If you find yourself thinking about the differences between geometric expected utility and expected utility in terms of utility functions, remind yourself that, for any utility function, one can choose* either* averaging method.

No, you can only use the geometric expected utility for nonnegative utility functions.

It's obvious to us that the prompts are lying; how do you know it isn't also obvious to the AI? (To the degree it even makes sense to talk about the AI having "revealed preferences")

Calvinists believe in predestination, not Protestants in general.

Wouldn't that mean every sub-faction recursively gets a veto? Or do the sub-faction vetos only allow the sub-faction to veto the faction veto, rather than the original legislation? The former seems unwieldy, while the latter seems to contradict the original purpose of DVF...

(But then: aren’t there zillions of Boltzmann brains with these memories of coherence, who are making this sort of move too?)

According to standard cosmology, there are also zillions of actually coherent copies of you, and the ratio is heavily tilted towards the actually coherent copies under any reasonable way of measuring. So I don't think this is a good objection.

“Only food that can be easily digested will provide calories”

That statement would seem to also be obviously wrong. Plenty of things are ‘easily digested’ in any reasonable meaning of that phrase, while providing ~0 calories.

I think you've interpreted this backwards; the claim isn't that "easily digested" implies "provides calories", but rather that "provides calories" implies "easily digested".

In constructivist logic, proof by contradiction must construct an example of the mathematical object which contradicts the negated theorem.

This isn't true. In constructivist logic, if you are trying to disprove a statement of the form "for all x, P(x)", you do not actually have to find an x such that P(x) is false -- it is enough to assume that P(x) holds for various values of x and then derive a contradiction. By contrast, if you are trying to prove a statement of the form "there exists x such that P(x) holds", then you do actually need to construct an example of x such that P(x) holds (in constructivist logic at least).

Just a technical point, but it is not true that most of the probability mass of a hypothesis has to come from "the shortest claw". You can have lots of longer claws which together have more probability mass than a shorter one. This is relevant to situations like quantum mechanics, where the claw first needs to extract you from an individual universe of the multiverse, and that costs a lot of bits (more than just describing your full sensory data would cost), but from an epistemological point of view there are many possible such universes that you might be a part of.

As I understood it, the whole point is that the buyer is proposing C as an alternative to A and B. Otherwise, there is no advantage to him downplaying how much he prefers A to B / pretending to prefer B to A.

Hmm, the fact that C and D are even on the table makes it seem less collaborative to me, even if you are only explicitly comparing A and B. But I guess it is kind of subjective.