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I think you would HAVE to pull it right? Regardless of how many times the lever can be given to the next person, you are either killing 1/3rd lives in the scenario, or you are killing 1/8bil.

I think I like this more than the original prompt.

I guess it depends how far down it goes. Infinitely? Only enough for every person on the planet to be considered?
Theoretically, the correct option is to always switch down. Which, according to the original problem, would be doing nothing. So.. what if everyone just went home?
Also to consider; The people (and track) gets smaller every time. Maybe it ends?

Eventually somebody's going to pull the lever, either accidentally or deliberately, so it's best to flip it while it kills the least amount of people.
I guess b/c of that it's sort of like the regular trolley problem.

I've been thinking about this. I estimate a few people per 1000 would do an atrocity for no reason if they were guaranteed no consequences, and the deaths if the switch is pulled are 2^(n-1)^ for the nth switch. The expected deaths will cross 1 somewhere in the high single-digits, then (since it's outcome*chance), so the death minimising strategy is actually to pull yours if the chain is at least that long.

In theory if the chain never ends this might be the only trolley problem where nobody has to die as long as nobody interacts. (If I understand it correctly)