> No, I was not speaking from a Bayesian perspective, I was laying out the propensity-theoretic explanation of probability.

Unless you can explain this "propensity" in terms of actual physical properties, propensity by itself is… unjustified. The only domain I know of so far where we could possibly argue propensities are a thing is quantum mechanics. And even then it seems to rest on an anthropic argument: which universe am I living in?

> Some people think that you need to explain why a die can be fair,

A die by itself is not fair, right? A die might be balanced, and the way it is thrown it might have enough unpredictable variability to cause everyone in the room to think "uniform distribution over [1..6]".

Likewise, a cryptographic pseudo random generator is unpredictable (and thus "fair"), to anyone who doesn't know its internal state. Even though the process itself is deterministic, it's just not computationally feasible to guess its output just from the observation of past inputs. (Though for this one I'm relying on the fact we're not logically omniscient.)

> I'm an expert on this topic.

Good. Then you know that any inference strategy that falls prey to Dutch Books is not rational. Right?

To be fair, probability theory is not computationally tractable. I did not verify, but I guess any feasible approximation is vulnerable to some more or less subtle Dutch Books.

Now the way you talk about Dutch Books sound like all the other strategies you mention are vulnerable, not just in practice, but in theory as well. They are thus not perfectly rational. Do their authors at least have the grace to admit this is a flaw that should be corrected?

But then I suspect that correcting the flaw inevitably leads to probability theory itself: if you accept Jaynes three "desiderata" as required for any kind of rational reasoning, as he shows, the result is necessarily equivalent to probability theory as we know it (where probabilities are subjective assessments of plausibility, otherwise known as "degrees of belief").

I can only conclude that you do not accept Jayne's desiderata as necessary for correct inference. And this is the point where I look at you like you're not quite sane.

For reference, Jaynes Desiderata:

(1) Degrees of plausibility are represented by real
numbers. (And a continuity assumption.)

(2) Qualitative correspondence with common sense.
(explained in more detailed in the book)

(3a) If a conclusion can be reasoned out in more than
one way, then every possible way must lead to the
same result.

(3b) The robot always takes into account all of the
evidence it has relevant to a question. It does
not arbitrarily ignore some of the information,
basing its conclusions only on what remains. In
other words, the robot is completely non
ideological.

(3c) The robot always represents equivalent states of
knowledge by equivalent plausibility assignments.
That is, if in two problems the robot’s state of
knowledge is the same (except perhaps for the
labeling of the propositions), then it must assign
the same plausibilities in both.

Good luck convincing me (and I suspect, the majority of people, including frequentist statisticians), that we should reject any of these desiderata.

I don't care it's reverse engineering, those desiderata match the way I think. I accept the conclusion that probability theory is the correct (albeit intractable) way to think, because I ultimately agree with the postulates it rests on. Vehemently so. They're not just true, they're obvious.

If you don't accept them, then I can only give up, and remember what Yudkowsky once wrote: "How do you argue a rock into becoming a mind?"