I don't get all the criticism of PUAs, submitter B mentions them but doesn't provide any elaborate arguments and I don't think it's fair to compare them to gay converters(gay converters want to change other people PUAs don't, on the contrary they accept woman exactly how they are). In effect PU is understanding how women work and adjusting your behavior to become attractive to them. Could you be more specific in what exactly is wrong with them?

The strategy I have been considering in my attempt to prove a paradox inconsistent is to prove a contradiction using the problem formulation.

This seems like a worthy approach to paradoxes! I'm going to suggest the possibility of broadening your search slightly. Specifically, to include the claim "and this is paradoxical" as one of the things that can be rejected as producing contradictions. Because in this case there just isn't a paradox. You take the one box, get rich and if there is a decision theory that says to take both boxes you get a better theory. For this reason "Newcomb's Paradox" is a misnomer and I would only use "Newcomb's Problem" as an acceptable name.

In Newcomb's problem, suppose each player uses a fair coin flip to decide whether to one-box or two-box. Then Omega could not have a sustained correct prediction rate above 50%. But the problem formulation says Omega does; therefore the problem must be inconsistent.

Yes, if the player is allowed access to entropy that Omega cannot have then it would be absurd to also declare that Omega can predict perfectly. If the coin flip is replaced with a quantum coinflip then the problem becomes even worse because it leaves an Omega that can perfectly predict what will happen but is faced with a plainly inconsistent task of making contradictory things happen. The problem specification needs to include a clause for how 'randomization' is handled.

Alternatively, Omega knew the outcome of the coin flip in advance; let's say Omega has access to all relevant information, including any supposed randomness used by the decision-maker. Then we can consider the decision to already have been made; the idea of a choice occurring after Omega has left is illusory (i.e. deterministic; anyone with enough information could have predicted it.)

Here is where I should be able to link you to the wiki page on free will where you would be given an explanation of why the notion that determinism is incompatible with choice is a confusion. Alas that page still has pretentious "Find Out For Yourself" tripe on it instead of useful content. The wikipedia page on compatibilism is somewhat useful but not particularly tailored to a reductionist decision theory focus.

In this case of the all-knowing Omega, talking about what someone should choose after Omega has left seems mistaken. The agent is no longer free to make an arbitrary decision at run-time, since that would have backwards causal implications; we can, without restricting which algorithm is chosen, require the decision-making algorithm to be written down and provided to Omega prior to the whole simulation. Since Omega can predict the agent's decision, the agent's decision does determine what's in the box, despite the usual claim of no causality. Taking that into account, CDT doesn't fail after all.

There have been attempts to create derivatives of CDT that work like that. That replace the "C" from conventional CDT with a type of causality that runs about in time as you mention. Such decision theories do seem to handle most of the problems that CDT fails at. Unfortunately I cannot recall the reference.

I would love to hear from someone in further detail on these issues of consistency. Have they been addressed elsewhere? If so, where?

I'm not sure which further details you are after. Are you after a description of Newcomb's problem that includes the details necessary to make it consistent? Or about other potential inconsistencies? Or other debates about whether the problems are inconsistent?

Also,

Experiments have shown that many people prefer (1A) to (1B) and (2B) to (2A)...So independence implies that anyone that prefers (1A) to (1B) must also prefer (2B) to (2A).

Shouldn't independence have people who prefer (1A) to (1B) prefer (2A) to (2B)?

EDIT:

But because the direct approach is very recent (Peterson 2008; Cozic 2011), and only time will show whether it can stand up to professional criticism.

Either the word "because" or "and" is out of place here.

I only notice these things because this FAQ is great and I'm trying to understand every detail that I can.

If I understand correctly, Peterson is defining "acts" and "risky acts" as completely separate things (functions from states to outcomes, and lotteries over outcomes, respectively). If that's true, it clears up the confusion, but that seems like extraordinarily bad terminology.

Either Peterson does things wrong, you're misunderstanding Peterson, or I'm misunderstanding you. When I have time, I'll look at that book to try to figure out which, unless you manage to sort things out for me before I get to it.

In what ways does this differ from Nozick's recommendation in Nature of Rationality where he combines the results from EDT and CDT but gives them different weights depending on the priors (about the applicability to the situation and truth value of each decision theory)?

Perhaps worth noting that earlier in the document we defined acts as functions from world states to outcomes so this seems to resolve the second concern somewhat.

What? That's what I thought "acts" meant the first time, before I read the document more thoroughly and decided that you must mean that acts are lotteries. If you are using "act" to refer to functions from world states to outcomes, then the statement that the VNM system only applies to acts is simply false, rather than misleading.

Oops, you are absolutely right. (a-b)/|c-d| is meaningful after all. Not sure why I failed to notice that. Thanks for pointing that out.

Perhaps worth noting that earlier in the document we defined acts as functions from world states to outcomes so this seems to resolve the second concern somewhat.

What? That's what I thought "acts" meant the first time, before I read the document more thoroughly and decided that you must mean that acts are lotteries. If you are using "act" to refer to functions from world states to outcomes, then the statement that the VNM system only applies to acts is simply false, rather than misleading.

The problem is with the word "acts". Some lotteries might not be achievable by any act, so this phrasing makes it sound like the VNM only applies to the subset of lotteries that is actually possible to achieve. And I realize that you're using the word "act" more specifically than this, but typically, people consider doing the same thing in a different context to be the same "act", even though its consequences may depend on the context. So when I first read the paragraph I quoted after only skimming the rest, it sounded like it was claiming that the VNM system can only describe deontological preferences over actions that don't take context into account, which is, of course, ridiculous.

Also, while it is true that the VNM system defines utility over lotteries, it is fairly trivial to modify it to use utility over outcomes (see first section of this post)