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You would need a crazy low probability of a lunatic or a mass murderer being down the line to justify not to kill one person
Edit: Sum(2^n (1-p)^(n-1) p) ~ Sum(2^n p) for p small. So you'd need a p= (2×2^32 -2) ~ 1/(8 billion) chance of catching a psycho for expected values to be equal. I.e. there is only a single person tops who would decide to kill all on earth.
You don't even need a lunatic or mass murderer. As you say, the logical choice is to kill one person. For the next person, the logical choice is to kill two people, and so on.
It does create the funny paradox where, up to a certain point, a rational utilitarian would choose to kill and a rational mass murderer trying to maximise deaths would choose to double it.
It's always "double it" Anyone after 34 flips the kill all humans, that's their fault not yours
Why do you care whose fault it is? You'd want to minimise human deaths, not win a blame game.
Doubling action forever minimizes human deaths.
Unless someone decide to hit kill. In that case, it's them doing it. I'm invalidating the argument that pre-empting imaginary future mass murders justifies killing one person today.
Idk which moral system you operate under, but I'm concerned with minimising human suffering. That implies hitting kill because chances of a mass murderer are too high not to. You also don't follow traffic laws to a t, but exercise caution because you don't really care whose fault it ends up being, you want to avoid bad outcomes (in this case the extinction of humankind).
My moral system somehow does not chose to kill people through action against an imagined threat and is therefore objectively superior as is it not susceptible to hostile memetic manipulation (Molloch, Pascal's wager, Pascal's mugging, basilisks, social hysteria etc.) and is capable of escaping false choices and other contrived scenarios, breaking premise and the rules of the game as needed to obtain the desired outcome.
Even if your moral system solves those "problems", you just "solved" them by substituting the obvious and logical base of utility through personal responsibility. Personal responsibility is no inherent good, unlike utility, if people are unhappy/"feel bad", it doesn't matter how personally responsible everyone is being, that world is still a shit place.
Also, the threat isn't imagined. I can assure you that there are a lot more than one person on earth who would choose to kill as many people as possible if given the option.