PRESIDENT TRUMP’S claim that 3 million to 5 million undocumented immigrants voted illegally in last fall’s elections is as evidence-based as the assertion that space aliens on Saturn are bombarding planet Earth with marshmallows. Nonetheless, Washington being Washington, Mr. Trump’s declaration has generated its own politically charged momentum in the form of a presidential commission to investigate voter fraud — a topic that has been endlessly investigated for years, with consistent results: There is no evidence that it is widespread or has materially affected the outcome of any U.S. election.

Now Mr. Trump’s Presidential Advisory Commission on Election Integrity is beginning its work under the guidance of its vice chair, Kansas Secretary of State Kris Kobach, a Republican notorious for his efforts at vote suppression. As an opening salvo, Mr. Kobach has written to state election officials requesting that they hand over voter rolls, including not only names, addresses and dates of birth, but also party affiliation, voting history back to 2006 and the last four digits of Social Security numbers — all of which he says will be made public.

Mr. Kobach’s preposterous request — making public millions of partial Social Security numbers: Seriously? — has generated well-founded fears about privacy and data security; more than two dozen states have already announced they will refuse to convey the data he requested. Those same concerns have blocked the compilation until now of any such all-in-one list of every registered voter in the United States. In addition, Mr. Kobach’s elaborate past efforts at voter suppression in Kansas, mainly blocked by federal and state courts, provide ample cause for alarm that the commission’s real goal is an aggressive purge of voter rolls — a meat-cleaver approach whose inevitable effect would be widespread disenfranchisement.

No question, voter lists should be as up-to-date and accurate as possible. In the vast majority of cases where they’re not, however, it has nothing to do with fraud — it’s because people have died or moved, evidence of nothing more than a mobile society and decentralized election system. (Among those whose names have appeared simultaneously on more than one state’s rolls are several people in Mr. Trump’s immediate orbit, including Jared Kushner, his son-in-law and senior adviser; Stephen K. Bannon, chief White House strategist; and Tiffany Trump, Mr. Trump’s daughter.)

The trouble is that commonplace and often minor inaccuracies on the rolls, along with inconsistencies in data collection and formatting among the states, give rise to the high likelihood of false “matches” from one roll to another, and also that many voters may be purged unfairly, without safeguards or recourse. That would provide Mr. Kobach with a pretext for what Vanita Gupta, former chief of the Justice Department’s civil rights division, called “voter suppression, plain [and] simple.”

The commission’s endgame may be an attack on the 1993 National Voter Registration Act, the so-called “motor voter” law that requires states to offer registration at public service agencies such as motor vehicles departments. That would amount to an assault on American democracy and a damning indictment of the GOP’s commitment to free and fair elections.