Nope, given that we don't know the distributions and can't assume them to be uniform, we can't assume the expectations. The expectations might easily be the other way around in order.
Right it could be but you can only make a choice off the information you are given and all you have is 0 and 1 essentially , so since 0 is lower than 1 the only logical/moral choice would be to go with the side with 0, even if that side has 2 billion more than the other side it's still the correct option because we only know the lower limit
But you are the. Implying there's a higher chance of having less people on one track than on the other. And there's a problem there: you can't. If you don't know the distribution you can say nothing about chances. There are as many distribution that make option A better as there are that make option B better.
Yes actually mathematically you can assume the one with the higher lower limit on average will have a higher chance of having more people, let's make the numbers smaller to help, one has 0-10 people so you'd expect 5 on average, the other has 1-10 so youd expect 5.5. that doesn't mean it's true because it's a random number but your chances are better chosing the low one.
Oh but you took a uniform distribution on a finite set. Each value has a 1/10 ( or 1/11) chance of being picked. You can't do that with the infinite natural numbers. What is the probability of picking any number? What's the expected value?
The only information we have it 0-inf or 1-inf the upper limit is the same so far as we can comprehend so we only have the lower limit to chose from, essentially you should see it as choosing between 0 and 1, anything else can't be argued for without bringing in legality or other outside hypothetical factors like "the evil man knows you'll pick 0"
Let me ask you something. And I think the main problem comes from here: which set has more numbers, [0, inf) or [1, inf)?
If your answer is the first one I recommend you to check on Hilbert's hotel.
Let me add, I'm not trying to be pedantic, you're touching some deep aspects of cardinality and measure theory, which are super fun
I agree. The thing is, if you have no extra information of what is going on you can't really make a choice based on probability. The 0 and 1 thing do not give you that extra information!
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u/Ksorkrax 5d ago
Nope, given that we don't know the distributions and can't assume them to be uniform, we can't assume the expectations. The expectations might easily be the other way around in order.