In his latest effort to recast his election win as an even bigger victory than the ballot box showed, President Donald Trump tweeted out an eye-popping — but unsubstantiated — claim.

"Wow, Report Just Out! Google manipulated from 2.6 million to 16 million votes for Hillary Clinton in 2016 Election!" Trump tweeted. "This was put out by a Clinton supporter, not a Trump Supporter! Google should be sued. My victory was even bigger than thought!"

Trump’s claim appears to trace back to a research paper published online in June 2017. He may have become aware of the paper after the right-wing website Town Hall ran an article that heavily cited it. The Washington Post reported that the same research paper was mentioned in a segment on Fox Business Network.

The paper, by psychologist Robert Epstein, seeks to build off earlier research Epstein did on how bias in search engine results can affect voting preferences. (For the record, Epstein’s estimate was that between 2.6 million and 10.4 million votes may have been manipulated in 2016 — not up to 16 million votes, as Trump said.)

But a number of experts we reached out to said the latest paper’s methodology is freighted with too many flaws and unexplained assumptions to assert the kind of claim Trump makes here.

A questionable approach

We reached out to Epstein to ask if he took issue with how Trump characterized his findings.

"I sure do," said Epstein, who supported Clinton in 2016. "I have never said that Google deliberately manipulated the 2016 election."

When we asked what formula and assumptions Epstein used to reach his bottom-line conclusion, we did not hear back. The White House did not respond to a request for comment.

Experts cited several major flaws in Epstein’s paper.

First, here’s the study’s basic setup: In the run-up to the 2016 election, researchers recruited 95 people, 21 of whom identified as "undecided."

Over a 25-day period — from Oct. 15 through Election Day, Nov. 8 — researchers analyzed between 50 and 483 of these subjects' daily web searches.

Those search results were then farmed out to a crowdsourcing website, where raters voted on whether they found search results biased or not.

Their key finding: that "election-related search terms were, on average, biased in Mrs. Clinton’s favor."

Experts we spoke to cited a slew of problems with this methodology.

One common complaint was a lack of definitions.

"They can't even define what biased search results are — they simply piped them off to a crowd-sourcing site and asked random people, ‘Is this search results page biased or not?’ " said Ryan Singel, a media and strategy fellow at Stanford Law School’s Center for Internet and Society. "What does that even mean?"

The researchers also discarded search results from users who operated Gmail accounts, after finding these users’ searches yielded less biased results. To the researchers, this raised concerns that "perhaps Google identified our confidants through its gmail system and targeted them to receive unbiased results."

But others doubted that explanation.

"They eliminated anyone using a Gmail address because their search results weren't considered ‘biased,’ speculating that Google was intentionally poisoning their research," Singel said. "That's both equally laughable and sad."

Setting aside the methodological flaws, others took exception to the researchers assumption about how well an experiment of this kind would translate to the voting booth. To some, the holes in the definitions and unexplained formulas used to extrapolate created more questions than answers.

We reached out to Nicholas Diakopoulos, a professor in communication studies and computer science at Northwestern University, to ask how researchers could get from 25 days’ worth of search results from 95 subjects to millions of manipulated votes.

"There's not enough information in the whitepaper about how the estimate was done," Diakopoulos said.

He said the researchers likely developed a mathematical formula that seeks to translate examples of bias they collected into estimates of voter impact.

"But again there is not enough information in the whitepaper to say definitively how their ‘computational model’ works," he said, "and whether it is a valid estimate based on the assumptions built into the model."

Google refuted Trump’s statement, noting it was an old claim.

"This researcher's inaccurate claim has been debunked since it was made in 2016," a Google spokesman said in a statement. "As we stated then, we have never re-ranked or altered search results to manipulate political sentiment."

Our ruling

Trump said a new report shows "Google manipulated from 2.6 million to 16 million votes for Hillary Clinton in 2016 Election." The general idea here is that Google gave people search results that in some way affected their vote in the lead-up to the election for president.

Whether such indirect interactions could cause people to change their votes is questionable, and the paper — which is not new — does nothing to establish how that might happen. The paper doesn’t explain its methodology, and other academics questioned whether its findings were valid. Finally, Trump seems to have exaggerated the outer bound of the questionable findings.

Overall, we rate his statement False.