A Game (Theory) of Attrition
There’s been a lot of buzz lately about parents not wanting to vaccinate their kids and the government’s responsibility to enforce either vaccinations or the freedom to opt-out. Blog writer Will Rosenbaum has looked at the parent’s logic through game theory to try to understand their reasoning in his post which can be found at http://www.willrosenbaum.com/?p=1160. In the article, Rosenbaum assigns numerical “harm” values to each individual in a population who can choose to either get vaccinated or not. The underlying logic is that while vaccinations benefit the population, they may pose harm to an individual, or at least the individual may think that the vaccination poses harm when he weighs his options. Thus, each person’s dominant strategy is to not get vaccinated in order to minimize their own personal harm, leading to a great threat of epidemics, and thus increased possibility of widespread population harm yielding the worst possible outcome for everyone involved, in parallel to the infamous prisoner’s dilemma set up.
The numerical harm formulas outlined in the article make some strong assumptions. The most problematic of these assumptions is that receiving a vaccination leads to four times more harm than not. While this is an unlikely reflection of reality, it is a fair assumption in the sense that people who argue against vaccination (for any of a number of reasons popular in the media) most likely do believe that this amount of harm is at stake, and base their decisions on this logic. The formula also assumes that in the event of an epidemic, everyone gets sick, regardless of vaccination status. This is inaccurate because the purpose of vaccinations is to make one immune to the possible epidemic and thus players who choose “no vaccination” would still only incur the harm value associated with the injection and not the harm associated with the disease. This, depending on the size of the population, would alter each players strategy by eliminating a dominant equilibrium. Instead, each individual’s choice to vaccinate would necessarily be dependent on everyone else’s choice.
While the article brought anti-vaccination logic into an interesting light, the assumptions made by the harm formulations do not seem to line up with reality, making the simulation imperfect. The underlying main point made by the author, however, is accurate: individuals subconsciously use game theory in every aspect of our lives to make decisions with the best outcome for ourselves and ourselves alone. Thus, a faulty understanding of science caused by media panic or misinformation can lead to widespread changes in social behavior that endanger entire populations.