This is a lie, part of Mr. Trump’s pattern, stretching back many years, of disregard for indisputable facts. There is no evidence of illegal voting on even a small scale anywhere in the country, let alone a systematic conspiracy involving “millions.” But this is the message that gets hammered relentlessly by right-wing propaganda sites like InfoWars, which is run by a conspiracy theorist who claims the Sandy Hook school massacre was a hoax — and whose absurdities Mr. Trump has often shouted through his megaphone, which will shortly bear the presidential seal. Mr. Trump added more fuel to the fire with the false claim of “serious voter fraud” in California, Virginia and New Hampshire — all states that went for Hillary Clinton.

In addition to insulting law-abiding voters everywhere, these lies about fraud threaten the foundations of American democracy. They have provided the justification for state voter-suppression laws around the country, and they could give the Trump administration a pretext to roll back voting rights on a national scale.

And why is Mr. Trump so hung up on the popular vote in the first place? After all, he won where it counts — in the Electoral College. And yet, in the three weeks since his victory, Mr. Trump has already admitted at least twice that he would prefer the presidency be determined by the popular vote, and not by 538 electors. It’s clear he feels threatened by Mrs. Clinton’s popular-vote lead — now more than 2.3 million and expected to exceed 2.5 million; as a percentage of the electorate, that is a wider margin than five presidents enjoyed. With support for third-party candidates added in, 54 percent of voters rejected Mr. Trump.

So maybe his touchiness is understandable. Like most people, Mr. Trump senses the fundamental unfairness of awarding the presidency to the loser of the popular vote. In fact, he made that argument himself, back on election night in 2012, calling the Electoral College “a disaster for democracy” when he believed, incorrectly, that President Obama would lose the popular vote and still win re-election. (In recent weeks he’s changed his tune, calling it a “genius” idea.) What Mr. Trump may not know, given his lack of interest in American history, is that the Electoral College was designed specifically to enhance the influence of white voters in Southern states, which were allowed to factor in their large slave populations.