Eliezer—I see better what you mean now. However I am still a bit confused because “common knowledge” usually refers to a state that is the end point of a computational or reasoning process, so it is inconsistent to speak of what participants “should” do after that point. If A and B’s disagreement is supposedly common knowledge, but A may still choose to change his estimate to more closely match B’s, then his estimate really isn’t common knowledge at all because B is not sure if he has changed his mind or not.
When you say, “they should each adjust their probability estimates in the direction of the others’”, do you mean that they should have done that and it would have been better for them, instead of letting themselves get into the state of common knowledge of their disagreement?
Sorry to belabor this but since you are critiquing this Modesty Argument it seems worthwhile to clarify exactly what it says.
Eliezer—I see better what you mean now. However I am still a bit confused because “common knowledge” usually refers to a state that is the end point of a computational or reasoning process, so it is inconsistent to speak of what participants “should” do after that point. If A and B’s disagreement is supposedly common knowledge, but A may still choose to change his estimate to more closely match B’s, then his estimate really isn’t common knowledge at all because B is not sure if he has changed his mind or not.
When you say, “they should each adjust their probability estimates in the direction of the others’”, do you mean that they should have done that and it would have been better for them, instead of letting themselves get into the state of common knowledge of their disagreement?
Sorry to belabor this but since you are critiquing this Modesty Argument it seems worthwhile to clarify exactly what it says.