I've encountered repeated references to fake news on Facebook influencing various elections. Example from a often quoted Facebook critique in Time Magazine:

As a result, when confronted with evidence that disinformation and fake news had spread over Facebook and may have influenced a British referendum or an election in the U.S.

There are of course many other references to the same in the press.

So, the question is:

Is there any systematic trust-worthy (e.g. performed by qualified people on large data sets, and preferably peer-reviewed) research that quantifies the influence of fake news on Facebook on US 2016 elections? Absent that, is there any data at all that these claims have or have not any factual basis, beyond mere conjectures driven by political beliefs of media writers?

For the purpose of this discussion, "fake news" are defined as content masquerading as news or news commentary, purposely written with the intent to deceive or mislead, or references to fictitious (satirical, fiction literature, just plain invented out of thin air) content as factual, for the purpose of convincing people to vote one way or another (or abstain from voting). It does not include sincere media news publications that proved to be erroneous later, or clearly marked opinion pieces that somebody considers wrong. This also does not include clearly attributed sincere political ads on social media or outside, even if those are getting some facts wrong.

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    The strong connection between the 2016 presidential election and the Brexit referendum is the participation of Cambridge Analytica, a political consulting firm which worked for the Trump campaign and reputedly was involved in the Brexit campaign. – Daniel R Hicks Jan 17 at 22:07
  • The problem with this question is that: "It does not include sincere media news publications that proved to be erroneous later" excludes almost everything. There is nothing so outlandish that someone won't believe it sincerely and repeat it. Also why would you think fake news (by whatever definition) would be less effective than non-fraudulent advertising, which has been shown to be effective both by peer-reviewed study and by market behavior? – antlersoft Jan 17 at 23:03
  • @DavePhD how it is related? – StasM Jan 18 at 0:09
  • @antlersoft It doesn't exclude everything. There's a lot of difference between sincere mistake and fake. I am not saying it excludes people that sincerely believe fake news. I am saying it excludes legitimate news reporting that was, for example, based on an error. It doesn't exclude fakery that somebody sincerely believed. Also, there's a good reason to suspect political ads aren't that effective either: papers.ssrn.com/sol3/papers.cfm?abstract_id=3042867 but anyway I'm not interested in conjecture but actual data. – StasM Jan 18 at 0:14

According to Less than you think: Prevalence and predictors of fake news dissemination on Facebook Science Advances 09 Jan 2019: Vol. 5, no. 1:

Some have gone so far as to assert that such content had a persuasive impact that could have affected the election outcome, although the best evidence suggests that these claims are farfetched [reference 2].

where reference 2 is Social media and fake news in the 2016 election J. Econ. Perspect. 31, 211–236 (2017)

which concludes:

the new evidence we present clarifies the level of overall exposure to fake news, and it can give some sense of how persuasive fake news would need to have been to have been pivotal. We estimate that the average US adult read and remembered on the order of one or perhaps several fake news articles during the election period, with higher exposure to pro-Trump articles than pro-Clinton articles. How much this affected the election results depends on the effectiveness of fake news exposure in changing the way people vote. As one benchmark, Spenkuch and Toniatti (2016) show that exposing voters to one additional television campaign ad changes vote shares by approximately 0.02 percentage points. This suggests that if one fake news article were about as persuasive as one TV campaign ad, the fake news in our database would have changed vote shares by an amount on the order of hundredths of a percentage point. This is much smaller than Trump’s margin of victory in the pivotal states on which the outcome depended.

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    This fails to take into account the targeted approach supposedly used by Cambridge Analytica, where a small number of people on Facebook were "targeted" based on their apparent "waveringness" and their presence in a pivotal district. – Daniel R Hicks Jan 18 at 1:58
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    Did CA distribute fake news? I thought they delt with legitimate political ads. – StasM Jan 18 at 7:39
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    @DanielRHicks TV, Radio, newspapers all target relevant districts when appropriate, but districts only matter for the House and in Nebraska and Maine for electors for president. Sometimes it's better to target supporters so they turn out, instead of actually trying sway people. If you have good info, add another answer. – DavePhD Jan 18 at 11:41
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    I feel that this is a flawed analysis. It would not surprise me at all if one fake news article had more affect on an individuals decision then one campaign ad, even significantly so. Campaign ads all start to look the same and get ignored quickly, there is little expected news in them either. Where as if someone read (and believed) that a candidate kicked puppies and burned down orphanages that could make a far more lasting affect. Put another way the ability to lie in fake news allows presenting more concerning, and thus vote swaying, news then campaign adds that are nominally true. – dsollen Jan 18 at 15:28
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    I'm categorically baffled by studies that imply major corporations (as well as candidates) are stupid in spending money on advertising. – Andrew Lazarus Jan 18 at 20:59

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