Taking that common starting point and "all of life" as the evidence, it seems likely that differences in opinion could take days or weeks or months of discussion to resolve, rather than 10 minutes of rhetorical hand waving.
All of our lives, or even a month of it, probably imparted to us far more evidence than we could explain to each other in a month of discussion. The trouble is that much of the learning got lodged in memory regions that are practically inaccessible to the verbal parts of our brains. I can't define Xs and you can't define Ys, but we know them when we see them.
"We just have different priors" is probably not the best way to describe these cognitive differences - I agree with you there. But we could still be at a loss to verbally reason our way through them.
I don't think people have any sort of capacity to fully describe their entire audio/video experience in full resolution, but if you think about the real barriers to more limited communication I predict that you'll be able to imagine plausible attempts to circumvent these barriers for the specific purpose of developing a model of a particular real world domain in common with someone with enough precision to derive similar strategic conclusions in limited domains.
I can't define Xs and you can't define Ys, but we know them when we see them.
Maybe I'm misun...
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).