Trump also alleged that former Republican senator Kelly Ayotte would not have lost to Democrat Maggie Hassan if Massachusetts voters hadn’t illegally voted in New Hampshire. These allegations repeat claims made by former senator Scott Brown, who stated in November that 100,000 Massachusetts residents had illegally voted in New Hampshire’s 2016 election.

How we did our research, and what we found

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In December, we studied Trump’s allegations of 2016 voter fraud and did not find any evidence of widespread problems consistent with those allegations. However, we did our work before these new allegations about New Hampshire.

Here’s what we found when we looked for oddities in observed election returns associated with the type of large-scale fraud that would be consistent with the Massachusetts busing allegations.

1) No evidence of dramatic turnout surges

New Hampshire has 259 vote-tabulating towns. If thousands of Massachusetts residents were bused in on Election Day to vote against Republicans like Ayotte, we might expect unusual surges in turnout and vote totals that were notably anti-Republican. We might expect this especially in southern New Hampshire, in towns relatively close to the Massachusetts border.

To look for these turnout spikes, we compared 2012 and 2016 Election Day turnout. The figure below shows that New Hampshire towns — whether located on the southern border or not — saw very similar voter turnout in 2012 and 2016, with no particular surges that would suggest thousands of out-of-staters voting there illegally. Some New Hampshire towns had more voters in 2016, but not in large numbers. The results are completely consistent with a legitimate election. (To keep the scale manageable, the plot does not depict two towns where more than 25,000 people voted.)

2) No evidence of dramatic downturns in Ayotte support

Beyond turnout itself, the Massachusetts busing hypothesis suggests that New Hampshire towns with surges in Election Day turnout should be disproportionately anti-Ayotte. Our second figure plots the change in votes received by Ayotte in 2010 and in 2016 against change in turnout in 2012 and 2016. The idea here is that if Democrats were bused in to support Clinton, they would also vote against Ayotte. We don’t find any evidence of such a pattern.

In the graph above, each dot or circle represents a town; larger dots indicate more populous towns. (To keep the scale of the plot manageable, 19 towns are not shown.) The placement of each dot reflects a town’s change in turnout between 2012 and 2016, plotted against its change in support for Ayotte between her two Senate runs.

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The red line shows the average relationship for towns in counties bordering the Massachusetts border, and the black lines summarize the rest of the state. As one can see, there is a slight positive relationship between the extent to which a New Hampshire town saw an increase in 2016 turnout and the extent to which the town was pro-Ayotte. In other words, towns with higher turnout in 2016 also had a higher proportion of votes for Ayotte. That’s the opposite of what you might expect to see if anti-Ayotte ringers had been bused in to vote in New Hampshire.

3) No evidence that New Hampshire voters with Massachusetts drivers licenses determined the outcome

New Hampshire records the state of issue when out-of-state drivers licenses are used to register to vote. If Massachusetts voters were bused into New Hampshire, we might expect large clusters of New Hampshire voters who used Massachusetts forms of voter identification.

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Of towns where at least 10 voters used out-of-state drivers licenses as identification, the median number of New Hampshire voters with Massachusetts IDs is one. Two of those were in towns close to the Massachusetts border. As permitted by New Hampshire, people use Massachusetts IDs to register in New Hampshire if they recently moved to the state and have yet to acquire a New Hampshire ID.

We find no relationship between the number of Massachusetts drivers licenses used for same-day New Hampshire voter registration and any increase or decrease in votes for Ayotte between 2010 and 2016.

4) No evidence that proximity to the Massachusetts border decreased support for Ayotte

Finally, the figure below shows the relationship between a town’s distance from the Massachusetts border and the fraction of its voters who cast 2016 ballots for Ayotte. If the busing hypothesis were correct, and if buses ferrying out-of-state voters avoided traveling far into New Hampshire, towns near the New Hampshire border should be relatively anti-Ayotte, all things equal.

In fact, New Hampshire towns near the Massachusetts border tended to favor Ayotte, not oppose her.

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This single result does not by itself show that the busing hypothesis is wrong, and many factors presumably influence a New Hampshire town’s political leanings. Still, this figure is yet another piece of evidence that is not consistent with the busing theory.

Conclusion

As with our first analysis of voter fraud in the 2016 election, we find no evidence to support the assertions of large-scale voter fraud that have been forthcoming from the Trump administration.

Because of these results and a total lack of photographic evidence of buses infiltrating New Hampshire on Election Day 2016, we believe that Trump’s claims about a tainted election in New Hampshire are at best unsupported and at worst an intentional mistruth.

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.