It is bad to apply statistics when you don’t in fact have large numbers—we have just one universe (at least until the many-world theory is better established—and anyway, the exposition didn’t mention it).
I think the following problem is equivalent to the one posed:
It is late at night, you’re tired, and it’s dark and you’re driving down an unfamiliar road. Then you see two motels, one to the right of the street, one to the left, both advertising vacant rooms. You know from a visit years ago that one has 10 rooms, the other has 100, but you can’t tell which is which (though you do remember that the larger one is cheaper). Anyway, you’re tired, so you just choose the one on the right at random, check in, and go to sleep. As you wake up in the morning, what are your chances that you find yourself in the larger motel? Does the number of rooms come into it? (Assume both motels are 90% full.)
The paradox is that while the other hotel is not contrafactual, it might as well be—the problem will play out the same. Same with the universe—there aren’t actually two universes with probabilities on which one you’ll end up in.
For a version where the Bayesian update works, you’d not go to the motel directly, but go to a tourist information stall that directs vistors to either the smaller or the larger motel until both are full—in that case, expect to wake up in the larger one. In this case, we have not one world, but two, and then the reasoning holds.
But if there’s only one motel, because the other burnt down (and we don’t know which), we’re back to 50⁄50.
I know that “fuzzy logic” tries to mix statistics and logic, and many AIs use it to deal with uncertain assertions, but statistics can be misapplied so easily that you seem to have a problem here.
It is bad to apply statistics when you don’t in fact have large numbers—we have just one universe (at least until the many-world theory is better established—and anyway, the exposition didn’t mention it).
I think the following problem is equivalent to the one posed: It is late at night, you’re tired, and it’s dark and you’re driving down an unfamiliar road. Then you see two motels, one to the right of the street, one to the left, both advertising vacant rooms. You know from a visit years ago that one has 10 rooms, the other has 100, but you can’t tell which is which (though you do remember that the larger one is cheaper). Anyway, you’re tired, so you just choose the one on the right at random, check in, and go to sleep. As you wake up in the morning, what are your chances that you find yourself in the larger motel? Does the number of rooms come into it? (Assume both motels are 90% full.)
The paradox is that while the other hotel is not contrafactual, it might as well be—the problem will play out the same. Same with the universe—there aren’t actually two universes with probabilities on which one you’ll end up in.
For a version where the Bayesian update works, you’d not go to the motel directly, but go to a tourist information stall that directs vistors to either the smaller or the larger motel until both are full—in that case, expect to wake up in the larger one. In this case, we have not one world, but two, and then the reasoning holds.
But if there’s only one motel, because the other burnt down (and we don’t know which), we’re back to 50⁄50.
I know that “fuzzy logic” tries to mix statistics and logic, and many AIs use it to deal with uncertain assertions, but statistics can be misapplied so easily that you seem to have a problem here.