Sure, we should put more weight on the suffering from flipping a single tail in B than the suffering from flipping a thousand heads followed by a tail in A (by a factor of 21000 times). But (at least intuitively) that’s because the former is more probable; there’s (roughly speaking) 21000 universes in which we flip a single tail for every one where we flip a thousand heads followed by a tail. This doesn’t generally seem relevant to the scenarios described in the post, where we’re specifying possibilities to compare, but of course it’s worth tracking in general, where simple phenomena are more likely.
there’s (roughly speaking) 21000 universes in which we flip a single tail for every one where we flip a thousand heads followed by a tail
This follows only if you assume that all probability measures must derive from some underlying uniform measure over a finite set, but there’s no reason that this has to be the case. In quantum mechanics, for instance, there’s no obvious underlying set on which the uniform measure gives the Born probabilities. Or if we’re considering an infinite set of possibilities like in this post, there is no uniform probability measure we can use. That’s arguably the source of the paradoxes, and one possible resolution is to allow non-uniform measures such as the simplicity prior.
Sure, we should put more weight on the suffering from flipping a single tail in B than the suffering from flipping a thousand heads followed by a tail in A (by a factor of 21000 times). But (at least intuitively) that’s because the former is more probable; there’s (roughly speaking) 21000 universes in which we flip a single tail for every one where we flip a thousand heads followed by a tail. This doesn’t generally seem relevant to the scenarios described in the post, where we’re specifying possibilities to compare, but of course it’s worth tracking in general, where simple phenomena are more likely.
This follows only if you assume that all probability measures must derive from some underlying uniform measure over a finite set, but there’s no reason that this has to be the case. In quantum mechanics, for instance, there’s no obvious underlying set on which the uniform measure gives the Born probabilities. Or if we’re considering an infinite set of possibilities like in this post, there is no uniform probability measure we can use. That’s arguably the source of the paradoxes, and one possible resolution is to allow non-uniform measures such as the simplicity prior.