<i>I propose a discussion system, where the rules are strictly enforced meaning on breaking them some number of times, after several warnings you are ejected from the discussion.</i><p>This seems to be a step backwards; instead of educating the debaters on a fluid congress of debate, it sets up hurdles and penalizes offenders. Ultimately, I think the recursive method of argument will result in cyclical hashes of thought, without the finality of debate providing an impetus for resolution.
If we're genuinely concerned about problem solving, why not use the scientific method?
Define the issues to be resolved, then each party proposes their hypothesis.
Then a moderator, who knows the issues ahead of time (and has information along with statistics about the subject), can keep the "testing/experimenting" phase on track.
Maybe even a whiteboard with notes so we can keep track of what each party proposed while allowing us the ability to make revisions.