Thread by @nomadj1s

A simple, *hypothetical* example of the Base Rate Fallacy:

Suppose w/o a vaccine, 9/10 get hospitalized

Suppose w/ a vaccine 1/10 get hospitalized

(Note: a very good vaccine!)

Suppose 90/100 get the vaccine

What share of the hospitalized are vaccinated?

Instead, suppose 50/100 are vaccinated

Now what’s the share of the hospitalized vaccinated?

When 90/100 are vaccinated:

9 vaccinated people are hospitalized

9 unvaccinated people are hospitalized

So 50% of the hospitalized are vaccinated, BUT there only 18 hospitalizations

When 50/100 people are vaccinated:

5 vaccinated people are hospitalized

45 unvaccinated people are hospitalized

So 10% of the hospitalized are vaccinated, BUT there are now 50 hospitalizations

So, just reporting the share of the hospitalized who are vaccinated can be misleading

This is example of what people are referring to as the “base rate fallacy”