In May, Sen. Tammy Baldwin (D-Wis.) tweeted that 200,000 fewer people voted because of the laws — more than enough to swing the result. Our fact-checkers, though, couldn’t find evidence of such a swing.

On Monday, a new study shed some light on the extent of the law’s effect. University of Wisconsin-Madison political science professor Kenneth Mayer and Ph.D. candidate Mike DeCrescenzo paired with Dane County (Wis.) Clerk Scott McDonell to ask people registered to vote in two counties, Dane and Milwaukee, what kept them from voting in 2016.

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The result? An estimated 16,800 people in the two counties may not have voted because they believed they lacked the proper identification or because they were actually turned away at the polling place. Given margins of error, the number could be as high as 23,000 — about as many votes as Trump’s margin of victory.

The researchers sent the nonvoters a survey asking them to identify the primary reason they didn’t vote and collecting demographic data. Acknowledging that precision can be tricky particularly for demographic groups for which less data was collected, the portion of nonvoters who said they were deterred by the law was 11.2 percent. White nonvoters, though, were much less likely to report being deterred by the ID law, as were more wealthy respondents to the survey.

“Blacks,” the report states, “are statistically significantly more affected than Whites in Dane and Milwaukee Counties” by the ID law. It’s important to note that the sample size of black respondents was small, hence the wide range of uncertainty in the graph below. But that the confidence intervals (light-colored bars) for black and white respondents don’t overlap indicates statistical significance.

Mind you, “deterred” is different from actually prevented from voting. Those who reported being turned away at the polls are included in the figures above but also broken out separately by the researchers. About 6 percent of nonvoters — 9,000 people in those two counties — are estimated to have tried to vote but not been allowed to.

Again, the effects on poorer and black nonvoters appear to be greater.

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What accounts for the difference between “deterred” and “prevented”? In part, misunderstandings about what the law mandated. Many individuals included in the report believed that they would not be allowed to vote because of a lack of identification but actually would have been allowed to cast a ballot had they tried.

The researchers also note that 80 percent of those who were deterred and 77 percent of those who tried to vote but couldn’t had cast ballots in 2012 — meaning that the drop in turnout in those two counties from 2012 can be estimated at about 13,600 (based on the deterred figure) due to the voter ID law. In 2016, Clinton won Milwaukee County by 163,000 votes and Dane County by 146,000.

Since the county clerk was involved, respondents weren’t asked which candidate they would have voted for. But we can roughly match up the demographic groups above with the actual results in the state and exit polling data. (The exit polls didn’t break down incomes in exactly the same way, so we used the closest approximation.)

Black voters and poorer voters more heavily supported Clinton; they were also more heavily affected by the voter ID law. This doesn’t mean that, barring the voter ID law, Clinton would have won the state. As we’ve reported, her loss was a function of any number of things, and losing a state by less than 1 percentage point means that any number of changes might have made the difference.

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At the very least, this study (again, looking only at two counties in the state, albeit the two most populous) reinforces the effects of voter ID laws. Those most likely to be affected tend to be those who are most likely to vote Democratic — a fact that’s often not lost on the laws’ Republican supporters.