The idea of ignorability helps us in science by playing a role in randomized trials. In the real world, there are too many potential variables to be able to comprehensively predict exactly how a given intervention will play out in every case. We almost always have outliers that have wildly different outcomes compared to what we would have predicted. Quite often some strange factor that could not be controlled or predicted caused the individual case to differ dramatically from the norm.
Thanks to concepts of ignorability, we don’t have to spend too much time worrying about the causal structures that created a single outlier. In The Book of Why Judea Pearl tries his best to provide a definition of ingorability for those who need to assess whether ignorability holds in a given outlier decision. He writes, “the assignment of patients to either treatment or control is ignorable if patients who would have one potential outcome are just as likely to be in the treatment or control group as the patients who would have a different potential outcome.”
What Pearl means is that ignorability applies when there is not a determining factor that makes people with any given outcome more likely to be in a control or treatment group. When people are randomized into control versus treatment, then there is not likely to be a commonality among people in either group that makes them more or less likely to have a given reaction. So a random outlier in one group can be expected to be offset by a random outlier in the other group (not literally a direct opposite, but we shouldn’t see a trend of specific outliers all in either treatment or control).
Ignroability does not apply in situations where there is a self-selection effect for control or treatment. In the world of the COVID-19 Pandemic, this applies in situations like human challenge trials. It is unlikely that people who know they are at risk of bad reactions to a vaccine would self-select into a human challenge trial. This same sort of thing happens with corporate health benefits initiatives, smart phone beta-testers, and general inadvertent errors in scientific studies. Outliers may not be outliers we can ignore if there is a self-selection effect, and the outcomes that we observe may reflect something other than what we are studying, meaning that we can’t apply ignorability in a way that allows us to draw a conclusion specifically on our intervention.