Doug_S. comments on The "Intuitions" Behind "Utilitarianism" - Less Wrong
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Let's see just what that number is...
0.394(1-e^(-NT/100 person*years) > 0.393
1-e(-NT/100 person*years) > 0.998
e^(-NT/100 person*years) < 0.002538
-NT/100 person*years < -5.976
NT > 597.6 person*years
In terms of the constants, it comes out to NT > -a*ln(1-I1/I2), where I1 is the lesser pain and I2 is the greater pain. This does strike me as somewhat undesirable; I would prefer that the required NT go to infinity when I1 and I2 are sufficiently close but not sufficiently far. Unfortunately, I can't do this and still be consistent; the limit can't depend on the difference between I1 and I2. I either have to accept a preference function in which all pains aggregate to the same limit, or there exits two pains arbitrarily close together such that a finite amount of one is worse than a Nearly Infinite amount of the other.
I'm not confident in my constants or in my ability to calculate I(brain state), but yes, I think I can "bite the bullet" on this one. I hereby declare that, for any two pains, if I1 > I2, then there is an amount of I1 pain that is worse than a Nearly Infinite amount of pain I2.
However, I believe that we live in a finite universe, so hopefully I don't have to deal with Nearly Infinite quantities of anything. ;) You'd best keep me well away from that button that destroys the world, because I find it very, very tempting.