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 preferences. 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 encompassing. 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 an action. 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 nature. 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 response. 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. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/HDdICaBPZTgJ. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
