The Book of Why: The New Science of Cause and Effect (Penguin Science)

by Judea Pearl

Out of 1 million children, 990,000 get vaccinated, 9,900 have the reaction, and 99 die from it. Meanwhile, 10,000 don’t get vaccinated, 200 get smallpox, and 40 die from the disease. In summary, more children die from vaccination (99) than from the disease (40). I can empathize with the parents who might march to the health department with signs saying, “Vaccines kill!” And the data seem to be on their side; the vaccinations indeed cause more deaths than smallpox itself. But is logic on their side? Should we ban vaccination or take into account the deaths prevented? Figure 1.7 shows the causal diagram for this example. When we began, the vaccination rate was 99 percent. We now ask the counterfactual question “What if we had set the vaccination rate to zero?” Using the probabilities I gave you above, we can conclude that out of 1 million children, 20,000 would have gotten smallpox, and 4,000 would have died. Comparing the counterfactual world with the real world, we see that not vaccinating would have cost the lives of 3,861 children (the difference between 4,000 and 139). We should thank the language of counterfactuals for helping us to avoid such costs.