I was just yesterday thinking: Everyone (in America at least) keeps mentioning having a "national conversation about X". Why don't we have an actual organization that hosts public debates that's free for everyone to watch (on TV or wherever)? Each side would have one person that most people on that side would feel comfortable represent them - a good debater, and someone that holds views that most people on that side agree with. There would be a moderator that is good at moderating - asking relevant questions, keeping the debate within the intended scope, etc. My idea is definitely different than yours though - in particular, mine would do a terrible job of getting people to actually listen to one another, and would actually probably be more polarizing and yours bringing people together through understanding (if it works out nearly as well as you hope). I'll definitely look into this when it comes out.