I propose that the key elements of a rational conversation are (where "you" refers collectively to all participants):

you must use only documented reasoning processes: using the best known process(es) for a given class of problem stating clearly which particular process(es) you use documenting any new processes you use

making every reasonable effort to verify that:

your inputs are reasonably accurate, and there are no other reasoning processes which might be better suited to this class of problem, and there are no significant flaws in in your application of the reasoning processes you are using, and there are no significant inputs you are ignoring

This definition seems to imply that something can only be rational if an immense amount of time and research is dedicated to it. But I can say something off the cuff, with no more of a reasoning process than "this was the output of my black-box intuition", and be rational. All that's required is that my intuition was accurate in that particular instance, and I reasonably expected it to be accurate with high enough probability relative to the importance of the remark. See How Much Thought.