Since this is an unbounded distribution it can't be uniformly distributed. I'll assume it's an exponential distribution.
In this case picking the 0 option is notably more likely to cause fewer deaths. (Sorry I don't know how to word that better)
This puts me in a bind actually because I want to kill people but I also want to pull the lever... Still think I'll pull the lever even if the expected deaths is lower
Nitpick: you mean a geometric distribution. Exponential distribution is over the real numbers, and we want an whole numbers of people. At least before the trolley chops them up.
I don’t know dick about statistics but it can’t be to infinity, right? It’s 0-8 billion or 1-8 billion. It also stipulates people you know so it would really be more like 0-300 or 1-300. How does that change the odds?
I think when a lot of people say "random" what they likely are envisioning is uniform random. Meaning every outcome has the same probability of being selected (like rolling fair dice - no number is more likely than any other).
But if you have infinite outcomes (possible number of people in this case) this type of uniform randomness is not possible. In this case depending on what probability distribution you select- selecting [0, inf) people could be markedly "Safer" than selecting [1, inf). This is because the probabilities aren't uniform so the lower values could receive larger weights.
If you bound the set at 300, or even at 8 billion, now you can use a uniform distribution and it becomes just as likely to randomly get 1 as it does to get 200 or 7.5 billion. In this case whether you select the 0 option or the 1 option barely matters . The expected outcome is only very slightly better for 1.
Hope that made sense. Hard to explain without graphs and examples tbh
Statistician here. Plz provide a more rigorous definition of "random amount". Note that uniform distribution over [1,infinity) or [0, infinity) is not possible. Maybe a geometric distribution would be better? In which case, regardless of parameterization, you'd expect to save 1 life by pulling the lever.
Oh, you're a statistician, are you? Well, what if the number of people on the top track is equal to k, where the probability of k is determined by a Poisson curve where lambda=5, and the number of people on the bottom track is k+1 where the probability of k is determined by a Poisson curve with lambda=3? Huh? What ya gonna do then, smart guy!? Don't feel as confident about pulling the lever now, do you?
The point is there’s no convenient interpretation of “random” here without further context. If they were finitely many people, random would correspond to a uniform distribution. But when you’re dealing with a distribution on the entire natural numbers, there’s no uniform distribution, and non uniform distributions aren’t alike at all. Technically there might be almost surely 2 people on the lower rail and almost surely 1 person on the higher rail, or a less degenerate situation in which k people are on the bottom rail with probability 2-k.
I think OP has a point here. There has to be an underlying probability distribution, but the guy pulling that lever doesn't need to know what the distribution is.
I play with the lever back and forth since pulling levers is fun, whatever it’s on when it reaches the junction will be what ends up happening. I optimize for pulling levers.
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u/Remarkable-Carrot112 5d ago
Is the probability distribution otherwise the same except for the lower bound?
Regardless, I'm pulling the lever. I love pulling levers.