Item 5 is wrong. Aumann agreement does not mean that the correct answer would necessarily be between the two initial positions, nor does it imply that the two ideal rationalists would move toward each others initial positions. Merely that two ideal rationalists, upon knowledge of each other’s disagreement, would end up updating in such a way as to ultimately end up agreeing. (But again, the agreement might very well outside the space bounded by the two initial positions).
(At least that’s my understanding of Aumann agreement)
Aumann agreement does not mean that the correct answer would necessarily be between the two initial positions, nor does it imply that the two ideal rationalists would move toward each others initial positions.
Item 5 is wrong. Aumann agreement does not mean that the correct answer would necessarily be between the two initial positions, nor does it imply that the two ideal rationalists would move toward each others initial positions. Merely that two ideal rationalists, upon knowledge of each other’s disagreement, would end up updating in such a way as to ultimately end up agreeing. (But again, the agreement might very well outside the space bounded by the two initial positions).
(At least that’s my understanding of Aumann agreement)
Indeed, here is an example of such a situation.