States do not have uniform rules for identifying people eligible to obtain a COVID-19 vaccine. In New York, for example, the eligible population includes health care workers, teachers, first responders, public safety workers, public transit workers, and individuals aged 65 and older.
Public health experts repeatedly assert that face masks can prevent people from spreading the virus to others and also protect the wearer. Currently, the United States does not have a national mask mandate. A majority of states, including New York, do have a mask mandate. (Happily, most ultra-Orthodox Jewish congregations accept the need to wear a mask.) Unfortunately, 13 states do not require face masks.
The federal government allocates COVID-19 vaccine to the states on the basis of the size of their eligible population. To induce all states to require people to wear face masks, we propose that the federal government announce that, after 2 weeks, it will implement the following new policy for allocating vaccine to the states.
Under the new policy, every state that fails to issue a mask mandate will have its weekly allocation of vaccine reduced by 1%. Vaccine doses denied to states without a mask mandate will be distributed to states with mask mandates in proportion to the size of their eligible population. When a state without a mask mandate issues such a mandate, its original allocation, based on the size of its eligible population, will be restored.
We present the following small numerical example to demonstrate how the new policy would work. Imagine a nation named X which consists of 3 states called A, B, and C. Suppose that nation X has a large population of eligible people, of whom 50% live in state A, 20% live in state B, and 30% live in state C. At the beginning of each week, the federal government of nation X allocates 100,000 doses of Covid-19 vaccine to its 3 states on the basis of the size of their eligible population. Therefore, state A will receive 50,000 doses or 50% of the weekly allocation, state B will receive 20,000 doses or 20%, and state C will receive 30,000 doses or 30%. Suppose that states A and B have mask mandates, but state C does not require masks. Suppose that the federal government of nation X announces that after 2 weeks it will implement the new policy for allocating vaccine to the 3 states. Suppose that 2 weeks after the announcement of the new policy, state C still declines to require people to wear masks. The allocation to state C is reduced by 1% of 30,000 doses, or 300 doses.
Thus, the allocation to state C is decreased from 30,000 doses to
30,000 – 300 = 29,700 doses. The total allocation to states A and B is increased by the 300 doses diverted from state C.
The number of additional full doses allocated to state A is
(300) (50%) / (50% + 20%) = 214.
The allocation to state A is increased from 50,000 doses to
50,000 + 214 = 50,214 doses.
The number of additional full doses allocated to state B is
(300) (20%) / (50% + 20%) = 85.
The allocation to state B is increased from 20,000 doses to
20,000 + 85 = 20,085 doses.
Suppose that 3 weeks after the announcement of the new procedure, state C still declines to require people to wear masks.
The allocation to state C is now reduced by 1% of 29,700 doses, or 297 doses.
The total allocation to states A and B is increased by the 297 doses diverted from state C.