In my previous post I advanced the idea that people turn to moralism and from there to government coercion when faced with a free-rider problem. I didn’t provide a detailed, concrete example of the kind of free-rider problem I had in mind but David Foster provided me one: vaccinations.
Let’s approach this as would game theorists by creating an abstract game which we will call “The Vaccination Game.” The players in the game are parents trying to provide their children maximum protection from harm in all matters related to vaccinations.
All acts have benefits and risk, and vaccinations are no exceptions. The vaccination game is defined by 3 numbers:
D: The chance of catching a disease if unvaccinated
R: The chance of having a negative reaction to the vaccine itself
V: Percentage of the population that is vaccinated
NV: Percentage of the population that is not vaccinated.
P: The propagation threshold, i.e., the percentage of the population that must remain unvaccinated in order for the disease to have a chance of spreading through the population.
Lets assume that vaccinations are perfect, i.e., after vaccination the chance of ever contracting the disease is zero. (In reality, this is never the case.)
Notice that D,V,NV and P are all linked together but that R stands independent.
A rationally selfish parent faces two choices. First, they can get their child vaccinated and assume the risk of R, a negative reaction to the vaccine. Second, they can skip the vaccination, avoiding R but assuming the risk of disease, D.
No matter what happens, R remains the constant. A certain predictable number of children who take the vaccine will have a negative reaction that will result in an outcome as or more severe than the disease itself.
D, however, fluctuates wildly based on one factor: How many other parents also forgo vaccination. D is proportional to NV. As long as only a few parents skip vaccination, P>NV and the unvaccinated child avoids both disease and the risk of an adverse reaction to the vaccine. As the percentage of unvaccinated people in the population rises, the chances an unvaccinated person will contract the disease increases. When NV>P, D increases rapidly and not being vaccinated may suddenly become very dangerous.
While P>NV, parents who do not vaccinate get a free ride on parents who do. By assuming the risk of vaccination, vaccinating parents parents drive NV.