I agree that, among other things, discussion of mechanisms for sending resources to the future would needed to make such a decision. I figured that all these other considerations were deliberately excluded from this post to keep its scope manageable.
However, I do think that one can interpret the post as making claims about a more insightful kind of probability: the odds with which the current century is the one which will have the highest leverage-evaluated-at-the-time (in contrast to an omniscient view / end-of-time evaluation, which is what this thread mostly focuses on). I think that William_MacAskill’s main arguments are broadly compatible with both of these concepts, so one could get more out of the piece by interpreting it as about the more useful concept.
Formally, one could see the thing being analysed as
P(i=0 maximises E[leverage of century i∣Fi]),
where Fi is the knowledge available at the beginning of century i. If we and all future generations may freely move resources across time, and some things that are maybe omitted from the leverage definition are held constant, this expression tells us with what odds we are correct to do ‘direct work’ today as opposed to transfer resources one century forward. (Confusion about what ‘direct work’ means noted here.)
However, you seem to be right that as soon as you don’t hold other very important factors (such as how well one can send resources to the future) constant, those additional terms go inside the maximisation evaluation, and hence the above expression still isn’t that useful. (In particular, it can’t just be multiplied by an independent factor to get to a useable expression.)
(Also, I feel like I’m mathing from the hip here, so quite possibly I’ve got this quite wrong.)
I agree that, among other things, discussion of mechanisms for sending resources to the future would needed to make such a decision. I figured that all these other considerations were deliberately excluded from this post to keep its scope manageable.
However, I do think that one can interpret the post as making claims about a more insightful kind of probability: the odds with which the current century is the one which will have the highest leverage-evaluated-at-the-time (in contrast to an omniscient view / end-of-time evaluation, which is what this thread mostly focuses on). I think that William_MacAskill’s main arguments are broadly compatible with both of these concepts, so one could get more out of the piece by interpreting it as about the more useful concept.
Formally, one could see the thing being analysed as
P(i=0 maximises E[leverage of century i∣Fi]),
where Fi is the knowledge available at the beginning of century i. If we and all future generations may freely move resources across time, and some things that are maybe omitted from the leverage definition are held constant, this expression tells us with what odds we are correct to do ‘direct work’ today as opposed to transfer resources one century forward. (Confusion about what ‘direct work’ means noted here.)
However, you seem to be right that as soon as you don’t hold other very important factors (such as how well one can send resources to the future) constant, those additional terms go inside the maximisation evaluation, and hence the above expression still isn’t that useful. (In particular, it can’t just be multiplied by an independent factor to get to a useable expression.)
(Also, I feel like I’m mathing from the hip here, so quite possibly I’ve got this quite wrong.)