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Caledonian: What fundamental principles? As far as I can tell the only fundamental principle is that it has to work. But I'm open to counterexamples, if you are.
The recognition of what 'working' is, and the tools that have been found useful in reaching that state, is what constitutes the scientific method.
The scientific method is actually pretty specific - and it is not a set of tools. There is no systematic method of advancing science, no set of rules/tools which are exclusively the means to attaining scientific knowledge.
Scientists do not concern themselves with what philosophers say about science -- it is my experience that they are actively contemptuous of such. . . It's almost as though the philosophers didn't know what they were talking about.
That's actually my point. Scientists do what works, and employ methodological diversity - the "scientific method" is not an actual description of how real scientists do their work, nor how real science has advanced. It's propaganda, made up by certain people who were/are absolutely horrified that science has no defining and fundamental underlying principles - which would throw their entire schema of epistemology into turmoil.
The "rules" of science, if they exist, are subject to change at any time. Science has physical reality at the input and useful models at the output - and no bona fide, tried and true, structure in between.
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Interesting stuff. I am all for trying to improve peoples reasoning skills, and understanding how particular people think initially is a good place to start, but I'm a bit concerned about the way you talked about knowledge in here (and where it comes from).
Frankly, I wouldn't really look to any person as a source of knowledge in the way you seem to be implying here.
Here's how knowledge & experts work: There's a whole bunch of information out there - literally more than any one person could/cares to know - and we simply don't have the time (or often the background) to fully understand certain fields and more importantly to evaluate which claims are true and which aren't. Experts are people who do have the background in a given field, and they usually know what research has been done in their field and can answer questions/make statements with legitimate authority when speaking on the subject with which they are well versed. Once you have a consensus of opinion between many such experts, you have raised the authority of that opinion further because you've reduced the likelihood of one guy misspeaking, making stuff up, being dishonest, etc. Also note that experts talking on subjects outside of their field of study have no more authority than anyone else (though they often are well informed on other subjects) - this is where the argument from authority fallacy comes from, e.g. "Einstein said that the sky is green" ... so what?
I suspect you know all of this already (I don't mean to come off as lecturing too much, just reiterating some baseline stuff)
After all that rambling about experts, the important thing to take away is that the knowledge (and by knowledge in this context I mean being aware of information which corresponds with reality, i.e. the truth) doesn't come from the experts; experts are just the people who go about investigating the truth and report back to the rest of humanity what they've found. In other words, reality is objective and claims should be evaluated based on their evidence, not the person who proposes them.
All of the examples you've used deal with things which actually do have an objective answer, whether or not we have or feasibly can test them empirically. (also, as a side note, that bit about the 50% chance of being true is ridiculous even if you don't have any knowledge going into it - you would simply say "I don't know if these claims are true")
People definitely have biases, and we should be particularly cautious when dealing with any claims that are related to contentious issues. Further, I'd like to stress the point that just because a large majority of the experts in a field say something it doesn't make it true - but it does mean that we should believe that it is true until new information says otherwise, because frankly an expert consensus is one of the highest certainties we can come up with as a species.
I guess the main thing I am trying to say that directly ties into your post is that we shouldn't really care how someone formed their beliefs when evaluating the veracity of a claim; when we should care is:
When we suspect that a bias may have lead to a false reporting of real information (in which case we would want independent, unbiased research/reporting)
When we want to change someone's mind about something
When we want to keep someone's faulty & infectious belief structure from propagating to other people (ex. Dark Side Epistemology) by teaching other people critical thinking/rationality and common mistakes like said structure.
Still, figuring out how people think has always been an interesting area of science that is worth pursuing, and the tools/sample size have gotten a lot bigger since the time of case studies. I hope you find more interesting stuff to share.