Common Knowledge and Aumann’s Agreement Theorem

Common Knowledge and Aumann’s Agreement Theorem(scottaaronson.com)

44 points by berekuk 10 years ago | 3 comments

tunesmith 10 years ago |

He mentions the built-in aversion to updating our own opinions more than a handful of times. I see that all over the place, even in the structure of online discussions. For instance, here on HN, comment threads that nest too deeply are discouraged through "wait periods", which can get in the way of actual deep exchange of ideas. Across discussion software, aesthetically it starts to look ugly, which also serves as a deterrent.

You see it in rhetoric and debate, also. Someone states an assertion, along with fourteen backing arguments that are each sufficient to support the assertion. In reality, each of those fourteen backing arguments might be bunk, but there's this huge psychological advantage to having those fourteen bedrocks in place. Seeing or hearing all fourteen increases the feeling of "probability" that at least one must be correct, and an effort to knock down all fourteen starts to look petty after a while.

That might just be an essential flawed part of being human, which might be another "way out" around Aumann's theorem? It shows how so much of our progress is dependent not just on being correct, but also pithy.

I've always wanted discussion software that wasn't so much oriented on representing the entire discussion history, but instead focused on representing the state of the discussion "right now", with irrelevant cruft removed and only the most concise, forceful information remaining to get readers up to date to where the discussion has evolved.

Yen 10 years ago | |

On the subject of new discussion software, I'm interested in finding or creating a system where the typical end result is consensus among the participants, and future readers reading the end result will be likely persuaded of that consensus.

Even the most civil of online discussions don't typically end with one or both people changing their views, and the end result is, like you say, just a chronological discussion. Not only chronological, it tends to end up a bit cyclic.

I'm imagining something like a flow-chart, seeded with a single node, some assertion under discussion. Someone can make an argument for or against that assertion - and then future participants cannot make the same argument again. They can refine it, substitute their own version, or offer supporting/denying evidence as sub-arguments.

Ideally, at the end of that discussion, their would be a single flowchart, with each argument laid out exactly once, in its strongest/most persuasive form.

jimhefferon 10 years ago | | |

> Ideally, at the end of that discussion, their would be a single flowchart, with each argument laid out exactly once, in its strongest/most persuasive form.

To some extent, that sounds like the StackExchange model, where editors feel free to come in and change what a person said in some way to create a permanent best answer. (Which, I have to admit, puts me off, personally.)