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.