> There are people who argue that having cyclic preferences is not only rational, but even sometimes the only rational representation of evaluations.

Wouldn't be the first time otherwise serious people are defending nonsense. Noted nonetheless.

> It is perfectly possible to make rational decisions with cyclic preferences.

It is perfectly possible to make rational decision while being insane. Just, not all decisions will be rational. Cyclic preferences are not insane with respect to all decision, but they do mean the decision system as a whole is not flawless.

While the absence of cyclic preferences is of course not sufficient for perfect rationality, it's obviously required.

> By the way, Expected Utility falls prey to Dutch Books. There is a money pump against every risk-averse or risk-seeking agent.

Well, if you're not evaluating risks correctly to begin with, of course you're gonna get ripped off (I'm not saying that's a good thing). Being either risk seeking or risk averse looks like a flaw too, though perhaps less severe than cyclic preferences.

> There is a vast array of literature on qualitative decision making for which this assumption does not hold.

Wait a minute, this one is only talking about epistemology. Jaynes does not mention utility functions at all, and for all I know those may still be allowed to be discontinuous. (That would be perhaps a bit surprising, but I have yet to have an opinion on that particular point.)

Discontinuous probabilities, that would be more surprising. Though I reckon this continuity business is the weak link here. It would be nice if we didn't have to assume it.

> even in probabilistic settings it completely controversial how to deal with conflicting evidence and how and when to revise beliefs in the face of evidence that directly conflicts with your existing beliefs.

There are lots of reason why a piece of data might not change one's mind, even if that piece of data seems to contradict their beliefs directly. For instance that piece of evidence might have been cherry piked from a mass of otherwise normal data.

Not even acknowledging the piece of data might be a good approximation in some cases, but in general it seems quite foolish. You don't just ignore a piece of evidence, you explain why it doesn't change your mind. (I believe Jaynes gives examples of beliefs diverging when exposed to the same piece of evidence.)

> But you seem to be hell-bent on taking Jayne's book as some sort of bible, which is weird.

Call it confirmation bias, but when I read that book, I already subscribed to probability theory as the correct way to think. I had for a long time. The intuition of probabilities being degrees of beliefs, I had for as long as I can remember.

Then this book comes up, and provide justifications for my intuitions that were even stronger than I anticipated. It's like suspecting there's a giant bearded man behind that cloud, and then actually see it. And take a photo, and show it to your friends. Perhaps not foolproof, but pretty damn close.

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Now we still have a problem. Jayne's Robot cannot exist. I mean, that would be something like AIXI, that's not tractable. Probability theory is not tractable (we wouldn't have Monte Carlo methods if it were, we'd just compute the probabilities directly). Any inference engine that runs in the real world (like humans), has to be imperfect. We have to take shortcuts, and from them, flawed reasoning will arise.

There's also the problem that thinking has a cost. It takes time and energy, and with those, utility. So not only a real engine will have flaws, it also needs to evaluate whether minimising those flaws is worth the trouble (and that evaluation also costs some thinking).

To take a concrete example, the first Alpha Go program lost one of its games in part because it failed to take more time in a particularly hard to evaluate game state. It was obvious to top human players that this particular move required more thought than usual, but the machine wasn't programmed that way.

As certain as I am that probability theory is the correct ideal to attain, I also have to admit that it is just that: an impossible ideal. How to instantiate that ideal into a good enough working implementation, I have no freaking clue.