An enduring Republican fantasy is that there are armies of fraudulent voters lurking in the baseboards of American life, waiting for the opportunity to crash the polls and undermine the electoral system. It’s never really been clear who these voters are or how their schemes work; perhaps they are illegal immigrants casting votes for amnesty, or poor people seeking handouts. Most Republican politicians know these criminals don’t actually exist, but they have found it useful to take advantage of the party base’s pervasive fear of outsiders, just as when they shot down immigration reform. In this case, they persuaded the base of the need for voter ID laws to ensure “ballot integrity,” knowing the real effect would be to reduce Democratic turnout.

Now a researcher has tried to quantify this supposed threat by documenting every known case of voter fraud since 2000 — specifically, the kind of impersonation that would be stopped by an ID requirement. (Note that this does not include ballot-box stuffing by officials, vote-buying or coercion: the kinds of fraud that would not be affected by an ID law.)

There have been more than 1 billion votes cast in local, state and federal elections over the last 14 years. Out of all of them, the researcher, Justin Levitt, a voting expert at the Loyola University Law School, found 31 cases of impersonation fraud. It’s hardly a surprise that the number is so low; as he writes in the Washington Post today, casting individual fake ballots “is a slow, clunky way to steal an election. Which is why it rarely happens.”

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But neither the Constitution nor plainly visible reality is likely to halt the Republican crusade to keep certain people from participating in democracy. As the National Commission on Voting Rights documented in a new report, voting discrimination remains “a frequent and ongoing problem,” particularly in the South and Southwest, in part because of new barriers to voting thrown up by state legislators. “It is difficult not to view these voting changes with a jaundiced eye,” the report says, “given the practical impediments they create and the minimal, if any, measurable legitimate benefit they offer.”