Of these four candidates, Mr. Weiner has the least room to grow, because nearly half of voters who recognize his name view him unfavorably. Mr. de Blasio and Mr. Thompson, by contrast, have more upside potential. Just as easily, Ms. Quinn could extend her lead, as her favorability ratings are the strongest even accounting for her strong name recognition.

But what if Ms. Quinn’s campaign goes poorly? Is it so impossible to imagine Mr. Weiner winning a plurality with perhaps 30 percent of the vote if support winds up being divided four or five ways?

It isn’t — but it also wouldn’t make Mr. Weiner mayor, or even the Democratic candidate. That’s because New York applies a runoff if no candidate receives more than 40 percent of the vote in the primary.

This is where the unfavorable views that many Democrats hold of Mr. Weiner would hurt him most. In a multicandidate race, it might be possible for a candidate to emerge with the plurality, even if many voters dislike him, so long as he turned out his loyal supporters. But the math becomes nearly impossible for a candidate in a two-way race when half of the voters who recognize his name dislike him. Mr. Weiner would be a huge underdog in a runoff against Ms. Quinn or one of the other major candidates.