After being embarrassed in the press, Mr. Cuomo on Monday expanded eligibility to seniors over age 75 as well as public safety officers, teachers and other school staff, child-care workers, public-facing grocery workers, transit workers and people living and working in homeless shelters. On Tuesday he added those 65 years old and up. This is better, but prioritizing based on occupation is arbitrary and will create bureaucratic headaches.

New York’s antibody study this spring showed that public safety and health-care workers were much less likely to be infected than the general population. Teachers have also had low rates of infection in part because children are significantly less likely than adults to transmit the virus. Vaccinating teachers might help reopen more schools, but unions will still oppose doing so.

In any case, how will workers prove their eligibility? A pay stub? Uniform? Mr. Cuomo has threatened to punish vaccine providers who give shots to people he hasn’t deemed eligible, so they will likely want documentation from workers to protect themselves from liability.