But shouldn’t you always update toward the others position? And if the argument isn’t convincing you can truthfully tell so that you updated only slightly.
But shouldn’t you always update toward the others position?
That’s not how Aumann’s theorem works. For example, if Alice mildly believe X and Bob strongly believes X, it may be that Alice has weak evidence for X, and Bob has much stronger independent evidence for X. Thus, after exchanging evidence they’ll both believe X even more strongly than Bob did initially.
One related use case is when everyone in a meeting prefers policy X to policy Y, although each are a little concerned about one possible problem. Going around the room and asking everyone how likely they think X is to succeed produces estimates of 80%, so, having achieved consensus, they adopt X.
But, if people had mentioned their particular reservations, they would have noticed they were all different, and that, once they’d been acknowledged, Y was preferred.
“Interesting point. I’m not entirely clear how you arrived at that position. I’d like to look up some detail questions on that. Could you provide references I might look at?”
doesn’t make clear that the other holds another position and that the reply may just address the validity of the evidence.
But even then shouldn’t you see it at least as weak evidence and thus believe X at least a bit more strongly?
But shouldn’t you always update toward the others position? And if the argument isn’t convincing you can truthfully tell so that you updated only slightly.
That’s not how Aumann’s theorem works. For example, if Alice mildly believe X and Bob strongly believes X, it may be that Alice has weak evidence for X, and Bob has much stronger independent evidence for X. Thus, after exchanging evidence they’ll both believe X even more strongly than Bob did initially.
Yup!
One related use case is when everyone in a meeting prefers policy X to policy Y, although each are a little concerned about one possible problem. Going around the room and asking everyone how likely they think X is to succeed produces estimates of 80%, so, having achieved consensus, they adopt X.
But, if people had mentioned their particular reservations, they would have noticed they were all different, and that, once they’d been acknowledged, Y was preferred.
Even if they both equally strongly believe X, it makes sense for them to talk whether they both used the same evidence or different evidence.
Obligatory link.
Of course.
I agree that
doesn’t make clear that the other holds another position and that the reply may just address the validity of the evidence.
But even then shouldn’t you see it at least as weak evidence and thus believe X at least a bit more strongly?