The struggle over who can vote on Election Day is becoming more heated in courtrooms, judges’ chambers and statehouses across the country, paralleling the intensity of the presidential race. And at the moment, the side that wants fewer voting restrictions seems to be winning.

The battle began in earnest after 2010, when several Republican state legislatures began tightening identification requirements on voters. It has reached a new level in the 2016 election, when voters in 17 states faced new restrictions that ranged from photo ID requirements to cutbacks on early voting and same-day registration. Republicans said the laws were necessary to prevent fraud; Democrats and voting rights advocates said the restrictions were really designed to reduce participation by minority groups and young voters who traditionally support Democrats.

“It’s the biggest rollback of voting since Jim Crow,” said Jonathan Brater, an attorney at NYU Law’s Brennan Center for Justice, which compiled the list of restrictions.

But in just the past few weeks, several of these laws have been blocked or overturned by federal judges. On Monday, a District Court judge issued a preliminary injunction against a voter ID law in North Dakota. In the previous 10 days, the 5th U.S. Circuit Court of Appeals ruled that the ID law in Texas violated the Voting Rights Act, a panel of the 4th U.S. Circuit Court of Appeals struck down a law in North Carolina, and a District Court judge in Wisconsin ruled that elements of the law there were unconstitutional. There is also major voting-law litigation ongoing in Alabama, Arizona, Georgia, Kansas, Ohio and Virginia.

Things are taking such a rapid turn that, while we were on the phone early this week, Brater was still deciphering the ruling fresh from North Dakota.

The legal fight has become a significant issue in the presidential race. Hillary Clinton has spoken forcefully against the voter ID laws in speeches and op-ed articles. “They’re doing everything they can to stop black people, Latinos, poor people, young people, people with disabilities from voting,” she said in Houston earlier this year.

On Tuesday, Donald Trump warned that the election would be “rigged” against him, and he cited as an example the court decisions throwing out voter ID laws. “If you don’t have voter ID, you can just keep voting and voting and voting,” he told The Washington Post. (As the Post pointed out, however, that kind of fraud almost never happens.)

The proliferation of these laws was spurred, in part, by the Supreme Court’s 2013 decision in Shelby County v. Holder, which declared key sections of the Voting Rights Act unconstitutional. This decision effectively eliminated the requirement that certain states with a history of racial discrimination in voting to clear changes to their election laws with the federal government. “The gutting of the Voting Rights Act certainly emboldened states to push forward with these restrictions,” Brater said. It also made it easier to pass new restrictions in places that had previously been covered by the pre-clearance requirement, such as North Carolina and Texas.

But 2013 wasn’t the beginning. The court’s decision merely “gave a green light to efforts that were already underway,” Ari Berman, a writer at The Nation and author of “Give Us the Ballot: The Modern Struggle for Voting Rights in America,” told me.

This avalanche of efforts to enact voting restrictions was really triggered a decade earlier, after the 2000 election, the chad debacle in Florida and the Supreme Court decision in Bush v. Gore. Many politicians came to a fateful realization. “In a very close election, the rules of the game matter,” said Richard Hasen, a professor of law and political science at the University of California, Irvine, who runs Election Law Blog. “So there was more litigation and more attempts to manipulate the system.” During the George W. Bush administration, the first strict voter ID laws were introduced in Indiana and Georgia.

The movement gathered further momentum after the 2008 election. “The effort to try to restrict the electorate really intensifies after Barack Obama’s election, because I think lots of Republicans were really scared,” Berman said. Scared not only of the election of the first black president, but that the record levels of turnout among young voters and voters of color in 2008 would become a “new normal.”

This momentum has led to ID laws that are of substantially different character from the early ones. They’ve gotten stricter. Rather than requesting an ID at the polls, new laws often require one. And in some cases the required ID must be a specific type of photo ID.

But now, it seems, some may have gone too far, outstripping their justification as checks on voter fraud, and being called out as racially discriminatory by the courts. In the North Carolina decision, Judge Diana Gribbon Motz wrote: “In response to claims that intentional racial discrimination animated its action, the State offered only meager justifications.” And in the Texas case, the 5th Circuit, one of the country’s most conservative, found that the law there discriminated against black and Hispanic voters.

Beyond the constitutional question, do these voting restrictions have a practical effect on voter turnout? In 2012, my boss Nate Silver found that the academic literature on this question was in broad agreement: Voter ID laws “seem to decrease turnout by about 2 percent as a share of the registered voter population.”

Indeed, a 2014 Government Accountability Office report, one of the most cited pieces of research on this topic, looked at two states (Kansas and Tennessee) that added voter ID requirements, compared with a handful of states that did not. It found, essentially, that the requirements depressed turnout somewhere between 2 and 3 percentage points.

But none of the academic studies available to Silver in 2012 measured the disparate impact on Democratic and Republican voters — in other words, none measured the “effectiveness” of these laws in suppressing certain subsets of the electorate. So he took it upon himself, performing some calculations and finding “some detrimental effect” of these laws on Democrats.

And now new research, with the aid of additional hindsight and data, suggests the disparate impact of these laws might be bigger than previously thought. A paper forthcoming in the Journal of Politics, titled “Voter Identification Laws and the Suppression of Minority Votes” and written by a trio of political scientists, finds that, in the presence of strict ID laws, the predicted gap in participation between black and white voters in general elections increases from 2.9 points to 5.1 points, and in primaries increases from 2.5 points to 11.6 points. A similar result holds for the gap between Latino and white voters. More starkly, they find “that voter ID laws skew democracy toward those on the political right.”

“The enactment of strict voter ID laws tends to double or triple the gap in turnout between whites and racial and ethnic minorities,” Zoltan Hajnal, a political scientist at the University of California, San Diego, and one of the paper’s authors, told me.

The paper is only able to come to these sharp conclusions as a result of the proliferation of stricter voting laws. The paper draws on data from the 2010, 2012 and 2014 elections, for example — elections with strict ID laws in place in more than one or two states, increasing its sample size from that in earlier studies.

Although there’s lots of evidence that minorities are less likely to have the required identification, the exact mechanism driving the results isn’t yet well understood. It might be that some voters are going to the polls and being turned away, some might not go to the polls at all, some might not think they have the required ID when they in fact do, and some may have a sense, given a history of racially exclusionary laws, that they are not welcome at the polls.

Could these laws change the outcome of the election? Some of the states with new voting restrictions are high on FiveThirtyEight’s list of likely tipping points: Ohio, North Carolina, Virginia, Wisconsin.

But even if we have evidence of a widening gulf in the electorate, we don’t know how that will play out on Election Day. “We don’t have a lot of conclusive evidence about how these laws have affected an electoral outcome,” Hajnal said.

“Turnout is a really hard nut to crack,” Hasen said. Indeed, a 2009 paper in the Election Law Journal concluded that, when it came to turnout effects, “the data are not up to the task of making a compelling statistical argument.”

But perhaps this is the wrong question to ask. “The right question is: ‘Is the state making it harder for people to register and vote for any good reason?’” Hasen said.

Proponents of voter ID laws typically offer several reasons. The laws may curb voter impersonation fraud, they say, or instill a sense of confidence in the fairness and proper functioning of the system. But impersonation fraud is all but nonexistent, with research revealing only 31 cases in over a billion ballots cast since 2000 — about 0.000003 percent. And a 2008 paper in the Harvard Law Review found no relationship between voters’ perceptions of fraud and their likeliness to vote and, further, no increase in confidence for voters under strict ID laws.