Thanks, Vasco. I agree with your nice point that when all risks are very close to zero, the counterintuitive phenomenon we talk about in the paper makes very little difference. (Toby Ord also notes this in The Precipice (Appendix D).)
Adam Elga
Karma: 49
Thanks!
I like your idea of doing a back-of-the-envelope calculation assuming that there are just two risks. Suppose that risk #1 has survival probability s1 and risk #2 has survival probability s2. Assume s1 < s2. Let’s compare two alternative interventions:
Intervention 1: Increase the survival probability for risk #1 by some small amount x.
Intervention 2: Increase the survival probability for risk #2 by that same amount x.
Now we have:
Intervention 1 will increase the overall survival probability from s1*s2 to (s1+x)*s2. That is an increase of x*s2.
Intervention 2 will increase the overall survival probability from s1*s2 to s1*(s2+x). That is an increase of x*s1.
So the increase in overall survival probability produced by intervention #1 is 100 * (s2/s1 − 1) percent greater than the increase in overall survival probability produced by intervention #2.
Plugging in some toy numbers:
Suppose that risk #1 has survival probability 90% and risk #2 has survival probability 99%. Then an intervention that increases s1 by a small amount will produce 10% more increase in overall survival probability than an intervention that increases s2 by that same small amount.
If risk #1 had survival probability 80% instead, then intervention 1 would produce approximately 24% more increase in overall survival probability than intervention 2.
So a risk’s base survival probability does make some difference to how much one increases overall survival probability by mitigating that risk. But overall I agree with you that for risks with survival probability greater than 90%, the difference is modest.