This is definitely interesting. I commit to re-reading it on a plane ride on Monday and posting a better comment. Currently the biggest issue sticking out to me is that we actually need to throw away information, or else the “distribution in every detail of books read so far” is just a point distribution over the actual books read. So we have to pick what information to throw away, which is basically equivalent to picking a coarse-grained model of the world.
Thanks. The issue you identify is related to what I’m vaguely indicating with “I don’t know how convergence plays out in practical situations”—I thought of trying to explain in more detail, but 5 minutes of effort didn’t yield a clear explanation and I was keen to get something out rather than spend a long times tidying up all the loose ends.
Although it’s also worth noting that the general merging of opinions result doesn’t depend on long run relative frequencies (which is to say: I think “point distribution over books read” is a useful image of why convergence concerns might bite, but it doesn’t capture the precise difficulty with convergence)
This is definitely interesting. I commit to re-reading it on a plane ride on Monday and posting a better comment. Currently the biggest issue sticking out to me is that we actually need to throw away information, or else the “distribution in every detail of books read so far” is just a point distribution over the actual books read. So we have to pick what information to throw away, which is basically equivalent to picking a coarse-grained model of the world.
Thanks. The issue you identify is related to what I’m vaguely indicating with “I don’t know how convergence plays out in practical situations”—I thought of trying to explain in more detail, but 5 minutes of effort didn’t yield a clear explanation and I was keen to get something out rather than spend a long times tidying up all the loose ends.
Although it’s also worth noting that the general merging of opinions result doesn’t depend on long run relative frequencies (which is to say: I think “point distribution over books read” is a useful image of why convergence concerns might bite, but it doesn’t capture the precise difficulty with convergence)