Also, I should make it clear that either/both approaches can be rational and that I am not advocating for any particular approach. My complaint, as I have stated several times now, is that you have grossly misrepresented what minimax can accomplish under the circumstances that you laid out. If you had done the same thing with a Bayesian approach, I would have the same complaint.
I do not think I have misrepresented what minimax can accomplish under the circumstances. What have I said that you think is a grossly misrepresention? Are you sure you haven't simply misunderstood what I've said about it? Your comments regarding minimax don't indicate much depth of understanding on your part.
fls said:
Damn. It finally all made sense and now you've gone and spoilt it.
I've been saying all along I find different approaches equally rational. You're the one who's been saying that mine isn't rational. I've never said that yours wasn't. I don't see it as a one size fits all, but try to select the approach I think will work best. Clearly you do too. That we disagree on which method would work best in this situation does not mean that one answer is right and the other wrong.
I don't really care whether or not we discuss other stuff. I just didn't want to get sidetracked from the main discussion by a red herring (since whether or not there are other reasonable approaches doesn't really speak to whether or not your approach is reasonable).
It would help me to understand what you consider reasonable and rational and what you don't. So far I have one example, the one we've been discussing. Another example would allow me to draw parallels and contrasts between them.
The frequency of true ideas in amongst all possible ideas? I suspect the ratio is something like one in a thousand, although I haven't put any real work into estimating it; I could easily be off by several orders of magnitude. But considering that those ideas that represent a much better ratio (maybe even as high as 50/50) would be excluded as the product of science (i.e. a different form of discovery), there's not going to be much to work with.
The frequency of true ideas in amongst all possible ideas? is not the question I was asking, though it does give me a glimmer of insight into your assessment of the probability.
This was a question I asked earlier in the thread. Let me see if can rephrase your answer to it in such a way that you agree with it, okay. That's a fairly good way to establish if I understand you correctly.
How is it you feel comfortable setting the probability of those particular "indistinguishable ideas" so close to a 0/1 distribution (indicating near certainty) that you find it very silly to use the choice of .5/.5 for such situations?
You feel that the probability of ANY "indistibuishable idea" being true is very very small because you feel the probability of any idea being true is very very small, thus you find the idea that I rate them at 50/50 is ludicrous.
Before I respond to this, I would like to know if this is an accurate statement of your position. Thanks.
Beth