Amid a crush of pre-election media coverage seeking his theory of the case — it drove more than 1.5 million clicks to Trafalgar’s site on Monday, he said — the big question seems to be: Is it possible to believe a guy whose polls consistently give Mr. Trump just enough support for a narrow lead in most swing states, and who refuses to reveal much of anything about how he gets his data?

In his last few polls of this election season, Mr. Cahaly has found Mr. Trump with two-to-three-point advantages in North Carolina, Arizona, Michigan and Florida, and wider leads elsewhere. That puts him far out of line with almost all major pollsters, whose surveys in those states are generally showing Mr. Biden with the edge. As different as things are this year, it’s hard to miss the echo of 2016, when Trafalgar occupied a similarly lonely position on the eve of Nov. 8.

Above all, Mr. Cahaly’s approach centers on the belief that everyone lies, but especially conservatives. This has largely been disproved by social science, but that hasn’t softened his conviction. To hear him explain it, traditional pollsters (he calls them “dinosaurs”) are crippled by “social desirability bias”: the tendency for respondents to say what they think an interviewer wants to hear, not what they actually believe. In Mr. Trump’s America, he says, that problem has grown worse.