FDT says you should not pay because, if you were the kind of person who doesn't pay, you likely wouldn't have been blackmailed. How is that even relevant? You are being blackmailed.

I'm quoting this because, even though it's wrong, it's actually an incredibly powerful naive intuition. I think many people who have internalized TDT/UDT/FDT-style reasoning have forgotten just how intuitive the quoted block is. The unstated underlying assumption here (which is unstated because Schwarz most likely doesn't even realize it is an assumption) is extremely persuasive, extremely obvious, and extremely wrong:

If you find yourself in a particular situation, the circumstances that led you to that situation are irrelevant, because they don't change the undeniable fact that you are already here.

This is the intuition driving causal decision theory, and it is so powerful that mainstream academic philosophers are nearly incapable of recognizing it as an assumption (and a false assumption at that). Schwarz himself demonstrates just how hard it is to question this assumption: even when the opposing argument was laid right in front of him, he managed to misunderstand the point so hard that he actually used the very mistaken assumption the paper was criticizing as ammunition against the paper. (Note: this is not intended to be dismissive toward Schwarz. Rather, it's simply meant as an illustrative example, emphasizing exactly how hard it is for anyone, Schwarz included, to question an assumption that's baked into their model of the world.) And if even if you already understand why FDT is correct, it still shouldn't be hard to see why the assumption in question is so compelling:

How could what happened in the past be relevant for making a decision in the present? The only thing your present decision can affect is the future, so how could there be any need to consider the past when making your decision? Surely the only relevant factors are the various possible futures each of your choices leads to? Or, to put things in Pearlian terms: it's known that the influence of distant causal nodes is screened off by closer nodes through which they're connected, and all future nodes are only connected to past nodes through the present--there's no such thing as a future node that's directly connected to a past node while not being connected to the present, after all. So doesn't that mean the effects of the past are screened off when making a decision? Only what's happening in the present matters, surely?

Phrased that way, it's not immediately obvious what's wrong with this assumption (which is the point, of course, since otherwise people wouldn't find it so difficult to discard). What's actually wrong is something that's a bit hard to explain, and evidently the explanation Eliezer and Nate used in their paper didn't manage to convey it. My favorite way of putting it, however, is this:

In certain decision problems, your counterfactual behavior matters as much--if not more--than your actual behavior. That is to say, there exists a class of decision problems where the outcome depends on something that never actually happens. Here's a very simple toy example of such a problem:

Omega, the alien superintelligence, predicts the outcome of a chess game between you and Kasparov. If he predicted that you'd win, he gives you $500 in reality; otherwise you get nothing.

Strictly speaking, this actually isn't a decision problem, since the real you is never faced with a choice to make, but it illustrates the concept clearly enough: the question of whether or not you receive the $500 is entirely dependent on a chess game that never actually happened. Does that mean the chess game wasn't real? Well, maybe; it depends on your view of Platonic computations. But one thing it definitely does not mean is that Omega's decision was arbitrary. Regardless of whether you feel Omega based his decision on a "real" chess game, you would in fact either win or not win against Kasparov, and whether you get the $500 really does depend on the outcome of that hypothetical game. (To make this point clearer, imagine that Omega actually predicted that you'd win. Surprised by his own prediction, Omega is now faced with the prospect of giving you $500 that he never expected he'd actually have to give up. Can he back out of the deal by claiming that since the chess game never actually happened, the outcome was up in the air all along and therefore he doesn't have to give you anything? If your answer to that question is no, then you understand what I'm trying to get at.)

So outcomes can depend on things that never actually happen in the real world. Cool, so what does that have to do with the past influencing the future? Well, the answer is that it doesn't--at least, not directly. But that's where the twist comes in:

Earlier, when I gave my toy example of a hypothetical chess game between you and Kasparov, I made sure to phrase the question so that the situation was presented from the perspective of your actual self, not your hypothetical self. (This makes sense; after all, if Omega's prediction method was based on something other than a direct simulation, your hypothetical self might not even exist.) But there was another way of describing the situation:

You're going about your day normally when suddenly, with no warning whatsoever, you're teleported into a white void of nothingness. In front of you is a chessboard; on the other side of the chessboard sits Kasparov, who challenges you to a game of chess.

Here, we have the same situation, but presented from the viewpoint of the hypothetical you on whom Omega's prediction is based. Crucially, the hypothetical you doesn't know that they're hypothetical, or that the real you even exists. So from their perspective, something random just happened for no reason at all. (Yes, yes, if Omega used some method other than a simulation to make his prediction, the hypothetical you wouldn't have existed and wouldn't have had a perspective--but hey, that doesn't stop me from writing from their perspective, right? After all, real people write from the perspectives of unreal people all the time; that's just called writing fiction. And besides, we've already established that real or unreal, the outcome of the game really does determine whether you get the $500, so the thoughts and feelings of the hypothetical you are nonetheless important in that they partially determine the outcome of the game.)

And now we come to the final, crucial point that makes sense of the blackmail scenario and all the other thought experiments in the paper, the point that Schwarz and most mainstream philosophers haven't taken into account:

Every single one of those thought experiments could have been written from the perspective, not of the real you, but a hypothetical, counterfactual version of yourself.

When "you're" being blackmailed, Schwarz makes the extremely natural assumption that "you" are you. But there's no reason to suppose this is the case. The scenario never stipulates why you're being blackmailed, only that you're being blackmailed. So the person being blackmailed could be either the real you or a hypothetical. And the thing that determines whether it's the real you or a mere hypothetical is...

...your decision whether or not to pay up, of course.

If you cave into the blackmail and pay up, then you're almost certainly the real deal. On the other hand, if you refuse to give in, it's very likely that you're simply a counterfactual version of yourself living in an extremely low-probability (if not outright inconsistent) world. So your decision doesn't just determine the future; it also determines (with high probability) which you "you" are. And so then the problem simplifies into this: which you do you want to be?

If you're the real you, then life kinda sucks. You just got blackmailed and you paid up, so now you're down a bunch of money. If, on the other hand, you're the hypothetical version of yourself, then congratulations: "you" were never real in the first place, and by counterfactually refusing to pay, you just drastically lowered the probability of your actual self ever having to face this situation and (in the process) becoming you. And when things are put that way, well, the correct decision becomes rather obvious.

But this kind of counterfactual reasoning is extremely counterintuitive. Our brains aren't designed for this kind of thinking (well, not explicitly, anyway). You have to think about hypothetical versions of yourself that have never existed and (if all goes well) will never exist, and therefore only exist in the space of logical possibility. What does that even mean, anyway? Well, answering confused questions like that is pretty much MIRI's goal these days, so I dunno, maybe we can ask them.