The trolley is barreling down the tracks towards a number of love letters, which you know will each lead to the birth of a future person (only if the trolley is diverted). If you divert the trolley you will kill one person. Do you pull the switch?
(edited to clarify in response to Gietz comment)
The main problem I see with this thought experiment is assuming away replaceability. It is implausible that the 10 people involved in these love letters would have zero children in the absence of these love letters, but that is what we are asked to believe. I suspect that virtually all scenarios where an action causes someone to be born suffer from replaceability. Even abortion does: most people want children, they just don't want them at the time they have an unintended pregnancy. So I'm not sure how much we learn from this thought experiment.
Is this kind of replaceability compatible with current practices in Longtermism?
What is the consequence of the claim that if I fail to take an action to preserve Future People, Other Future People likely replace them?
Let's say I give money to MIRI instead of saving current people, based on some calculations of future people I might save. Are we discounting those Future People by the Other Future People? Why don't we value Other Future People just as much as Future People? Of course we do.
Perhaps that is the point of this thought experiment. Perhaps "of course you don't pull the switch" is the only right answer precisely because of replaceability.
If one holds a non-person-affecting view and believes that a marginal human life today is positive in expectation, they should save the letters. Many longtermists are sympathetic to these moral views.
Some possible objections to this, not necessarily held by me:
Not sure what the motivation behind this post is; it would be good for you to clarify.
I think the question isn't framed very well, since a love letter doesn't make a person happy for their entire life. Clearly more QALYs or WELLBYs or whatever are preserved by running over the letters.
The love letter leads to the conception and birth of a new human.