But the risk of dying is around 50x higher[1] for a 70yo compared to a 30y, which means you have to vaccinate ~15x as many 30yos as 70yos to save the same amount of life-years.
So vaccinating the elderly first both saves lives and more life-years.
[1] https://www.cdc.gov/coronavirus/2019-ncov/covid-data/investi...
This makes the fallacious assumption that if life expectance at age X is n years, life expectancy at age X+k is n-k years.
This is very much not true. See, e.g., https://www.ssa.gov/oact/STATS/table4c6.html
Using actual life expectancy by age makes the number of life years saved at age 70 much closer to that at age 30.
...which is still a factor of ~3x, which means my napkin math wasn't too shabby, which means this tangent was completely irrelevant, because my main point is unchanged.