ON JANUARY 7TH , a day after a mob of his supporters stormed the Capitol in Washington, leaving five people dead and America shaken, Donald Trump had the sixth-most-popular account on Twitter, with nearly 90m followers. A day later he had none. The outgoing president was permanently booted off his social-media platform of choice for inciting violence.

Free-speech advocates—including Angela Merkel, Germany’s chancellor and no Trump fan—bristled. So did investors. Twitter’s share price has fallen by around 10% since @RealDonaldTrump’s expulsion. That of Facebook, which suspended his account “indefinitely” on its main social network and Instagram, its sister photo-sharing app, has also dipped.

This looks like an over-reaction, at least by the stockmarket. Social-media firms’ ad-sales departments may be glad to be rid of the troll-in-chief. Before being displaced by “coronavirus” last year, “Trump” was the most blocked keyword by online advertisers, loth to have their logos appear alongside content that might repel customers.

Twitter’s algorithms prioritise tweets that generate greatest engagement. Mr Trump’s were highly engaging, to put it mildly, and often ended up at the top of users’ feeds. This coveted online real estate is sold through automated auctions. If many potential bidders block “Trump”, this may depress prices. With Mr Trump gone, says Mark Shmulik of Bernstein, a broker, this ad inventory becomes more valuable.

Twitter may experience a decline in engagement in the short term. People who came to the site to gawp at Mr Trump’s latest outrage, and stuck around to read about movies or sports (or some lesser dust-up) may not return with the same frequency. But the upside of being more brand-friendly may offset losses from the Trump dump. The share price of Snap, which also suspended the presidential account, jumped on the news. Twitter’s remains well above pre-Trump levels (see chart).

For Facebook, Instagram and YouTube, which blocked Mr Trump’s account on January 12th, the impact is probably going to be negligible. Their monthly users (2.6bn, 1bn and 2bn, respectively) are more numerous and more global than Twitter’s (300m).

A bigger concern is whether muting Mr Trump undermines social-media firms’ claim that they are impartial platforms, and thus shielded from liability for what their users post, rather than publishers, who do not enjoy such protections. That is why they have been careful to couch their decision in the language of process and consistency with their own rules.

Even before the latest outrage, the firms had been stepping up moderation efforts, without giving up claims to platformdom. They employ tens of thousands of moderators between them to wade through toxic posts and remove those that break their terms of service. They have tried to limit the spread of misinformation around elections and other febrile times. Facebook has a semi-independent oversight body to hear appeals to disputed moderation decisions.

The social-media giants may welcome clearer rules, the need for which enjoys bipartisan support in America. These would raise barriers to entry for upstart rivals; Parler, a newish social network popular among American right-wingers, was boycotted into oblivion when it showed itself unable, as well as unwilling, to excise dangerously inflammatory content (see article). If muting Mr Trump engenders greater regulatory clarity, the thinking goes, so much the better for deep-pocketed incumbents. As an added bonus, it earned them rare plaudits from Democrats, who are about to take unified control of the federal government. ■

This article appeared in the Business section of the print edition under the headline “Capitol gains”