’s 2014 report, which found that Internet freedom, as measured by online access, availability of content, and the robustness of civil rights, had declined for the fifth straight year. Wednesday’s report marks the sixth year of declines. The authors note that the losses aren’t as sharp as in the past, because they’re tempered by developments like an Indian Supreme Court decision, in March, that rendered unconstitutional a restrictive provision of a law that had been used to criminalize online speech, especially on social media. Still, the report leaves a bleak over-all impression. Only thirty-one per cent of people who are online live in countries, like the U.S., where they can freely use the Internet. Twenty-three per cent are in partly free countries, and thirty-four per cent—the greatest proportion—live in countries that are not free. (Freedom House didn’t assess the remaining twelve per cent of Internet users, who live in countries that the report doesn’t cover and who might belong to any of those categories.)

In particular, it is becoming more common for countries to punish people who express sensitive opinions on social media and in other forums. Perhaps the most high-profile example of the past year occurred in March, following the death of Singapore’s first Prime Minister, Lee Kuan Yew. Five days after Lee died, a sixteen-year-old named Amos Yee tweeted mild criticism of the former Prime Minister and linked to an eight-and-a-half-minute YouTube clip in which he condemned Lee as a “horrible person” whose legacy was to make people afraid to criticize him. Yee appears to have had a point, because, days later, the police arrested him, charging him with having violated Singapore’s Harassment Act, which restricts “threatening, abusive, or insulting communication.” The Freedom House report lists some other incidents involving teen-agers:

In western Turkey, police visited a classroom to question a 13-year-old on suspicion of “insulting” President Recep Tayyip Erdoğan on Facebook. An 18-year-old was among six people arrested in Venezuela for tweeting about the death of a national lawmaker. Police in Belarus threatened to fine student Dmitry Dayneko after an opposition website shared his YouTube video calling on President Alyaksandr Lukashenka to take the “ice bucket challenge,” whose participants—including several international politicians—sought charitable sponsorships for publicly drenching themselves in cold water.

Over all, of sixty-five countries reviewed by Freedom House, forty had imprisoned people for sharing political or social content through digital networks. That represented only a slight rise, from thirty-eight, in last year’s report, but two of the report’s authors told me that they believe it is part of a larger trend of countries arresting and intimidating Internet users. (It’s not clear whether the number of arrests of young people, in particular, is increasing, because these statistics aren’t readily available.)

I asked Sanja Kelly, the project director for the report, about the significance of these kinds of incidents. She pointed out that the people who broadcast their beliefs in an earlier, offline era—and were liable to get in trouble for it—were different from the ones who are now sharing their opinions online. “I think generally people on social media, many of them average people—they just don’t think about threats that they might face,” she told me. “That’s what makes them different from activists and journalists. If you’re a human-rights activist, you’ve already chosen a profession where you know you might be arrested. But, if you’re a teen-ager or a housewife, you just write these things down, and you don’t think anyone apart from your friends or family are going to see it—and then, when you get that knock on the door, you realize what kind of trouble you’re in.”

As it happens, China, whose citizens and government are being courted not only by Zuckerberg but by other tech C.E.Os., has the lowest level of Internet freedom among all the countries that Freedom House surveyed; India is around the middle of the pack, but remains only “partly free.” When the heads of tech companies visit these countries, and others with limited Internet freedom, they tend to sidestep the topic. But, to operate in a given place, any company has to abide by local rules. In the countries where Internet users are only partly free, or not free at all—in other words, the countries where many of these sites are expanding their presence—that means governments consider themselves free to use their citizens’ social-media comments against them. Sites like Facebook do, as Zuckerberg notes, help people to learn much more about the world around them, and that can be powerful. But they also help governments learn much more about their own citizens, and that is also powerful. We may soon start to learn the extent to which companies are willing to abide that power.