And that approximation works for only needing to believe as many levels of commonality as is required for the action calculation.
Note that the standard theory of common knowledge contains explicit claims against this part of your statement. The importance of common knowledge is supposed to be that it has a different quality from finite levels, which is uniquely helpful for coordination; eg, that’s the SEP’s point with the electronic messaging example. Or in the classic analysis of two-generals, where (supposedly) no finite number of messages back and forth is sufficient to coordinate, (supposedly) because this only establishes finite levels of social knowledge.
So the seemingly natural update for someone to make, if they learn standard game theory, but then realize that common knowledge is literally impossible in the real world as we understand it, is that rational coordination is actually impossible, and empirical signs pointing in the other direction are actually about irrationality.
I’ve realized that I’m not the target of the post, and am bowing out. I think we’re in agreement as to the way forward (no knowledge is 1 or 0, and practically you can get “certain enough” with a finite number of iterations). We may or may not disagree on what other people think about this topic.
Fair enough. I note for the public record that I’m not agreeing (nor 100% disagreeing) with
practically you can get “certain enough” with a finite number of iterations
as an accurate characterization of something I think. For example, it currently seems to me like finite iterations doesn’t solve two-generals, while p-common knowledge does.
However, the main thrust of the post is more to question the standard picture than to say exactly what the real picture is (since I remain broadly skeptical about it).
Note that the standard theory of common knowledge contains explicit claims against this part of your statement. The importance of common knowledge is supposed to be that it has a different quality from finite levels, which is uniquely helpful for coordination; eg, that’s the SEP’s point with the electronic messaging example. Or in the classic analysis of two-generals, where (supposedly) no finite number of messages back and forth is sufficient to coordinate, (supposedly) because this only establishes finite levels of social knowledge.
So the seemingly natural update for someone to make, if they learn standard game theory, but then realize that common knowledge is literally impossible in the real world as we understand it, is that rational coordination is actually impossible, and empirical signs pointing in the other direction are actually about irrationality.
I’ve realized that I’m not the target of the post, and am bowing out. I think we’re in agreement as to the way forward (no knowledge is 1 or 0, and practically you can get “certain enough” with a finite number of iterations). We may or may not disagree on what other people think about this topic.
Fair enough. I note for the public record that I’m not agreeing (nor 100% disagreeing) with
as an accurate characterization of something I think. For example, it currently seems to me like finite iterations doesn’t solve two-generals, while p-common knowledge does.
However, the main thrust of the post is more to question the standard picture than to say exactly what the real picture is (since I remain broadly skeptical about it).