Only in the sense that you’ve said things that contradict one another. You said that knowing that you’re listening to CA modifies your prior estimate of P(his preferred conclusion) from the outset, and then you said that actually if you stop him speaking immediately then your prior shouldn’t be modified. These can’t both be right.
I don’t see any way to make the “modified prior” approach work that doesn’t amount to doing the same calculations you’d do with the “modified estimation of evidence provided by each point made” approach and then hacking the results back into your prior to get the right answer, and I don’t see any reason for preferring the latter.
Of course, as a practical matter, and given the limitations of our reasoning abilities, prior-tweaking may be a useful heuristic even though it sometimes misleads. But, er, “useful heuristics that sometimes mislead” is a pretty good characterization of what’s typically just called “bias” around here :-).
Only in the sense that you’ve said things that contradict one another. You said that knowing that you’re listening to CA modifies your prior estimate of P(his preferred conclusion) from the outset, and then you said that actually if you stop him speaking immediately then your prior shouldn’t be modified. These can’t both be right.
I don’t see any way to make the “modified prior” approach work that doesn’t amount to doing the same calculations you’d do with the “modified estimation of evidence provided by each point made” approach and then hacking the results back into your prior to get the right answer, and I don’t see any reason for preferring the latter.
Of course, as a practical matter, and given the limitations of our reasoning abilities, prior-tweaking may be a useful heuristic even though it sometimes misleads. But, er, “useful heuristics that sometimes mislead” is a pretty good characterization of what’s typically just called “bias” around here :-).