CurtAdams@aol.com wrote:
> >If there are constraints on what beliefs are rational, then upon discovering
> >that your beliefs violate those constraints, you should want to change
> >your beliefs to avoid those violations. This sort of change seems
> >perfectly rational to me, even if it violates a naive Bayesianism.
>
> Bayesianism is a certain process for updating beliefs based on evidence.
> Maintaining your priors isn't a part of "naive" Bayesianism; it's an
> essential part of Bayesianism, period. Change your beliefs any other way and
> you're bookable. If your claim is that Bayesians are naive and you have a
> better way, fine, but a) that needs justification and b) be upfront about it.
You are in essence arguing that there can be no further constraints on
what beliefs are rational than standard probability coherence and updating
by conditionalization. Your argument is that if you found that your beliefs
violated some constraint, you could not change your beliefs to avoid the
violation because doing so would violate conditionalization. Once you
have some beliefs the only rational thing to do is conditionalize, no matter
what.
This flies in the face of a long philosphy literature considering further
constraints on rational beliefs. And I think it takes a good idea too far.
Violating conditionalization only opens you to a dutch book if you do it
in a predictable way. Your expectation of your future belief must equal
your conditional belief, but a non-zero variance is allowed around this.
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