On Monday morning, President Donald Trump tweeted that a "report just out" confirmed Google had "manipulated" millions of votes in favor of Hillary Clinton in the 2016 election.

The president's claims, however, were based on past studies by the psychologist Robert Epstein that Google describes as "debunked" and that experts tell Business Insider made "weird methodological choices."

One of Epstein's studies — which claims 2.6 million votes could have been shifted in favor of Clinton because of a bias in Google's search results — surveyed only 95 participants, for instance, and even then, some of the results were thrown out for suspicious reasons.

Epstein told CNN on Monday that Trump misrepresented his findings, saying he didn't have evidence to prove Google actively "manipulated" millions of voters, but rather the bias he found in its search results was "sufficient to have shifted between 2.6 and 10.4 million votes" to Clinton.

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On Monday morning, President Donald Trump tweeted that a "report just out" showed that Google "manipulated" millions of votes in favor of Hillary Clinton in the 2016 US presidential election.

"Google should be sued," the president declared in his tweet, which said Google manipulated 2.6 million to 16 million votes in Clinton's favor. "My victory was even bigger than thought!"

Trump, who won the presidency through the Electoral College while receiving 2.9 million fewer votes than Clinton, did not link to or explicitly cite the report. His tweet immediately sent surprised industry observers scrambling to find the blockbuster research report they had somehow missed.

It turns out, the report Trump appears to have been referring to was a 2017 report by a San Diego psychologist with a history of feuding with Google. The report, which one expert on the US election process characterized to Business Insider as having a "weird" methodology and lots of "red flags," was based on 95 participants.

So what is this report?

One of the figures Trump cited in his tweet, the 2.6 million votes, tied his comments to the recent testimony of the San Diego psychologist Robert Epstein, who appeared before a Senate Judiciary Committee hearing in July titled "Google and Censorship through Search Engines."

In his testimony, Epstein — a self-proclaimed Democrat — said that at a "rock-bottom minimum" Google swayed 2.6 million votes in favor of Clinton because of biases in its search results.

"The range is between 2.6 and 10.4 million votes depending on how aggressively they were in using the techniques that I've been studying now for 6 1/2 years," Epstein told the committee. (It's not clear where Trump arrived at the 16 million figure at the high end of his range.)

But Epstein told CNN on Monday that Trump misrepresented his findings, saying that they didn't prove Google actively "manipulated" millions of voters but rather that the bias he found in its search results was "sufficient to have shifted between 2.6 and 10.4 million votes" to Clinton.

Epstein, a former editor-in-chief of Psychology Today, is now a senior research psychologist at the American Institute for Behavioral Research and Technology, a nonprofit California group that promotes and conducts research it says has the potential to "increase the well-being and functioning of people worldwide."

Epstein had a public spat with Google in 2012 after the search engine warned users that his website had been infected by malware. Epstein also is quoted about Google's supposed search manipulation in a series of 2016 articles on Russian sites such as RT and Sputniknews.com that claimed the search engine was hiding information indicating Clinton had health problems.

Just how Epstein got to his "rock bottom" number of how many votes Google swayed, however, is being questioned by law experts.

What's the evidence Google 'manipulated' 2.6 million votes for Clinton?

Epstein's findings are based on a phenomenon he says he's been studying for more than six years. He calls it the "Search Engine Manipulation Effect."

The crux of the theory, as he explained it in the 2016 Sputniknews article, is simple. "All Google has to do is show people search results that favor one candidate, in this case Hillary Clinton, higher in search results," he said.

In other words, the theory goes, the more positive information about one candidate shows up in search results, the more likely voters will be to favor that candidate.

How Google ranks its search results is a black box. The algorithms Google uses to decide which websites are most relevant are considered one of its crown jewels. And while Google provides guidance on how websites can improve their search rankings, it keeps the specific criteria a secret to prevent the system from being gamed.

The lack of transparency by Google has caused a lot of suspicion over the years, with competitors such as Yelp arguing that the search engine does not give everyone equal treatment. And in 2017 the European Union fined Google $2.9 billion for demoting rival comparison shopping sites in its search results. More recently, conservative commentators have charged that Google is deliberately suppressing them from its results — a claim that has so far not been proved.

The 2.6 million Clinton vote number appears to have originally turned up in a 2017 study coauthored by Epstein, which sought to find whether Google introduced bias in search results ahead of the 2016 presidential election and whether those results affected the election.

The study — which was based on 95 participants in 24 US states — stated, in part, that when extrapolating from a 2015 study also authored by Epstein, at least 2.6 million votes might be "shifted" in favor of Clinton because of bias in Google's search results.

But the 2015 study's findings were based on asking US residents to cast hypothetical votes for candidates in Australia's 2010 prime ministerial election based on information they saw in Google search results.

Dr. Michael McDonald, an associate professor of political science at the University of Florida, expressed skepticism to Business Insider that Epstein's 2015 findings regarding Google's search rankings influencing American decisions about elections in Australia — a topic most American study participants would have little information about beforehand — could be applied directly to the US presidential elections.

"I'm not sure if this really applies to US elections where we have partisan politics going on and lots of other information that people have," McDonald said. "You don't need to look at the top of Google search results for your information about how you're going to cast your vote for president."

'That's something that sets off a bunch of red flags'

Justin Levitt, an associate dean for research and professor at Loyola Law School who focuses on constitutional law and the law of democracy, told Business Insider there were multiple points of contention with Epstein's 2017 findings, which have become the basis for the president's tweet on Monday.

For one, Epstein wrote in his report that after the study was completed, results from participants using Google's email service, Gmail, were discarded, thus changing the number of eligible participants to a lower, undisclosed number.

Epstein said Gmail users were removed because some of their search queries appeared "automated" and, overall, those using Google's email service saw results that were far less biased than non-Gmail users.

"That's a weird methodological choice to take some of your results and throw them out after you've done the experiment because they seem to not fit your designed story," Levitt said. "That's something that sets off a bunch of red flags."

In his study, Epstein wrote that the decisions to discard Gmail-using participants came, in part, because Google itself had identified the study's "confidants through its gmail system and targeted them to receive unbiased results."

Another problem Levitt has with the study is Epstein's definition of the word "bias." Levitt says the mainstream media tends to be left-leaning, and so finding more pro-Clinton results in 2016 may have been less Google bias and more a result of the media landscape.

What does Google say?

Google told Business Insider that Epstein's claims were "inaccurate" and said his 2015 study, which found search rankings could easily influence undecided voters, had since been "debunked."

"This researcher's inaccurate claim has been debunked since it was made in 2016," a Google representative said. "As we stated then, we have never re-ranked or altered search results to manipulate political sentiment. Our goal is to always provide people with access to high quality, relevant information for their queries, without regard to political viewpoint."

Rick Pildes, a New York University law professor, told Business Insider that tech companies — including Google — indeed had the power to sway elections in major ways but that it didn't necessarily mean search results had the potential to shift millions of votes, as Epstein's report claims.

"We absolutely have to worry about the social-media giants manipulating election-related information, whether intentionally or not," Pildes said. "But it's massively irresponsible to claim to know anything this specific and concrete about what information moved millions of voters to cast votes as they did."

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