Thats actually a really good dilemma if you think about it. Like if everyone doubles it you basically don’t kill anyone. But you’ll always risk that there’s some psycho who likes killing and then you will have killed more. And if these choices continue endlessly you will eventually find someone like this. So killing immediately should be the right thing to do.
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.
People always miss the bigger picture with these things. Why do these trolleys' brakes keep failing? Is it a design flaw in the braking system? Is the maintenance crew severely underfunded? Is it a slippage problem due to improper rail maintenance? It's a shame we can't even organize a work stoppage to sort this out since congress blocked the trolley union from striking...
this is not a purely theoretical question. in practice, autonomous vehicles face exactly this dilemma. or rather the manufacturers of the vehicles who have to set the specifications
Switch the track from the bottom to the top as the train is half way over the switch, causing the train to drift across both rails hitting all three tied up people and the second switch operator.
I think everyone here is missing the real answer. If you look at the picture you will notice a third option, there are track switches, two of them, you can bypass the people tied to the track, then kill the monster forcing you to kill for no reason.