I understand the normal version of newcombs perfectly fine, I understand the normal version of counterfactual mugging (or at least the wiki version of it) perfectly fine, I get that the transparent boxes are mostly the same if you follow the logic , but in this case, the choice is presented AFTER you've picked boxes. "Here are two boxes. Would you like one or both. 'Both please.' Okay, also I'd like to inform you that if you pick both, you don't get the million. No backsies."
Saying that this is predicted in advance is weird, because there is no possibility of a meaningful loop: the moment of timeline separation is AFTER the choice has been made. The choice is set in stone. There is no possible change. You can pay, but it won't change a thing. Unless you were somehow determined to pay people in scenarios like this - which requires knowledge of scenarios like this.
In the original version, something happens, and then the losing you is contacted and asked whether you'd want to pay. And you'd be able to choose at that point, and even think about it. And then it turns out this was all a simulation and because you paid, the winning real you gets paid.
In this version, we could make it work by taking the result of the previous simulation (I flipped a coin you lost, pay me $100 or I won't pay $10000 if you had won), and then going through the prophet who either says you're fine if losing you paid, or that you're not fine if losing you didn't pay.
But what we cannot do is simulate this and loop it on itself. You are doomed in the future. You are always doomed in the future. There is no possibility of you being not doomed in the future. But, if you pay, then there is a possibility that you are not doomed in the future. That's a contradiction right there. If I accept that the statement about my unchanging future is false, then I'll pay because then I can go from 100% doomed to 50% doomed. If I accept that the statement about changing my future is false, then I won't pay, because you're a snake oil salesman, your cure will do me no good.
To fix this, the wording needs to be altered so that there is no contradiction and that there is a clear result of paying the money that will reduce the chance.
In short, I think this problem relies too much on UDT's ability to magically teleport between possible situations and failed to left a path for Time to take.
I think even with the ordinary phrasing the omegas prediction can be thought to sit in a sealed envelope as the real you picks. You don't think about the problem until then with your own brain. But in a way the contents of the envelope can be deduced from the transparent boxes.
I think it exhibits the same kind of wierdness. It doesn't really make sense to ever have the player choose only the empty transparent box, because the box will only be left empty if the player is predicted to pick both. So committing to not take both boxes means the boxes will be full. It doesn't really mean that the impossible "presented with two empty boxes" scenario is destroyed.
Edit as of June 13th, 2016: I no longer believe this to be easier to understand than traditional CM, but stand by the rest of it. Minor aesthetic edits made.
First post on the LW discussion board. Not sure if something like this has already been written, need your feedback to let me know if I’m doing something wrong or breaking useful conventions.
An alternative to the counterfactual mugging, since people often require it explained a few times before they understand it -- this one I think will be faster for most to comprehend because it arose organically, not seeming specifically contrived to create a dilemma between decision theories:
Pretend you live in a world where time travel exists and Time can create realities with acausal loops, or of ordinary linear chronology, or another structure, so long as there is no paradox -- only self-consistent timelines can be generated.
In your timeline, there are prophets. A prophet (known to you to be honest and truly prophetic) tells you that you will commit an act which seems horrendously imprudent or problematic. It is an act whose effect will be on the scale of losing $10,000; an act you never would have taken ordinarily. But fight the prophecy all you want, it is self-fulfilling and you definitely live in a timeline where the act gets committed. However, if it weren’t for the prophecy being immutably correct, you could have spent $100 and, even having heard the prophecy (even having believed it would be immutable) the probability of you taking that action would be reduced by, say, 50%. So fighting the prophecy by spending $100 would mean that there were 50% fewer self-consistent (possible) worlds where you lost the $10,000, because its just much less likely for you to end up taking that action if you fight it rather than succumbing to it.
You may feel that there would be no reason to spend $100 averting a decision that you know you’re going to make, and see no reason to care about counterfactual worlds where you don’t lose the $10,000. But the fact of the matter is that if you could have precommitted to fight the choice you would have, because in the worlds where that prophecy could have been presented to you, you’d be decreasing the average disutility by (($10,000)(.5 probability) - ($100) = $4,900). Not following a precommitment that you would have made to prevent the exact situation which you’re now in because you wouldn’t have followed the precommitment seems an obvious failure mode, but UDT successfully does the same calculation shown above and tells you to fight the prophecy. The simple fact that should tell causal decision theorists that converting to UDT is the causally optimal decision is that Updateless Decision Theorists actually do better on average than CDT proponents.
(You may assume also that your timeline is the only timeline that exists, so as not to further complicate the problem by your degree of empathy with your selves from other existing timelines.)