I'm not very sanguine about our prospects there. It might be possible, but I've never seen anyone else do it -- there are relatively civil politics boards without limits on scope, but all the ones I'm aware of got that way by effectively banning dissension or by being small enough that the users all know and trust each other. Neither one's practical for LW, and our existing methodology is obviously inadequate.
Well, the journey of a thousand miles and all that... :-)
In LW it could be a rationalist dojo: "So you think you can rationally discuss what the government should do about late-term abortions? SHOW ME!" :-D
LW is already a step above the usual 'net forums. I haven't seen exhortations to think of the children, no one called anyone a traitor recently, direct personal attacks are strongly discouraged, etc.
One of my favourite Less Wrong articles is Politics is the mindkiller. Part of the reason that political discussion so bad is the poor incentives - if you have little chance to change the outcome, then there is little reason to strive for truth or accuracy - but a large part of the reason is our pre-political attitudes and dispositions. I don't mean to suggest that there is a neat divide; clearly, there is a reflexive relation between the incentives within political discussion and our view of the appropriate purpose and scope of politics. Nevertheless, I think it's a useful distinction to make, and so I applaud the fact that Eliezer doesn't start his essays on the subject by talking about incentives, feedback or rational irrationality - instead he starts with the fact that our approach to politics is instinctively tribal.
This brings me to Joseph Bottum's excellent recent article in The American, The Post-Protestant Ethic and Spirit of America. This charts what he sees as the tribal changes within America that have shaped current attitudes to politics. I think it's best seen in conjunction with Arnold Kling's excellent The Three Languages of Politics; while Kling talks about the political language and rhetoric of modern American political groupings, Bottum's essay is more about the social changes that have led to these kinds of language and rhetoric.
Video of a related lecture can also be found here.