I don’t have much to add on the original question, but I do disagree about your last point:
In fact, any kind of second-order probability must be trivial. We have introspective access to our own beliefs. So given any statement about our beliefs we can say for certain whether or not it’s true. Therefore, any second-order probability will either be equal to 0 or 1.
There is a sense in which, once you say “my credence in X is Y”, then I can’t contradict you. But if I pointed out that actually, you’re behaving as if it is Y/2, and some other statements you made implied that it is Y/2, and then you realise that when you said the original statement, you were feeling social pressure to say a high credence even though it didn’t quite feel right—well, that all looks a lot like you being wrong about your actual credence in X. This may end up being a dispute over the definition of belief, but I do prefer to avoid defining things in ways where people must be certain about them, because people can be wrong in so many ways.
Okay, sure. But an idealized rational reasoner wouldn’t display this kind of uncertainty about its own beliefs, but it would still have the phenomenon you were originally asking about (where statements assigned the same probability update by different amounts after the introduction of evidence). So this kind of second-order probability can’t be used to answer the question you originally asked.
I don’t have much to add on the original question, but I do disagree about your last point:
There is a sense in which, once you say “my credence in X is Y”, then I can’t contradict you. But if I pointed out that actually, you’re behaving as if it is Y/2, and some other statements you made implied that it is Y/2, and then you realise that when you said the original statement, you were feeling social pressure to say a high credence even though it didn’t quite feel right—well, that all looks a lot like you being wrong about your actual credence in X. This may end up being a dispute over the definition of belief, but I do prefer to avoid defining things in ways where people must be certain about them, because people can be wrong in so many ways.
Okay, sure. But an idealized rational reasoner wouldn’t display this kind of uncertainty about its own beliefs, but it would still have the phenomenon you were originally asking about (where statements assigned the same probability update by different amounts after the introduction of evidence). So this kind of second-order probability can’t be used to answer the question you originally asked.
FYI there’s more about “credal resilience” here (although I haven’t read the linked papers yet).