The example of stochastic evidence is indeed interesting. But I find myself stuck on the first example.
If a new reasoner C were to update Pc(X) based on the testimony of A, and had an extremely high degree of confidence in her ability to generate correct opinions, he would presumably strongly gravitate towards Pa(X).
Alternatively, suppose C is going to update Pc(X) based on the testimony of B. Further, C has evidence outlining B's apathetic proclivities. Therefore, he would presumably only weakly gravitate towards Pb(X).
The above account may be shown to be confused. But if it is not, why can C update based on evidence of infomed-belief, but A and B are precluded from similarly reflecting on their own testimony? Or, if such introspective activity is not non-normative, should they not strive to perform such an activity consistently?
Okay. I'm assuming everyone has the same prior. I'm going to start by comparing the case where C talks to A and learns everything A knows, to the case where C talks to B and learns everything B knows; that is, when C ends up conditioning on all the same things. If you already see why those two cases are very different, you can skip down to the second section, where I talk about what this implies about how C updates when just hearing that A knows a lot and what Pa(X) is, compared to how he updates when learning what B thinks. It's the same scenario as you d...
Previously: round 1, round 2, round 3
From the original thread:
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