Sounds like a neat idea! I've been looking for these kinds of "meta" approaches to political discussion, and this looks like a pretty good one I hadn't thought of!

An improvement might be to restrict the discussion to a topic narrower than "libertarians vs. liberals" or "christians versus atheists" - for example "labour laws", "immigration", "the documentary hypothesis", "morality of homsexuality", etc.

This looks like it'd have a much better likelihood-I-change-my-mind / invested-time ratio than an "ordinary" poltical debate.