[The confusion over Mr. Crowley’s third-party ballot line caused Ms. Ocasio-Cortez and Mr. Crowley to spar on Twitter Thursday morning. Read here.]

In Mr. Crowley’s case, vacating the line is not that simple. The Working Families Party must go through a convoluted legal maneuver, essentially nominating the unwanted primary winner for another electoral position on the ballot — often one that he or she has little chance of winning, like a county clerkship in a region of the state dominated by the other party.

“It’s very quirky,” said Jerry H. Goldfeder, an election lawyer and an adjunct professor at Fordham University School of Law. “It demonstrates how the various minor parties sometimes have inordinate control over the way the ballot looks, and that causes confusion in the electorate.”

In the case of a write-in victory, a candidate can accept or decline the nomination. If the candidate declines, the party is free to nominate someone else; if the candidate accepts, the party is stuck.

In the unlikely event that the candidate neither accepts nor declines, then the nomination is null and void and the party cannot back anyone in the fall, said John Conklin, a spokesman for the state Board of Elections.

In last month’s primary, for instance, Tedra Cobb won the Democratic primary in the 21st Congressional District, which stretches from the New York-Vermont border to Lake Ontario. The distant runner-up, Dylan Ratigan, won the Women’s Equality Party as a write-in candidate, snagging just two of four votes cast.

The Women’s Equality Party, however, wanted to back Ms. Cobb; Mr. Ratigan, a former host of MSNBC, agreed to decline the nomination, said Susan Zimet, the party’s chairwoman.