What’s good for each subgroup can be bad for the group: Simpson’s

Why? Simpson’s “paradox” or observation …

There’s actually nothing odd about this. While interpretation depends upon the semantics of individual measurements, it should be expected that, at times, improving things for the overall group will mean as a matter of policy that subgroups will end up being less well off. Conversely, in some circumstances, if policy insists subgroups be more well off in each instance, the result can be that the group overall is worse off.

The obvious case is vaccination. It is true that for some subgroups the risk to the subgroup is higher than it would be were it merely exposed to the risk from the surrounding population. However, that risk increases if there is substantial abstinence from vaccination in some subgroups.