In a recent conversation with Sam Harris, Jack Dorsey said that they are trying to measure the health of conversations using the following metrics:
Shared attention: What percentage of the conversation is “about” the same thing versus about dispersed.
Shared reality: What percentage of the conversation is sharing the same “facts” (irrespective of whether they agree with them or not)
Receptivity: How ‘toxic’ is the conversation right now? How likely are people to walk away from the conversation?
Variety of perspective: How diverse are the ideas being discussed?
All of these look like interesting problems to study, I have worked on the last problem myself.