If the utility function U(t) does not diminish to zero—people keep living happy lives on earth—at a rate faster than the rate at which the survival probability function decreases, then the integral that defines the change in world utility can diverge, implying an infinite loss. In short, expected values don’t fare well in the presence of infinities.
It is unclear to me what you mean here. I have two possible understandings:
(1): You claim if U(t) does not go to zero (eg a constant U(t)=1 because people keep living happy lives on earth) then the integral diverges. If this is your claim, given your choice for p(t) I think this is just wrong on a mathematical level.
(2): You claim if U(t) grows exponentially quickly (and grows at a faster rate than the survival probability function decreases), then the integral diverges. I think this would mathematically correct. But I think the exponential growth here is not realistic: there are finite limits to energy and matter achievable on earth, and utility per energy or matter is probably limited. Even if you leave earth and spread out in a 3-dimensional sphere at light speed, this only gives you cubic growth.
I still think that one should be careful when trying to work with infinities in an EV-framework. But this particular presentation was not convincing to me.
It is unclear to me what you mean here. I have two possible understandings:
(1): You claim if U(t) does not go to zero (eg a constant U(t)=1 because people keep living happy lives on earth) then the integral diverges. If this is your claim, given your choice for p(t) I think this is just wrong on a mathematical level.
(2): You claim if U(t) grows exponentially quickly (and grows at a faster rate than the survival probability function decreases), then the integral diverges. I think this would mathematically correct. But I think the exponential growth here is not realistic: there are finite limits to energy and matter achievable on earth, and utility per energy or matter is probably limited. Even if you leave earth and spread out in a 3-dimensional sphere at light speed, this only gives you cubic growth.
I still think that one should be careful when trying to work with infinities in an EV-framework. But this particular presentation was not convincing to me.