I would rather see politics at LW done in a way that playfully respects the complications that are obvious, and ends up doing something surprising and hopefully awesome. Let me see if I can develop this a bit...
Imagine starting with a pool of people who think their brains are turbo-charged and who "enjoy the possibility of discussing political topics in a 'rational' atmosphere (truth-searching, not us-vs-them, aware of biases and fallibility, etc.)". If they're really actually rational, you'd kind of expect them to be able to do things like Aumann update with people with similar capacities and inclinations but different conclusions on a given hot-button political subject. So the trick would be to find two people whose starting points on a political topic was radically different and have them be each other's chavutra, and discuss the subject with each other until they either agree on the relevant and substantive facts or agree to disagree.
Now, maybe this is just me, but it seems to me that having chavutra discussions in a public forum would introduce all kinds of signalling complications and potentially cause negative externalities if other people run into it without adequate background. To avoid both problems, it seems like it would be better to do this via the phone, or IM, or email. IM and email would be easier to log, but voice would probably be helpful for issues of tone and hashing out a common vocabulary fast.
I would expect this to be quite educational. Also I think it would be neat to read a joint write-up of how it went afterwards, where the reader finds out about the initial dramatically different opinions, and hears about the sort of higher level surprises came up in the process itself: how long it took, what was helpful, what was learned in general.
I'd personally prefer not to hear the details of the final conclusion other than the single yes/no bit about whether agreement was reached or not, because I would expect it would re-introduce signaling issues into the discussion itself, make future updates harder, and sort of implicitly suggest to the community and the wider world that these two people's conclusion is "endorsed by all reasonable people in general". (Which suggests a second order thing to try: have two pairs of people update on the same subject and then compare each pair's agreements...)
It would be pretty awesome if LW had a thread every so often where people broadcasted interest in finding an "aumann chavutra" for specific topics, including political topics. This might help with people specific "dialogue cravings". It might eventually start clogging up the site itself (the way meetup posts clogged things up for a while) but that seems like it would be a good problem to have to solve :-)
The reason why I am not optimistic about this sort of thing is because many people know someone clever who has radically different political opinions from them, and they often talk about politics quite a bit. So those sort of Aumann updates often happen, but they often end at a stance like "we both understand each other's opinions of the facts, but have different value systems, and so disagree" or something like "we both assign the same likelihood ratio to evidence, but have very different priors."
Summary: I propose we somewhat relax our stance on political speech on Less Wrong.
Related: The mind-killer, Mind-killer
A recent series of posts by a well-meaning troll (example) has caused me to re-examine our "no-politics" norm. I believe there has been some unintentional creep from the original intent of Politics is the Mind-Killer. In that article, Eliezer is arguing that discussions here (actually on Overcoming Bias) should not use examples from politics in discussions that are not about politics, since they distract from the lesson. Note the final paragraph:
So, the original intent was not to ban political speech altogether, but to encourage us to come up with less-charged examples where possible. If the subject you're really talking about is politics, and it relates directly to rationality, then you should be able to post about it without getting downvotes strictly because "politics is the mind-killer".
It could be that this drift is less of a community norm than I perceive, and there are just a few folks (myself included) that have taken the original message too far. If so, consider this a message just to those folks such as myself.
Of course, politics would still be off-topic in the comment threads of most posts. There should probably be a special open thread (or another forum) to which drive-by political activists can be directed, instead of simply saying "We don't talk about politics here".
David_Gerard makes a similar point here (though FWIW, I came up with this title independently).