Republican presidential candidate Donald Trump speaks during a campaign rally March 11 in St. Louis. (Seth Perlman/AP)

With recounts underway and President-elect Donald Trump alleging that Democrats benefited from illegal voting, the Nov. 8 election is under intense scrutiny. Although voter fraud in U.S. elections is extremely rare, Trump, Mike Pence and others have claimed during the campaign, during early voting and again this week that Trump might be the victim of voter fraud. Trump himself tweeted: “In addition to winning the electoral college in a landslide, I won the popular vote if you deduct the millions of people who voted illegally.”

We have now completed an extensive study of voter fraud in the 2016 election. We have found no evidence that could support anything like Trump’s accusations.

Here’s what we did. First, we predicted Trump’s county vote share in 2016 relative to Romney’s in 2012. Our statistical model drew on a wide array of demographic factors — like the percent white, percent immigrant, percent without a college degree and so forth. Second, we estimated a similar model of Democratic turnout for Clinton in 2016 relative to Obama in 2012.

The statistical models provide a baseline explanation for how well Trump did in each county. The question, then, is where he may have done better or worse than these models would predict, and whether his over- or under-performance was in any way correlated with possible sources of fraud.

Non-citizens

One possibility is that the presence of non-citizens was associated with decreased support for Trump, as Trump himself intimated might happen. But we found no evidence of this. The graph below shows little relationship between the percent of non-citizens of voting age and unexpectedly high or low Trump support or Democratic turnout (in technical terms, the “residuals” from our regression models).


In both graphs the blue line capturing the relationship is basically flat. This is not consistent with a surge of non-citizens voting for Hillary Clinton. The purple line in each graph summarizes the relationship in battleground state counties in particular. Again, the lines are flat.

Dead people voting

Another claim was that some voters would cast ballots using registration records of deceased individuals. Trump even proclaimed that dead people will not vote for him.

If this had happened, then counties with the greatest number of recent deaths should have unusually small Trump vote shares and yet unusually large Democratic turnout.  We gathered county death data from 1999-2014 from the Centers for Disease Control and Prevention to test this claim. The graphs below report the finding:


In fact, Trump does better in counties with a higher proportion of recently deceased people — as the upward-sloping blue lines show.

In other words, Trump’s vote share is greater than expected — and Democratic turnout is lower than expected — in counties with larger deceased populations. Once again, this is inconsistent with the claim that voters impersonating dead people helped Clinton and hurt Trump.

Tampering from election officials

One interpretation of Trump’s “rigged election” claim is that the officials who ran the election were biased against Trump. If so, then we might see odd shifts in whether Trump or Clinton was leading as the votes were being counted. For example, perhaps the count in one county would suddenly shift in Clinton’s favor as corrupt election officials started rigging things.

Over the course of election night, the Associated Press (AP) gathered county-level election returns from all counties. We subscribed to the AP results feed for the presidential election.  So, for counties across the United States, we got to observe how vote counts changed over the hours. We studied 3,111 total counties and have 15,796 separate measures of county votes during the counting process.

We find only 251 instances (1.6 percent of the total) where the vote leader in a county “flipped” from Trump to Clinton or from Clinton to Trump as the votes were being counted. The majority, 163, were in safe states.

If we focus only on counties that flipped toward the end of the counting process — exactly when you might think these corrupt officials would step in — there were 84 such flips, 24 in battleground states and 60 in safe states. Altogether these flips represented a net gain of 41,388 votes for Trump (and 33,165 votes in battleground states). In battleground states, only 12 flips were from Clinton to Trump

In other words, this is the opposite of what we would expect if the results were rigged against Trump.

Moreover, none of these flips would have decided the winner in a state. In two states that Trump won — Florida and Pennsylvania — flips only increased his lead. In Arizona, Michigan, New Hampshire, Virginia  and Wisconsin, flips decreased Trump’s margin but never by more than 6,833 votes.

Of course, our findings do not imply that there was no fraud at all in the 2016 presidential contest, nor do they imply that this contest was error-free. More refined data would be necessary to fully investigate claims of large-scale voter fraud.

Our findings do strongly suggest, however, that voter fraud concerns fomented by the Trump campaign are not grounded in any observable features of the 2016 presidential election. There is no evidence of millions of fraudulent votes.

David Cottrell is a postdoctoral fellow in the Program in Quantitative Social Science at Dartmouth College. Michael C. Herron is a visiting scholar at the Hertie School of Governance, and professor of government at Dartmouth College. Sean J. Westwood is an assistant professor of government at Dartmouth College.