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I found a fascinating study, (Social Media, Sentiment and Public Opinions: Evidence from #Brexit and #USElection by Yuriy Gorodnichenko, Tho Pham, Oleksandr Talavera, 2018), which gave numerical estimates for the effect of Twitter bots (regardless of their origin) on the outcome of two recent elections:

  • 1.76% (absolute) boost for the pro-leave vote in the Brexit referendum
  • 3.23% for the pro-Trump vote in the 2016 presidential election

The authors come up with these numbers by estimating the impact that bots have on human Twitter accounts' [re]posts, and also correlate tweets pro-something with actual votes for that cause. Subtracting the bot-induced human tweets thus gives them a corresponding estimate for the change in actual votes. They do this for both sides in an election and finally compute the difference in votes without bots.

However Twitter was just a part of the social media issue with recent elections. In my recollection, most of the media articles emphasized fake news (and chiefly singled out Facebook as the venue), rather than Twitter bots. So, are there any papers trying to put a numerical vote figure for the fake news spread on Facebook (or more generally on the web at large)? Since such papers seem hard to come by, even partial aspects, like estimating the effect of automated spreading of fake news on the actual election results would appreciated.

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    Does "fake news" also encompass the hard-left organizations like CNN and the NYT? Define your terms carefully. – user5904 Aug 3 '18 at 20:15
  • % of what? Facebook did their own review. – K Dog Aug 3 '18 at 20:19
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    @MathematicsStudent1122: since I'm asking for studies, not wild guesses, they'd presumably have a reasonable operational definition of fake news (otherwise the study couldn't even proceed). Supposedly Facebook now has a fake news detector which cross-checks with a database. Presumably other research can do that. – Fizz Aug 3 '18 at 20:20
  • I found a study that estimates the amount of exposure during the 2016 US election, but doesn't go as far as trying to translate that into votes dartmouth.edu/~nyhan/fake-news-2016.pdf In fact there's probably a lot more like this one, since just estimating exposure isn't that hard. More on npr.org/2018/04/11/601323233/… – Fizz Aug 3 '18 at 20:35
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    @user4012 partially, but the retweets might show the tweets to a new audience. The degree to which that new audience continues to spread (retweet) could (I am not claiming that it is per se, I am no expert on that) be indicative of influence. – JJ for Transparency and Monica Sep 2 '18 at 22:15
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I did find one study on the 2016 US elections, of course. Their approach was to survey a sample of voters for belief in a fixed set of falsehoods that had been spread via fake news.

As for determining the impact of the beliefs spread by fake news on voters, the authors used a multiple regression model, with other possible explanatory variables included

The first equation we ran included gender, race, age, education, ideological orientation, dissatisfaction with the condition of the economy and party identification. All together, these variables “explained” 38 percent of the likelihood of defection.

We then added the fake news items to the equation to measure their impact. The three fake news items explained an additional 14 percent of the likelihood of Obama voters defecting after the influence of all of the other variables had been taken into consideration.

We also added one more compelling element to our study. Using “feeling thermometers,” we measured how much each respondent liked or disliked Hillary Clinton and Donald Trump. If defection of Obama voters was only due to disliking Hillary Clinton or liking Donald Trump, then the introduction of this thermometer variable into the equation should make the link with fake news disappear.

Belief in fake news remained a significant predictor of defecting from Clinton. In sum, even after the impact of all of these other factors is taken into consideration, former Obama voters who believed one or more of these fake news stories were 3.3 times more likely to defect from the Democratic ticket in 2016 than those who did not believe any of these false claims.

That may not seem like much, but Clinton lost the presidency by about 78,000 votes (0.6 percent of nationwide vote) cast in the key battleground states of Pennsylvania, Michigan and Wisconsin. Though our evidence does not “prove” that belief in fake news “caused” these former Obama voters to defect from the Democratic candidate in 2016, our study results suggest that it is highly likely that the pernicious pollution of our political discourse by fake news was sufficient to influence the outcome of what was a very close election.

So they don't quite give an absolute percentage, but just the odds ratio for Democrats switching their vote after believing a certain set of fake news...

  • What they didn't do is to prove causality at all. It's far more likely that people already predisposed to defect because they believed Trump's pitch about jobs etc..., would believe fake news because {insert long and complicated explanation that boils down to motivated reasoning}. Their study did not - at least based on your quote - show even "influence". – user4012 Aug 5 '18 at 0:42
  • According to the NYT, a former newspaper, media is heavily biased to the left. nytimes.com/roomfordebate/2015/11/11/… Donation tallies back this up. time.com/money/4533729/… Did your study look at any fake anti-Trump stories? – user21424 Sep 3 '18 at 23:43
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From: Allcott, H., & Gentzkow, M. (2017). Social media and fake news in the 2016 election. Journal of Economic Perspectives, 31(2), 211-36.

This study may be found here (link) and it has a link to the full pdf version (open access).

From its abstract, regarding how many stories an average American saw and how they perceived them:

3) the average American adult saw on the order of one or perhaps several fake news stories in the months around the election, with just over half of those who recalled seeing them believing them

From its conclusion:

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.

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