The reason saving lives is ~linear while watching the same movie is not, is about where you are on your utility curve.
Let’s assume for a minute that utility over movies and lives are both a square root or something. Any increasing function with diminishing returns will do. The point is that we are going to get this result even if they are exactly the same utility curve.
Watching the movie once gives 1 utilon. Watching it 100 times gives 10 utilons. Easy peasy.
Saving lives is a bit different. We aren’t literally talking about the difference between 0 people and n people, we are talking about the difference between a few billion and a few billion+n. Any increasing function with diminishing returns will be linear by this point, so for small games, shut up and multiply.
By this same argument, the fact that lives are locally linear is not much evidence at all (LR = ~1) that they are globally linear, because there aren’t any coherent utility functions that aren’t linear at this scale at this point. (unless you only care about how many lives you, individually save, which isn’t exactly coherent either, but for other reasons.)
(I think the morally proper think to talk about is people dieing, not people living, because we are talking about saving lives, not birthing babies. But the argument is analogous; you get the idea.)
Sqrt(a few billion + n) is approximately Sqrt(a few billion). Increasing functions with diminishing returns don’t approach Linearity at large values, their growth becomes really Small (way sub-linear, or nearly constant) at high values.
This may be an accurate description of what’s going on (if, say, our value for re-watching movies falls off slower than our value for saving multiple lives), but it does not at all strike me as an argument for treating lives as linear. In fact, it strikes me as an argument for treating life-saving as More sub-linear than movie-watching.
It’s not the overall growth rate of the function that becomes linear at high values; it’s the local behavior. We can approximate: sqrt(1000000), sqrt(1001000), sqrt(1002000), sqrt(1003000) by: 1000, 1000.5, 1001, 1001.5. This is linear behavior.
The reason saving lives is ~linear while watching the same movie is not, is about where you are on your utility curve.
Let’s assume for a minute that utility over movies and lives are both a square root or something. Any increasing function with diminishing returns will do. The point is that we are going to get this result even if they are exactly the same utility curve.
Watching the movie once gives 1 utilon. Watching it 100 times gives 10 utilons. Easy peasy.
Saving lives is a bit different. We aren’t literally talking about the difference between 0 people and n people, we are talking about the difference between a few billion and a few billion+n. Any increasing function with diminishing returns will be linear by this point, so for small games, shut up and multiply.
By this same argument, the fact that lives are locally linear is not much evidence at all (LR = ~1) that they are globally linear, because there aren’t any coherent utility functions that aren’t linear at this scale at this point. (unless you only care about how many lives you, individually save, which isn’t exactly coherent either, but for other reasons.)
(I think the morally proper think to talk about is people dieing, not people living, because we are talking about saving lives, not birthing babies. But the argument is analogous; you get the idea.)
I hope this helps you.
Uh… what?
Sqrt(a few billion + n) is approximately Sqrt(a few billion). Increasing functions with diminishing returns don’t approach Linearity at large values, their growth becomes really Small (way sub-linear, or nearly constant) at high values.
This may be an accurate description of what’s going on (if, say, our value for re-watching movies falls off slower than our value for saving multiple lives), but it does not at all strike me as an argument for treating lives as linear. In fact, it strikes me as an argument for treating life-saving as More sub-linear than movie-watching.
It’s not the overall growth rate of the function that becomes linear at high values; it’s the local behavior. We can approximate: sqrt(1000000), sqrt(1001000), sqrt(1002000), sqrt(1003000) by: 1000, 1000.5, 1001, 1001.5. This is linear behavior.