From a decision-theory perspective, I should essentially just ignore the possibility that I'm in the first 100 rooms - right?
Similarly, if I'm born in a universe with infinite such rooms and someone tells me to guess whether my room is a multiple of 10 or not. If I guess correctly, I get a dollar; otherwise I lose a dollar.
Theoretically there are as many multiples of 10 as not (both being equinumerous to the integers), but if we define rationality as the "art of winning", then shouldn't I guess "not in a multiple of 10"? I admit that my intuition may be broken here - maybe it just truly doesn't matter which you guess - after all its not like we can sample a bunch of people born into this world without some sampling function. However, doesn't the question still remain: what would a rational being do?
From a decision-theory perspective, I should essentially just ignore the possibility that I'm in the first 100 rooms - right?
Well, what do you mean by "essentially ignore"? If you're asking if I should assign substantial credence to the possibility, then yeah, I'd agree. If you're asking whether I should assign literally zero credence to the possibility, so that there are no possible odds -- no matter how ridiculously skewed -- I would accept to bet that I am in one of those rooms... well, now I'm no longer sure. I don't exactly know how to go...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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