The math makes it clear why giving everyone absolute freedom to choose whether to immunize or not doesn't work very well.
If everyone else is immunized to the point where there is significant herd immunity, but immunization has a low but non-zero cost (e.g. feeling crappy for a few days), then the rational selfish action is to be a free rider and not immunize.
However, if everyone did that, then herd immunity can collapse down to a level where there is no herd immunity; people rationally choose to immunize only to protect themselves. However, given that immunizations aren't perfect shields, in that scenario, even immunized individuals will be at risk to infections spreading through the population.
If everyone else is immunized to the point where there is significant herd immunity, but immunization has a low but non-zero cost (e.g. feeling crappy for a few days), then the rational selfish action is to be a free rider and not immunize.
However, if everyone did that, then herd immunity can collapse down to a level where there is no herd immunity; people rationally choose to immunize only to protect themselves. However, given that immunizations aren't perfect shields, in that scenario, even immunized individuals will be at risk to infections spreading through the population.