President Donald Trump’s claims about voter fraud are preposterous. No credible evidence suggests that millions of people cast illegal ballots, or that candidates who outpoll rivals by several percentage points can accomplish that by fraud under modern election administration.

Now that I’ve completed the requisite throat-clearing, I have a question for progressive readers: does the recent contest for control of the Virginia House of Delegates make you even a little bit uncomfortable?

Thanks primarily to the prevailing anti-Trump political winds, Virginia Democrats did very well in November. Their net gain of 15 GOP-held seats put them just one seat away from a tie and a likely power-sharing deal in the Virginia House.

That seat might have been won by Democrat Shelly Simonds in a Newport News-centered district. After the election-night tally showed her just 10 votes behind incumbent Republican David Yancey, Simonds sought a recount. It put her ahead by a single ballot. Republicans then successfully challenged that ballot in court.

The resulting tie was settled by drawing a name out of a bowl. Yancey got the luck of the draw. The GOP retained control of the legislative chamber, however unimpressively.

Tied elections aren’t unknown in North Carolina. As The Charlotte Observer recently reported, tied municipal races in Alleghany County, Sampson County, and Mecklenburg County have been resolved by chance in recent memory. If we broaden the category a bit to include races settled by dozens or hundreds of votes, there are many more cases in municipal, county, and even legislative races.

For that matter, who can forget the 2000 Florida recounts? A few hundred ballots separated George W. Bush and Al Gore in a state with enough electoral votes to sway the presidential race. Complaints about hanging chads, butterfly ballots, and premature media calls depressing turnout in the Florida panhandle weren’t the only relevant controversies. Another was illegal voting, either by felons or by snowbirds and students with residences in multiple states.

Over the years, North Carolina has implemented a number of policies to deter illegal voting. Still, after 2016 the State Board of Elections conducted an audit that found 508 votes cast that shouldn’t have counted. Most involved felons whose right to vote had not yet been restored. But there were also 41 substantiated cases of votes by non-citizens, 24 substantiated cases of double-voting, and two substantiated cases of impersonation fraud, one in person and one by absentee ballot.

Some activists claimed this post-election audit proved that additional measures to ensure election integrity were unneeded. Their reasoning was faulty. The audit established a floor, not a ceiling, for illegal votes cast.

Impersonation fraud, for example, is likely done most of the time by people voting on behalf of their relatives, as was the case with the two substantiated cases in 2016. But such an audit can catch that only if the titular voters are deceased. What about voting on behalf of shut-ins or relatives with mental disabilities? Rules for both absentee and in-person voting need to be stricter to deter that.

Residency fraud also merits more attention, and could be better policed in part by voter-ID requirements. If people with living quarters in multiple states — be they retirees, professionals, or students — want to make North Carolina their residence for the purposes of voting, they should be required to possess a state-issued ID as an indication of their true intention. (Most are already required by state law to have North Carolina driver’s licenses, if they want to operate a vehicle in the state for more than a few weeks, although they don’t always realize that.)

If you think election-integrity initiatives are nothing more than a Republican plot to suppress the vote, you should know that downplaying rare but potentially consequential cases of voter fraud only strengthens the resolve of those who favor voter-ID laws and the like, as a new Public Opinion Quarterly study confirms. A more productive response would be to work with Republicans to implement a low-cost insurance policy against fraudulent electoral outcomes.

John Hood is chairman of the John Locke Foundation and appears on the talk show “NC SPIN.” You can follow him @JohnHoodNC.