In some years, labor unions have largely flocked to a particular candidate. Mr. Stringer, for example, had overwhelming support from labor groups in his 2013 race for comptroller, when he defeated the former governor, Eliot Spitzer. But this year, the labor endorsements are diffuse.
One of the biggest open questions in the mayoral race is whether there will be any union-affiliated independent expenditure effort to stop Mr. Yang — but it is not yet clear which organizations, if any, would have both the resources and the inclination to do so.
Mr. Stringer has won the backing of other education unions, including the union representing school principals and administrators, and the union representing teachers and staff at the City University of New York. Mr. Yang has not earned a major union endorsement yet, but is leading in all publicly available polling.
The teachers’ union membership includes about 75,000 active classroom teachers and roughly 64,000 retirees, many of whom no longer live in New York. The U.F.T.’s delegate assembly — a group of about 3,400 elected representatives, including educators from each school in the city — voted to back Mr. Stringer on Monday afternoon.
The union has, for decades, played a major and occasionally decisive role in key education decisions, and that has been particularly true over the last year.
The union made a number of safety demands last summer, and tensions escalated to the point that the U.F.T. president, Michael Mulgrew, suggested that the union would strike if safety demands were not met. Many of those demands, such as improved ventilation, were supported by public health experts, but some families were angered by the union’s insistence that all rules remain in place even as teachers were vaccinated.
Advisers for Mr. Yang are hoping to attract at least some of those disaffected families.
During a recent interview on Fox Business, Bradley Tusk, the powerful political strategist and lobbyist who is, with his team, managing Mr. Yang’s campaign, said his candidate “takes positions that are a little at odds with the Democratic orthodoxy on things like education.