Have you read An Intuitive Explanation of Bayes' Theorem, or any of the other explanations of Bayesian reasoning on this site?
I have read them repeatedly, and explained the concepts to others on multiple occassions.
If you have a buddy who is a football buff who tells you that the Sportington Sports beat the Homeland Highlanders last night, then you should treat this as evidence that the Sportington Sports won,
Not until such time as you have a reason to believe that he has a justification for his belief beyond mere opinion. Otherwise, it is a mere assertion regardless of the source -- it cannot have a correlation to reality if there is no vehicle through which the information he claims to have reached him other than his own imagination, however accurate that imagination might be.
You do not need the person to relate their assessment of the evidence to revise your belief upward based on their statement, you only need to believe that it is more likely that they would make the claim if it were true than if it were not.
Which requires a reason to believe that to be the case. Which in turn requires that you have a means of corroborating their claim in some manner; the least-sufficient of which being that they can relate observations that correlate to their claim, in the case of experts that is.
If you want to increase the reliability of your probability estimate, you should ask for a justification.
A probability estimate without reliability is no estimate. Revising beliefs based on unreliable information is unsound. Experts' claims which cannot be corroborated are unsound information, and should have no weighting on your estimate of beliefs solely based on their source.
If an expert's claims are frequently true, then it can become habitual to trust them without examination. However, trusting individuals rather than examining statements is an example of a necessary but broken heuristic. We find the risk of being wrong in such situations acceptable because the expected utility cost of being wrong in any given situation, as an aggregate, is far less than the expected utility cost of having to actually investigate all such claims.
The more such claims, further, fall in line with our own priors -- that is, the less 'extraordinary' the claims appear to be to us -- the more likely we are to not require proper evidence.
The trouble is, this is a failed system. While it might be perfectly rational -- instrumentally -- it is not a means of properly arriving at true beliefs.
I want to take this opportunity to once again note that what I'm describing in all of this is proper argumentation, not proper instrumentality. There is a difference between the two; and Eliezer's many works are, as a whole, targetted at instrumental rationality -- as is this site itself, in general. Instrumental rationality does not always concern itself with what is true as opposed to what is practically believable. It finds the above-described risk of variance in belief from truth an acceptable risk, when asserting beliefs.
This is an area where "Bayesian rationality" is insufficient -- it fails to reliably distinguish between "what I believe" and "what I can confirm is true". It does this for a number of reasons, one of which being a foundational variance between Bayesian assertions about what kind of thing a Bayesian network is measuring when it discussed probabilities as opposed to what a frequentist is asserting is being measured when frequentists discuss probabilities.
I do not fall totally in line with "Bayesian rationality" in this, and various other, topics, for exactly this reason.
Not until such time as you have a reason to believe that he has a justification for his belief beyond mere opinion. Otherwise, it is a mere assertion regardless of the source -- it cannot have a correlation to reality if there is no vehicle through which the information he claims to have reached him other than his own imagination, however accurate that imagination might be.
If you know that your friend more often makes statements such as this when they are true than when they are false, then you know that his claim is relevant evidence, so you should adj...
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.