However, what about the prior probability of a good-faith statement in presence of a strong conflict of interest? Having no ability to directly verify the truth, wouldn’t you require stronger evidence if you were to rely on that statement in your decision-making?
The definition of your prior would incorporate that.
>Having no ability to directly verify the truth, wouldn’t you require stronger evidence if you were to rely on that statement in your decision-making?
That is exactly the purpose of priors and Bayesian belief systems. If you could verify any truth, you'd not need a prior or Bayesian probability concepts for that.
In none of these cases do you change the prior after some evidence is obtained, You'd use the prior and Bayesian update to make a new belief, which is then the prior for making decisions as future evidence is obtained.
Retroactively changing the prior is demonstrably bad at reaching the proper conclusions over time. E.T. Jaynes "Probability Theory" [1] has detailed proofs of all of this, covered in the first few chapters.
[1] https://www.cambridge.org/core/books/probability-theory/9CA0...