I need to think about this more, but if Aumann agreement is done properly, people eventually converge on correct models of other reasoners, which should also stop info-cascades.
There has been work on this. I believe this is a relevant reference, but I can’t tell for sure without paying to access the article:
The idea is this: Aumann agreement is typically studied with two communicating agents. We can instead study networks of agents, with various protocols (ie, rules for when agents talk to each other). However, not all such protocols reach consensus, the way we see with two agents!
I believe the condition for reaching consensus is directly analogous to the condition for correctness of belief prop in Bayesian networks, IE, the graph should be a tree.
Good find—I need to look into this more. The paper is on scihub, and it says it needs to be non-cyclical, so yes.
“All the examples in which communicating values of a union-consistent function fails to bring about consensus… must contain a cycle; if there are no cycles in the communication graph, consensus on the value of any union consistent function must be reached.”
So, epistemically virtuous social graphs should contain no cycles? ;3
“I can’t be your friend—we already have a mutual friend.”
“I can’t be your friend—Alice is friends with you and Bob; Bob is friends with Carol; Carol is friends with Dennis; Dennis is friends with Elane; and Elane is my friend already.”
“Fine, I could be your friend so long as we never discuss anything important.”
Or perhaps less unreasonably, we need clear epistemic superiority hierarchies, likely per subject area. And it occurs to me that this could be a super-interesting agent-based/graph theoretic modeling study of information flow and updating. As a nice bonus, this can easily show how ignoring epistemic hierarchies will cause conspiracy cascades—and perhaps show that it will lead to the divergence of rational agent beliefs which Jaynes talks about in PT:LoS.
Another more reasonable solution is to always cite sources. There is an analogous solution in belief propagation, where messages carry a trace of where their information came from. Unfortunately I’ve forgotten what that algorithm is called.
There has been work on this. I believe this is a relevant reference, but I can’t tell for sure without paying to access the article:
Protocols Forcing Consensus, Paul Krasucki
The idea is this: Aumann agreement is typically studied with two communicating agents. We can instead study networks of agents, with various protocols (ie, rules for when agents talk to each other). However, not all such protocols reach consensus, the way we see with two agents!
I believe the condition for reaching consensus is directly analogous to the condition for correctness of belief prop in Bayesian networks, IE, the graph should be a tree.
Good find—I need to look into this more. The paper is on scihub, and it says it needs to be non-cyclical, so yes.
“All the examples in which communicating values of a union-consistent function fails to bring about consensus… must contain a cycle; if there are no cycles in the communication graph, consensus on the value of any union consistent function must be reached.”
So, epistemically virtuous social graphs should contain no cycles? ;3
“I can’t be your friend—we already have a mutual friend.”
“I can’t be your friend—Alice is friends with you and Bob; Bob is friends with Carol; Carol is friends with Dennis; Dennis is friends with Elane; and Elane is my friend already.”
“Fine, I could be your friend so long as we never discuss anything important.”
Or perhaps less unreasonably, we need clear epistemic superiority hierarchies, likely per subject area. And it occurs to me that this could be a super-interesting agent-based/graph theoretic modeling study of information flow and updating. As a nice bonus, this can easily show how ignoring epistemic hierarchies will cause conspiracy cascades—and perhaps show that it will lead to the divergence of rational agent beliefs which Jaynes talks about in PT:LoS.
Another more reasonable solution is to always cite sources. There is an analogous solution in belief propagation, where messages carry a trace of where their information came from. Unfortunately I’ve forgotten what that algorithm is called.