I almost dread entering into this discussion, but I think it should be
pointed out that this discussion occurs in various forms in both Leonard
Jimmie Savage's "Foundations of Statistics" and E T Jaynes "Probability
Theory." I would also point out that you are missing key elements of both
the non-mathematical discussion of rationality (such as that from
neuroscience) and the mathematical discussion of the properties of utility
functions upon which a discussion of rationality must set. There are
probably a dozen good and separate formalizations of utility, the major
ones are of course von Neumann's, Savages, Thaler's and Machina's.
Savage really formalized the discussion on "personalistic" statistics, but
I really think you need to go back and look at both the axiomization he
uses and the proofs. Likewise, ET Jaynes really covers much of your
discussion quite early on in his book. Another person to consider is
Moesteller, though I cannot remember where at the moment. If it comes to
me, I will post it.
Finally, there is an empiricism issue here.
I take some of the comments here as mistaking the model for the reality it
models. Models are valuable, by the definition of "valuable", only to the
extent they provide utility. It follows from heterogeneous preferences
that any discussion like this is foreclosed by the actors personal
Let us take some Bayesian mathematical construction as both all
encompassing AND valid for the problem of reasoning. This does not mean
alternate constructions are invalid nor does it mean others cannot be all
It is dangerous to do mathematical reasoning by analogy, though it is
valuable for the purpose of thrashing out the problem.
A second danger to your discussion is that it is confusing intuition with
If intuition is seen as a set of perceptions following a stimulus given a
state of the brain, then Bayesian reasoning must not only follow from it,
but intuition creates a difference in the brain between the perceived
likelihood function and the likelihood function actually happening in
It does not seem rational to treat intuition as a rational process.
Indeed, it is difficult to impossible to imagine intuition as "rational."
Rather it is a form of pattern association. Bayesian reasoning must be
framed in it, but it would be formulated either as a bias function in the
registering of the likelihood or as part of the prior. That is a very old
discussion in psychology going back at least into the 1920's. Brain scan
studies on people whose brains prefer intuitive over concrete responses
show that those that prefer concrete responses have high levels of activity
in the limbic system with localized responses on the cortex while those who
prefer intuitive response show very generalized response on the cortex.
Put simply a person observing the details of the concrete response is not
seeing the same perception as the person providing a more intuitive
It is important to note that perception must be irrational.
I think this discussion partly exists because there are parts of the
formalization that are taken as "well behaved" that when forgotten about
raise questions. I think you need to go back to the basics first and this
discussion will solve itself.
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