A Vaccination Antinomy
Here's an argument that Mary should vaccinate Violet. To do otherwise is to unfairly freeride on the other citizens. After all, Mary does believe in the vaccination program and does desire its benefits. She is only contemplating not vaccinating Violet because the others have vaccinated their children. If she goes through with it, she will be taking advantage of everyone else. She will be making an exception of herself, acting as she would not want others to act.
Here's an argument that Mary shouldn't vaccinate Violet. The vaccination is painful, and also poses slight risks. So Mary has to be able to justify the harm she would do to Violet. But she can't. We may harm our children a little or even a lot, to prevent a more serious harm to them. We may harm them a little, to prevent a very serious harm to others. But this case fits neither description. Having her vaccinated would not benefit Violet, since she's already immune to X. It wouldn't benefit anyone else either, since the whole population is immune. It wouldn't even benefit others by encouraging them to keep vaccinating their children, since records are confidential--no one will know if she doesn't vaccinate.
Note: in the real world, people aren't caught in this bind. We don't know there's herd immunity against any particular disease. We can always justifiably think vaccinating a child has some chance of benefitting both the child and others. (And by the way, my own children did receive all the routine vaccinations plus others.)
The scenario isn't real, but it also isn't far-fetched. People could be sure their community has herd immunity against X, and it seems to me these two arguments would genuinely compete for our attention in such a situation. Though I initially lean toward argument #1, it does strike me as strange for a parent to have a child jabbed, in the full knowledge that this is "for fairness" and without benefit to the child or anyone else. Thus: puzzlement.