What sort of problem is one where meta-probabilities are useful? One where you get different chance payouts depending on different models of the problem (e.g. one brown box vs. the good green box), and so you want to tell those models apart.
Or if we want meta-meta probabilities, then we could have different classes of models that you can tell apart (boxes or spheres?), and then different models that you have to tell apart (good box or bad box?), and then different outcomes that happen probabilistically (coins or no coins?).
But the key idea is that we gain something by differentiating these different known ways that the problem could be.
So in the case of someone who says “give me 5$ and I’ll get you into heaven when you die,” what are the layers? Well, they could be a charlatan or not. If they’re not a charlatan, then we can assume for the sake of argument that you’ll get into heaven with certainty, so no meta-probability there. But if they are a charlatan, then there’s some probability you’d get into heaven anyhow, so the probability of “they are a charlatan” is equivalent to a meta-probability for getting into heaven.
Okay, so: What experiment can you do that will let you change your mind about Pasal’s Mugger? Or to put it another way, how can someone convince you even a little that they are not a charlatan? What is the analogy between this and the boxes int he original post?
Has anyone used meta-probabilities, or something similar, to analyze the Pascal Mugger problem?
We can do it now! :)
What sort of problem is one where meta-probabilities are useful? One where you get different chance payouts depending on different models of the problem (e.g. one brown box vs. the good green box), and so you want to tell those models apart.
Or if we want meta-meta probabilities, then we could have different classes of models that you can tell apart (boxes or spheres?), and then different models that you have to tell apart (good box or bad box?), and then different outcomes that happen probabilistically (coins or no coins?).
But the key idea is that we gain something by differentiating these different known ways that the problem could be.
So in the case of someone who says “give me 5$ and I’ll get you into heaven when you die,” what are the layers? Well, they could be a charlatan or not. If they’re not a charlatan, then we can assume for the sake of argument that you’ll get into heaven with certainty, so no meta-probability there. But if they are a charlatan, then there’s some probability you’d get into heaven anyhow, so the probability of “they are a charlatan” is equivalent to a meta-probability for getting into heaven.
Okay, so: What experiment can you do that will let you change your mind about Pasal’s Mugger? Or to put it another way, how can someone convince you even a little that they are not a charlatan? What is the analogy between this and the boxes int he original post?