TROLLS, bots, hackers, propagandists and provocateurs of Russian origin have lately descended on Western democracies. The tentacles of the disinformation apparatus, thought to be rooted in the Kremlin, have been found fiddling with elections everywhere from Ukraine and Bulgaria to France and America. It is perhaps no surprise, then, that they may also have touched the Brexit campaign held in June 2016 by trying to steer social-media conversations before the referendum, as a spate of new academic research suggests.

The evidence unearthed so far establishes only a small-scale effort by sources in Russia to nudge Britain towards the European Union’s exit door. But new information is being dug out of online archives week by week. Theresa May, the prime minister, has accused Russia’s government of “planting fake stories” to “sow discord in the West.” MPs are pushing for an inquiry, which may yet reveal more meddling.

When it was summoned before Congress last month, Twitter published a list of 2,700 accounts run by the Internet Research Agency (IRA), a well-known troll farm with ties to the Kremlin. Two groups of British researchers who had collected Brexit-related tweets cross-referenced this list and found that some IRA accounts had pushed out content on the referendum. That discovery is disturbing in its own right. Russian interference is designed to erode trust in national institutions and weaken democracies.

On the current evidence, there are reasons to be sceptical that the interference swung the referendum, which was won by more than 1m votes. The volume of tweets was small. One study by the Oxford Internet Institute found 416 IRA tweets about Brexit among a data set of 23m on the subject. Another, from Edinburgh University, uncovered 3,468 tweets in a set of 62m. Both studies noted that around 80% of the IRA tweets they spotted came after the vote. And although the messages were mostly pro-Leave, some also argued for Remain, presumably to stir things up.

Another approach, taken by researchers at Swansea and Berkeley universities, was to examine the self-declared language of users tweeting about the vote in English. They found 150,000 Russian-language accounts, which fired off at least 45,000 tweets on the day of the referendum and the day after. But it is unclear how many such accounts were Kremlin-subsidised puppets. A handful are known to be trolls, but some could just as well be bilingual Russian bankers living in Kensington. The 45,000 tweets made up 1% of the messages in the data set. Japanese-language accounts published the same share, yet Shinzo Abe is not suspected of meddling.

But dismissal of the Russian connection would be premature. Researchers have not been given access to equivalent information by Facebook, which may be more influential over public opinion than Twitter, and would almost certainly be part of any sophisticated propaganda operation. “Internet researchers are always working from a position of weakness because Facebook is inscrutable,” says Siva Vaidhyanathan, director of the Centre for Media and Citizenship at the University of Virginia. “It’s about the most opaque media company in the world.” Facebook says only that it has not observed “significant co-ordination” by known Russian trolls targeting the Brexit vote.

In America, the extent of Russian disinformation efforts became clear only when Congress began investigating. After Donald Trump won the presidential election, Mark Zuckerberg, Facebook’s boss, pooh-poohed the “pretty crazy idea” that fake news spread on his social network may have influenced the vote, which he attributed to “a profound lack of empathy”. (In the most recent quarter, Facebook received over $10bn in advertising revenues on the pretty crazy idea that its ads could in fact influence users.) But Congress pushed the company to disclose in October that 10m Americans had seen divisive political advertisements bought in Russia. Three weeks later, ahead of a big hearing, it said that 126m Americans may have seen Russia-linked posts. Mr Zuckerberg has since said he regrets his earlier remarks.

In Britain, the Electoral Commission is already investigating whether various pro-Leave organisations broke campaign-finance rules in the run-up to the referendum. The chairman of the parliamentary committee in charge of media matters has written to Facebook and Twitter requesting information about Russian-bought ads linked to the Brexit vote and to the general election this June. MPs plan to go to Washington, DC, in February to seek answers in person. The prospect of bad media coverage seems to spur Facebook into some action. A full parliamentary inquiry could yet spur even more.