I think the ability to notice this kind of consideration, figure out how to study it, and come up with a cluster of results that shed light on it in various ways is a key part of what gives me such a high level of trust in GiveWellâs endline recommendations :)
To clarify something that confused me at first: if in the first year we save a random proportion P of people, then in the second year we will save another P of people, and if theyâre totally uncorrelated we expect P*P of overlap between people saved in the first and second years. This doesnât require any adjustment (AIUI), because the conditional life expectancy that you credited yourself with for saving them the first time should already include the possibility that they could die in the next year. The only problem is if the first-year people occur at a higher rate than background in the second-year beneficiaries.
However, in these cases the underlying P is 0.25%, so the number of people who are ânaturallyâ saved twice is 0.0006%, so the distinction between âno overlapâ and ânatural /â uncorrelated overlapâ is so small as to be ignorable.
Yes, that sounds right. If we assume that lives saved across years are completely uncorrelated, the probability of us saving the same life consecutively is so small (0.25%*0.25%=0.0006%) that we can effectively assume âno overlapâ in lives saved. The uncorrelated scenario isnât our best guess, but I think itâs a helpful benchmark to think through this problem.
I think the ability to notice this kind of consideration, figure out how to study it, and come up with a cluster of results that shed light on it in various ways is a key part of what gives me such a high level of trust in GiveWellâs endline recommendations :)
To clarify something that confused me at first: if in the first year we save a random proportion P of people, then in the second year we will save another P of people, and if theyâre totally uncorrelated we expect P*P of overlap between people saved in the first and second years. This doesnât require any adjustment (AIUI), because the conditional life expectancy that you credited yourself with for saving them the first time should already include the possibility that they could die in the next year. The only problem is if the first-year people occur at a higher rate than background in the second-year beneficiaries.
However, in these cases the underlying P is 0.25%, so the number of people who are ânaturallyâ saved twice is 0.0006%, so the distinction between âno overlapâ and ânatural /â uncorrelated overlapâ is so small as to be ignorable.
Does that sound right?
Hi Ben,
Yes, that sounds right. If we assume that lives saved across years are completely uncorrelated, the probability of us saving the same life consecutively is so small (0.25%*0.25%=0.0006%) that we can effectively assume âno overlapâ in lives saved. The uncorrelated scenario isnât our best guess, but I think itâs a helpful benchmark to think through this problem.
Thanks for your kind words!