It is impossible to accurately estimate the number of Russian state-sponsored accounts operating on Twitter and Facebook. Researchers come up with a wide range of possibilities, suggesting that Russian interference in British political and cultural life could come from anywhere between 50 and 150,000 accounts.

The explanation for this is not because the Russians are particularly secretive or expert at covering their tracks, but the attitude of Twitter and Facebook who fight attempts by independent researchers to come up with an answer. As a result, academics and analysts attempting to come up with a definitive answer often produce wildly divergent estimates.

Q&A What is a Twitter bot? Show Hide Strictly defined, a Twitter bot is any automated account on the social network. That can be something as simple as automatically tweeting links to news articles – most of the Guardian's social media accounts are technically Twitter bots, for instance – to complex interactions like automatically generating Emoji-based art or automatically replying to climate change deniers with scientific evidence. But, as with "troll" and "fake news", the strict definition has been forgotten as the term has become one of political conflict. The core of the debate is the accusation that a number of political tweets were sent by "Russian bots", with the intention of subverting political debate, or simply creating chaos generally. Based on what we know about Russian information warfare, the Twitter accounts run by the country's "troll army", based in a nondescript office building in St Petersburg, are unlikely to be automated at all. Instead, accounts like @SouthLoneStar, which pretended to be a Texan right-winger, were probably run by individuals paid 45-65,000 rubles a month to sow discord in Western politics. In other ways, they resembled bots – hence the confusion. They rarely tweeted about themselves, sent far more posts than a typical user, and were single-minded in what they shared. People behaving like bots pretending to be people: this is the nature of modern propaganda.

Yin Yin Lu, a researcher at Oxford University, cited 54 Twitter accounts that had tweeted about Brexit during the referendum period, and were included on a list of 2,752 users that the social network had concluded were actually operating from a state-backed “troll factory” in St Petersburg. Another researcher, at the University of Edinburgh, found almost 10 times as many from the same list: at least 419, according to Prof Laura Cram, director of neuropolitics research.

Researchers at City, University of London give a figure two further orders of magnitude higher: in October, they documented a network of 13,493 accounts “that tweeted the United Kingdom European Union membership referendum, only to disappear from Twitter shortly after the ballot”. Those researchers declined to guess at who might be pulling the strings of the vast botnet, but did say that they did not believe it “substantively altered” the tenor of the campaign.

But a fourth set of researchers have produced a higher still estimate: 150,000 accounts with links to Russia tweeted about Brexit in the run-up to the referendum, according to Swansea University’s Oleksandr Talavera, working with researchers from his university and UC Berkeley in America. That network of accounts came from nowhere to post huge numbers of tweets in the run-up to the vote – almost 40,000 messages on one day alone – then disappearing.

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According to researchers from five different universities, then, the scale of Russian interference was somewhere between 50 and 150,000 accounts.

The problem for all the researchers is that only one organisation has the data they need, and Twitter is not willing to share it. We only know the names of any professional trolls at all because Twitter handed over a limited list of those accounts involved in US politics that it believed to be linked with the Internet Research Agency “troll army”.

Some researchers, such as Oxford’s Lu and Edinburgh’s Cram, started with that list, and worked backwards to find out which of those accounts had tweeted about British politics as well as American politics. Others, like Talavera at Swansea, instead attempted to independently link accounts to Russia using only public data, such as whether users slipped up and used Cyrillic letters (which are encoded differently even if they look the same) or if they set their interface language to Russian.

All of those efforts were hampered further by Twitter’s unwillingness to work with researchers. The company does not allow anyone except a few select corporate partners access to the “firehose” – the raw stream of public tweets in realtime – and no one outside the company can look at the full historical database. That means that researchers had to scramble to come up with novel ways to build their own datasets from what they could access.

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Talavera gathered every single tweet using the hashtag #Brexit over a two-month period; Lu selected 334 hashtags and 65 usernames, and collected any tweet mentioning any of them for a period of six months. That meant that Lu could go over her database after the fact, looking for accounts she had seen in 2016 which later showed up on Twitter’s list of Russian trolls.

Twitter could do more, the academics agree. “I would be absolutely happy if Twitter worked with researchers,” said Talavera. “They’ve already deleted a lot of accounts, so they do their job. But they should make data available for researchers.”

The social network says it has its own systems working internally to find and shut down bot and misinformation accounts, and some of the researchers’ findings suggest it is effective. Talavera reported that 90% of the automated accounts he had found in June 2016 had been deleted in the period since.

But even that is a double-edged sword. When Twitter deletes an account – or when the account holder deletes it themselves – all the information is lost. “We have them in our data, but we don’t know anything else about them,” said Talavera. That means that if the company does, eventually, publicise the names of the accounts it closed, it would be impossible to comprehensively assess the damage they did – while the trolls themselves simply make new accounts and start the process again.

• This article was amended on 17 November 2017 to clarify that the 54 Twitter accounts that had tweeted about Brexit did so during the referendum period, 15 April - 23 June 2016.

