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gjm comments on What can total utilitarians learn from empirical estimates of the value of a statistical life? - Less Wrong Discussion
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Comments (7)
At least one of us is very confused about pretty much everything here.
Not if you're serious about total utilitarianism, which needs to be able to add up utilities and therefore looks quite different (at least when the number of lives can vary) as the constant term varies.
[EDITED to add: The issues below are because the mathematical typesetting got messed up in a way that made + signs disappear; they are not real mistakes and the error has now been fixed in the original post.]
I must be misunderstanding. You've written U = psf(y) where the condition in question is f(y0)=0. But this implies U=p.s.0=0 when y=y0. So s is not the utility at minimum income. In fact it looks to me as if s is simply a scaling factor applied to utilities, and as such is perfectly arbitrary.
Then, a little later, you go from VL = s f(y)/f'(y) to s = VL.f'(y) - f(y) but that's completely wrong; it should be s = VL.f'(y)/f(y), which in the log case says s = VL / y log(y/y0); in the case y=y0 this just says that VL=0 whatever s may be, which is not surprising since you deliberately chose to rescale your utilities to make it so ("we can define the utility of being dead as 0").
Sorry, I was unclear. I meant that the constant term cannot be determined from empirical studies alone, since it doesn't affect decision-making. Estimates of the "value of life" compare the utility change from a small change in income to the utility change from a small change in survival probability, and the point of my post was to extrapolate these to large changes (creating a new person at a very low income level).
The conclusions are unchanged when the utility of death is nonzero, as long as you only look at "changes" in total utility (and not total utility itself, which will be infinite). For example, if the utility of death is fixed at 1 and your utility is fixed at 2, then creating a copy of you would make total utility "2+2+[lots of others]+1+1+1+..." instead of "2+1+[lots of others]+1+1+1+..." and total utility would increase from infinity to infinity+1. Obviously this is ill-defined mathematically (which is why I set death to 0), but you can see that it still makes sense to talk about utility changes.
When Vladimir_Nesov changed the images, the plus signs weren't URL-encoded, so they all disappeared. It's supposed to be U = p*(s + f(y)) and VL = (s + f(y))/f'(y).