Here's what may be tripping you up. Very often it doesn't even make sense for humans to pay attention to small bits of evidence, because we can't really process them very effectively. So for most bits of tiny evidence (such as most very weak appeals to authority) often the correct action given our limited processing capability is to simply ignore them. But this doesn't make them not evidence.
That's a given, and I have said exactly as much repeatedly. Reiterating it as though it were introducing a new concept to me or one that I was having trouble with isn't going to be an effective tool for the conversation at hand.
So, I'm confused about how you would believe that humans have limited enough processing capacity that this would be an issue but in an earlier thread thought that humans were close enough to being good Bayesians that Aumann's agreement theorem should apply. In general, the computations involved in an Aumann update from sharing posteriors will generally be much more involved than the computations in updating with a single tiny piece of evidence.
LessWrongers as a group are often accused of talking about rationality without putting it into practice (for an elaborated discussion of this see Self-Improvement or Shiny Distraction: Why Less Wrong is anti-Instrumental Rationality). This behavior is particularly insidious because it is self-reinforcing: it will attract more armchair rationalists to LessWrong who will in turn reinforce the trend in an affective death spiral until LessWrong is a community of utilitarian apologists akin to the internet communities of anorexics who congratulate each other on their weight loss. It will be a community where instead of discussing practical ways to "overcome bias" (the original intent of the sequences) we discuss arcane decision theories, who gets to be in our CEV, and the most rational birthday presents (sound familiar?).
A recent attempt to counter this trend or at least make us feel better about it was a series of discussions on "leveling up": accomplishing a set of practical well-defined goals to increment your rationalist "level". It's hard to see how these goals fit into a long-term plan to achieve anything besides self-improvement for its own sake. Indeed, the article begins by priming us with a renaissance-man inspired quote and stands in stark contrast to articles emphasizing practical altruism such as "efficient charity"
So what's the solution? I don't know. However I can tell you a few things about the solution, whatever it may be:
Whatever you may decide to do, be sure it follows these principles. If none of your plans align with these guidelines then construct a new one, on the spot, immediately. Just do something: every moment you sit hundreds of thousands are dying and billions are suffering. Under your judgement your plan can self-modify in the future to overcome its flaws. Become an optimization process; shut up and calculate.
I declare Crocker's rules on the writing style of this post.