Some people think it isn't rational to vote. Usually the argument is as follows: the probability of being pivotal, that is: the probability that your vote will 'decide' the winner, shrinks rapidly as the number of voters increases. So if you vote in the hope of determining an outcome, then the probability of that happening is small enough for it not to be worthwhile trying.

Let's leave aside the virtues of this argument and consider a hypothetical against vaccination.

Some people think it isn't rational to vaccinate people against nasty diseases. The argument is as follows: most people are already vaccinated, so the probability of catching one of these diseases is very small - small enough not to be worth getting oneself vaccinated.

Most people feel this second argument is not very good. But I'm more interested in its structural similarity to the first argument.

Consider the structural similarities by considering what would happen if people acted on these arguments. If people do not vote/vaccinate then fewer number of people in the population will vote/be vaccinated. As this pool gets smaller, the probability of being pivotal if they vote, and of avoiding a disease if they are vaccinated, rises. Which slowly makes it more rational to vote/vaccinate, and so on.

I'm willing to bet that people who like the first argument still don't care for the second. But I'm not sure why.