I don’t believe this is exactly correct. After all, when you’re just about to start listening to the clever arguer, do you really believe that box B is almost certain not to contain the diamond?
Where do you get that A is “almost certain” from? I just said the prior probability of B was “low”. I don’t think that’s a reasonable restatement of what I said.
Your actual probability starts out at 0.5, rises steadily as the clever arguer talks (starting with his very first point, because that excludes the possibility he has 0 points), and then suddenly drops precipitously as soon as he says “Therefore...” (because that excludes the possibility he has more points).
It doesn’t seem to me that excluding the possibility that he has more points should have that effect.
Consider the case where CA is artificially restricted to raising a given number of points. By common sense, for a generous allotment this is nearly equivalent to the original situation, yet you never learn anything new about how many points he has remaining.
You can argue that CA might still stop early when his argument is feeble, and thus you learn something. However, since you’ve stipulated that every point raises your probability estimate, he won’t stop early. To make an argument without that assumption, we can ask about a situation where he is required to raise exactly N points and assume he can easily raise “filler” points.
ISTM at every juncture in the unrestricted and the generously restricted arguments, your probability estimate should be nearly the same, excepting only that you need compensate slightly less in the restricted case.
Now, there is a certain sense of two ways of saying the same thing, raising the probability per point (presumably cogent) but lowering it as a whole in compensation.
But once you begin hearing CA’s argument, you know tautologically that you are hearing his argument, barring unusual circumstances that might still cause it not to be fully presented. I see no reason to delay accounting that information.
Where do you get that A is “almost certain” from? I just said the prior probability of B was “low”. I don’t think that’s a reasonable restatement of what I said.
It doesn’t seem to me that excluding the possibility that he has more points should have that effect.
Consider the case where CA is artificially restricted to raising a given number of points. By common sense, for a generous allotment this is nearly equivalent to the original situation, yet you never learn anything new about how many points he has remaining.
You can argue that CA might still stop early when his argument is feeble, and thus you learn something. However, since you’ve stipulated that every point raises your probability estimate, he won’t stop early. To make an argument without that assumption, we can ask about a situation where he is required to raise exactly N points and assume he can easily raise “filler” points.
ISTM at every juncture in the unrestricted and the generously restricted arguments, your probability estimate should be nearly the same, excepting only that you need compensate slightly less in the restricted case.
Now, there is a certain sense of two ways of saying the same thing, raising the probability per point (presumably cogent) but lowering it as a whole in compensation.
But once you begin hearing CA’s argument, you know tautologically that you are hearing his argument, barring unusual circumstances that might still cause it not to be fully presented. I see no reason to delay accounting that information.