The total incidence of both torture and dust specks is unknown in either case.
Where was this declared? (Not that it matters for the purpose of this point.) The agent has prior probabilities distributed over the number of possible incidence of torture and dustspecks. It is impossible not to. And after taking one such deal those priors will be different. Sure, restricting the access to information about the current tortured population will make it harder for an agent to implement preferences that are not linear with respect to additional units but it doesn’t make those preferences inconsistent and it doesn’t stop the agent doing its best to maximise utility despite the difficulty.
There is no information on the total incidence of either included in the problem statement (other than the numbers used), and I have seen no one answer conditionally based on the incidence of either.
The agent has prior probabilities distributed over the number of possible incidence of torture and dustspecks.
Yes, of course, I thought my previous comment clearly implied that?
And after taking one such deal those priors will be different.
Infinitesimally. I thought I addressed that? The problem implies the existence of an enormous number of people. Conditional on there actually being that many people the expected number of people tortured shifts by the tiniest fraction of the total. If the agent is sensitive to such a tiny shift we are back to requiring extraordinary precision.
Where was this declared? (Not that it matters for the purpose of this point.) The agent has prior probabilities distributed over the number of possible incidence of torture and dustspecks. It is impossible not to. And after taking one such deal those priors will be different. Sure, restricting the access to information about the current tortured population will make it harder for an agent to implement preferences that are not linear with respect to additional units but it doesn’t make those preferences inconsistent and it doesn’t stop the agent doing its best to maximise utility despite the difficulty.
There is no information on the total incidence of either included in the problem statement (other than the numbers used), and I have seen no one answer conditionally based on the incidence of either.
Yes, of course, I thought my previous comment clearly implied that?
Infinitesimally. I thought I addressed that? The problem implies the existence of an enormous number of people. Conditional on there actually being that many people the expected number of people tortured shifts by the tiniest fraction of the total. If the agent is sensitive to such a tiny shift we are back to requiring extraordinary precision.