I generally agree with the main message, and am happy to see it be written up, but see this less as a failure of Bayes theory than a rejection of a common misuse of Bayes theory. I believe I’ve heard a similar argument a few times before and have found it a bit frustrating for this reason. (Of course, I could be factually wrong in my understanding)
If one were to apply something other than a direct bayesian update, as could make the sense in a more complicated setting, they may as well do so in a process which includes other kinds of bayesian updates. And the decision process that they use to determine the method of updating in these circumstances may well involve bayesian updates.
I’m not sure how to solve such an equation, though doing it for simple cases seems simple enough. I’ll admit I don’t understand logical induction near as well as I would like, and mean to do so some time.
I generally agree with the main message, and am happy to see it be written up, but see this less as a failure of Bayes theory than a rejection of a common misuse of Bayes theory. I believe I’ve heard a similar argument a few times before and have found it a bit frustrating for this reason. (Of course, I could be factually wrong in my understanding)
If one were to apply something other than a direct bayesian update, as could make the sense in a more complicated setting, they may as well do so in a process which includes other kinds of bayesian updates. And the decision process that they use to determine the method of updating in these circumstances may well involve bayesian updates.
I’m not sure how to solve such an equation, though doing it for simple cases seems simple enough. I’ll admit I don’t understand logical induction near as well as I would like, and mean to do so some time.