Donald Trump says that illegal voting may have put Hillary Clinton ahead of him in the popular vote. Clinton leads Trump by around 2.5 million votes, so the president-elect’s claim seems far-fetched.

However, as Hans von Spakovsky and John Fund explain in the Wall Street Journal, we simply don’t know the extent of illegal voting in American elections. Moreover, the Obama administration has done everything it can to keep it that way.

For example, the Obama Justice Department has refused to file a single lawsuit to enforce the requirement of the National Voter Registration Act that states maintain the accuracy of their voter-registration lists. It has also opposed every effort by states—such as Kansas, Arizona, Alabama and Georgia—to verify the citizenship of those registering to vote.

In 2011, the Electoral Board in Fairfax County, Va., sent the Justice Department, under then-Attorney General Eric Holder, information about 278 noncitizens registered to vote in Fairfax County, about half of whom had cast ballots in previous elections. There is no record that the Justice Department did anything.

Here, via von Spakovsky and Fund, is some of what we do know:

[A] 2012 study from the Pew Center on the States estimat[ed] that one out of every eight voter registrations is inaccurate, out-of-date or duplicate. About 2.8 million people are registered in more than one state, according to the study, and 1.8 million registered voters are dead. In most places it’s easy to vote under the names of such people with little risk of detection. . . . In 2015 one Kansas county began offering voter registration at naturalization ceremonies. Election officials soon discovered about a dozen new Americans who were already registered—and who had voted as noncitizens in multiple elections. . . . One district-court administrator estimated in 2005 that up to 3% of the 30,000 people called for jury duty from voter-registration rolls over a two-year period were not U.S. citizens. A September report from the Public Interest Legal Foundation found more than 1,000 noncitizens who had been removed from the voter rolls in eight Virginia counties. Many of them had cast ballots in previous elections, but none was referred for possible prosecution.

There’s more:

A 2014 study by three professors at Old Dominion University and George Mason University used extensive survey data to estimate that 6.4% of the nation’s noncitizens voted in 2008 and that 2.2% voted in 2010. . . . A postelection survey conducted by Americas Majority Foundation found that 2.1% of noncitizens voted in the Nov. 8 election. In the battleground states of Michigan and Ohio, 2.5% and 2.1%, respectively, of noncitizens reported voting. In 2013, pollster McLaughlin & Associates conducted an extensive survey of Hispanics on immigration issues. Its voter-profile tabulation shows that 13% of noncitizens said they were registered to vote. That matches closely the Old Dominion/George Mason study, in which 15.6% of noncitizens said they were registered.

It would be astonishing if illegal voting were not a problem. It’s widely accepted that election fraud used to exist. Our political history is full of examples such as Mayor Daley’s Chicago.

If voting fraud is no longer a problem, what caused it to disappear. Is less at stake now in elections? Of course not? Do safeguards prevent fraud? No. As von Spakovsky and Fund point out, the voter-registration process in almost all states runs on the honor system. Have the big-city machines that promoted fraud in the old days vanished? They have not.

Donald Trump’s victory provides an opportunity to attack the problem of illegal voting. Von Spakovsky and Fund explain how:

The Trump administration should direct the Department of Homeland Security to cooperate with states that want to verify the citizenship of registered voters. Since this will only flag illegal immigrants who have been detained at some point and legal noncitizens, states should pass laws, similar to the one in Kansas, that require proof of citizenship when registering to vote. The Justice Department, instead of ignoring the issue, should again start prosecuting these cases.

The honor system doesn’t work. To maintain the integrity of our elections, it’s time to adopt measures that do.

UPDATE: The study referenced above by the Old Dominion and George Mason professors has come under attack. This Politico article claims it has been debunked.

Jason Richwine at NRO disputes that claim. Richwine concludes that “there is still too much uncertainty to draw strong conclusions, but the. . .study is certainly a valuable contribution.”