I think you should pull the lever, even if this ended after the entire human population was on the track and the experiment doesn’t go on infinitely. Hear me out:
When a person pulls the lever with a chance of 50% and in one case they kill 2 people and in the other case 0, the kind of average outcome is 0.5 * 2 + (1 - 0.5) * 0 = 1. Now let’s consider the last person in the chain of decision-makers. They would have 2^33 people on the tracks, or about the entire human population. To make the expected outcome be exactly one person, they’d have to pull the lever with likelihood x so that x * 2^33 + (1 - x) * 0 = 1 which would lead to x = 1/2^33 or about x≈0.0000000001. So only if the last person directs the train towards the people with less than this tiny chance, the expected outcome is smaller than 1. This chance is incredibly small, and far far smaller than I’d guess the actual percentage is. Think of the percentage of people that are psychopaths, or mass murderers, or maybe even just clumsy. If you evaluate the percentage as someone flipping that switch as anything above 1/2^33, you should therefore flip the switch yourself. You can guarantee that the outcome is ‘only’ one death, whereas the average outcome of just the last person likely exceeds 1 by a huge amount.
I really wanted to calculate the percentage so that the expected outcome is 1 even if every person in the chain flips the switch with that chance, but wolfram alphas character limit let me down :(
I 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?
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.
Got it! So you’re saying that the last choice is between 233 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 · 233 + (1-x) · 0. And the only way this is less than 1 is if x < 1 / 233, which is an absurdly tiny probability.
If we also consider the intermediary probabilities, this already tiny probability threshold of 1 / 233 of killing nobody gets SMALLER because we’re allowing more chances for killing way more than 1 person along the way.
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.
I think you should pull the lever, even if this ended after the entire human population was on the track and the experiment doesn’t go on infinitely. Hear me out:
When a person pulls the lever with a chance of 50% and in one case they kill 2 people and in the other case 0, the kind of average outcome is
0.5 * 2 + (1 - 0.5) * 0 = 1. Now let’s consider the last person in the chain of decision-makers. They would have 2^33 people on the tracks, or about the entire human population. To make the expected outcome be exactly one person, they’d have to pull the lever with likelihoodxso thatx * 2^33 + (1 - x) * 0 = 1which would lead tox = 1/2^33or aboutx≈0.0000000001. So only if the last person directs the train towards the people with less than this tiny chance, the expected outcome is smaller than 1. This chance is incredibly small, and far far smaller than I’d guess the actual percentage is. Think of the percentage of people that are psychopaths, or mass murderers, or maybe even just clumsy. If you evaluate the percentage as someone flipping that switch as anything above1/2^33, you should therefore flip the switch yourself. You can guarantee that the outcome is ‘only’ one death, whereas the average outcome of just the last person likely exceeds 1 by a huge amount.I really wanted to calculate the percentage so that the expected outcome is 1 even if every person in the chain flips the switch with that chance, but wolfram alphas character limit let me down :(
I 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?
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.
Got it! So you’re saying that the last choice is between 233 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 · 233 + (1-x) · 0. And the only way this is less than 1 is if x < 1 / 233, which is an absurdly tiny probability.
If we also consider the intermediary probabilities, this already tiny probability threshold of 1 / 233 of killing nobody gets SMALLER because we’re allowing more chances for killing way more than 1 person along the way.
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.
To be honest, I’ve kept thinking of this branching stuff for the past few days lol.
They choose between half the whole population and the whole population (very roughly as it aligns alongside exponents of 2)
That’s what the meme is. But the user’s calculation multiplies 1-x by 0, not 1-x by half the population. Or by the future expected value.
Wait, we were supposed to figure out how to get less ppl ran over?
Reading this analysis, I think it’s all but guaranteed that the person at the switch on the last step is Davros.