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.