DONALD TRUMP’S ACCOUNTS have been banned on Twitter, Facebook, and a host of other platforms. Every last one of @realdonaldtrump’s 47,000 weets vanished from the site in an instant, from the birther lies and election conspiracy theories to the 2016 taco bowl tweet. In an explanatory blog post, the company cited the attack on the Capitol and “the risk of further incitement of violence” that might occur by permitting further Trump tweets. His multiplatform removal has drawn cheers from many, as well as the ire of more than a few Trump supporters. The bans have also raised concerns that the companies had gone too far in exercising their power to shape what users see.

As it turns out, Trump is far from alone in having his content deleted by a tech company. With surprising regularity, online platforms flag or remove user content that they deem to be objectionable. Twitter’s recent ban of 70,000 accounts associated with QAnon mirrors other initiatives the company has had to combat extremist groups. It has banned well over a million accounts associated with terrorist groups, including a large set associated with the Islamic State. In the first half of 2020 alone, Twitter suspended roughly 925,000 accounts for rules violations.

While some content removal can be perceived as a matter of safety or ational security, the practice occurs in much more mundane situations as well. Yelp (where I have done consulting in the past), for example, has gathered hundreds of millions of local business reviews, and it has been shown to impact business outcomes. Its popularity has created new challenges, including fake reviews submitted by businesses in disguise trying to boost their online reputation (or to pan competitors).

To combat review fraud,

Yelp and other platforms flag reviews they deem spammy or objectionable and remove them from the main listings of the page. Yelp puts these into a section labeled “not currently recommended,” where they are not factored into the ratings you see on a business’s page. The goal of approaches like this is to make sure people can trust the content they do see.

In a 2016 paper published in Management Science, my collaborator Giorgos Zervas and I found that roughly 20 percent of reviews for Boston restaurants were getting pulled off Yelp’s main results pages. Platform-wide estimates show even higher rates of content removal, some 25 to 30 percent of all reviews aren't shown on businesses’ main review pages. Yelp is of course not alone in this practice. Tripadvisor and other review platforms also invest in removing reviews that seem likely to be fake.

Online marketplaces also have a history of kicking users off the platform for bad behavior. In a series of papers, my collaborators and I found widespread evidence of racial discrimination on Airbnb. In response to our research and proposals, coupled with pressure from users and policymakers, the platform committed to a broad set of changes aimed at reducing discrimination. One of these steps (which we had proposed in our research) involved creating new terms of service requiring users to agree not to discriminate on the basis of race in their acceptance decisions. The new terms had considerable bite: Airbnb ended up kicking off more than a million users for refusing to agree to it. Uber also has a history of removing users, from drivers who don’t maintain a high enough rating to 1,250 riders who were banned from the platform for refusing to wear a mask during the pandemic.

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MOSCOW — For years, the Kremlin tried to ignore the opposition leader Aleksei A. Navalny, right down to avoiding the very mention of his name.

But by Sunday, Russian officials had drastically reversed course.

President Vladimir V. Putin’s spokesman appeared on a prime-time show on state television and denied Mr. Navalny’s assertion that Mr. Putin had a secret palace on the Black Sea. On another marquee program, the host devoted 40 minutes to Mr. Navalny, who was described as engaging in “political pedophilia.” And the evening newscast showed tweets by Western officials in support of Mr. Navalny as proof that he was working against Russian interests.

The tightly scripted, all-hands attack on Mr. Navalny on Sunday underlined how the opposition leader’s dramatic

return to Russia a week earlier and his arrest have changed the landscape of Russian politics.

Mr. Putin remains in firm control of the levers of power. But Russians unhappy with their president — long a weak, diverse and atomized group — suddenly have a clear leader around whom to rally, and the government appears unsure about how to fight back.

On Saturday, tens of thousands of Russians took to the streets in support of Mr. Navalny in more than 100 Russian cities — protest on a scale unseen in the country in years. Quiet Siberian cities saw crowds in the thousands, while in Moscow, a survey showed that more than one-third of the participants had never protested before.

“People are tired of this authoritarian regime, of the chaos, of the corruption,” said Viktor F. Rau, a liberal activist in one of those Siberian cities, Barnaul. “Navalny was the spark.”