They choose between half the whole population and the whole population (very roughly as it aligns alongside exponents of 2)
Comment on 2³² will get interesting...
LanguageIsCool@lemmy.world 1 day agoI am not seeing it. Are you saying the last person chooses between killing nobody and killing the entire population? Also, what about the intermediary likelihoods of pulling the lever?
Credibly_Human@lemmy.world 1 day ago
LanguageIsCool@lemmy.world 1 day ago
That’s what the meme is. But the user’s calculation multiplies 1-x by 0, not 1-x by half the population.
xxd@discuss.tchncs.de 1 day ago
That was my assumption, yes. Because the last person would have the entire population on the tracks, and you can’t really continue after that.
I neglected the intermediary likelihoods, because that calculation was too long for wolfram alpha, but I have since managed to get it working, and the conclusion is not significantly different. The expected number of deaths skyrockets, even if the chance of pulling the lever is tiny for every person.
LanguageIsCool@lemmy.world 1 day ago
Got it! So you’re saying that the last choice is between 2^33^ or 0 and the last guy has a probably x of pulling the lever and killing everyone (therefore a (1-x) probability of killing nobody).
So, even if it’s guaranteed that nobody along the way pulls the lever (the best case scenario if we want 0 dead), the expected value at the last branch is x · 2^33^ + (1-x) · 0. And the only way this is less than 1 is if x < 1 / 2^33^, which is an absurdly tiny probability.
If we also consider the intermediary probabilities, this already tiny probability threshold of 1 / 2^33^ of killing nobody gets SMALLER because we’re allowing more chances for killing way more than 1 person along the way.
xxd@discuss.tchncs.de 14 hours ago
That’s exactly right, you got it!
The intermediary probabilities make it even worse, yes! But the overall probability is already ridiculously tiny, so I don’t think it changes the conclusion by a lot.