CDT, TDT, and UDT would not give away the money because there is no causal (or acausal) influence on the number of universes.
I'm not so sure about UDT's response. From what I've heard, depending on the exact formal implementation of the problem, UDT might also pay the money? If your thought experiment works via a correlation between the type of universe you live in and the decision theory you employ, then it might be a similar problem to the Coin Flip Creation. I introduced the latter decision problem in an attempt to make a less ambiguous version of the Smoking Lesion. In a comment in response to my post, cousin_it writes:
Here's why I think egoistic UDT would one-box. From the problem setup it's provable that one-boxing implies finding money in box A. That's exactly the information that UDT requires for decision making ("logical counterfactual"). It doesn't need to deduce unconditionally that there's money in box A or that it will one-box.
One possible confounder in your thought experiment is the agent’s altruism. The agent doesn’t care about which world he lives in, but only about which worlds exist. If you reason from an “updateless”, outside perspective (like Anthropic Decision Theory), it then becomes irrelevant what you choose. This is because if you act in a way that’s only logically compatible with world A, you know you just wouldn’t have existed in the other world. A way around this would be if you’re not completely updateless, but if you instead have already updated on the fact that you do exist. In this case you’d have more power with your decision. “One-boxing” might also make sense if you're just a copy-egoist and prefer to live in world A.
A way around this would be if you’re not completely updateless, but if you instead have already updated on the fact that you do exist.
It's not a given that you can easily observe your existence. From updateless point of view, all possible worlds, or theories of worlds, or maybe finite fragments of reasoning about them, in principle "exist" to some degree, in the sense of being data potentially relevant for estimating the value of everything, which is something to be done for the strategies under agent's consideration. So in case of worlds, or ...
I recently had a conversation with a staunch defender of EDT who maintained that EDT gives the right answer in the Smoker’s Lesion and even Evidential Blackmail. I came up with the following, even more counterintuitive, thought experiment:
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By doing research, you've found out that there is either
(A) only one universe or
(B) a multiverse.
You also found out that the cosmological theory has a slight influence (via different physics) on how your brain works. If (A) holds, you will likely decide to give away all your money to random strangers on the street; if there is a multiverse, you will most likely not do that. Of course, causality flows in one direction only, i.e. your decision does not determine how many universes there are.
Suppose you have a very strong preference for (A) (e.g. because a multiverse would contain infinite suffering) so that it is more important to you than your money.
Do you give away all your money or not?
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This is structurally equivalent to the Smoker's lesion, but what's causing your action is the cosmological theory, not a lesion or a gene. CDT, TDT, and UDT would not give away the money because there is no causal (or acausal) influence on the number of universes. EDT would reason that giving the money away is evidence for (A) and therefore choose to do so.
Apart from the usual “managing the news” point, this highlights another flaw in EDT: its presumptuousness. The EDT agent thinks that her decision spawns or destroys the entire multiverse, or at least reasons as if. In other words, EDT acts as if it affects astronomical stakes with a single thought.
I find this highly counterintuitive.
What makes it even worse is that this is not even a contrived thought experiment. Our brains are in fact shaped by physics, and it is plausible that different physical theories or constants both make an agent decide differently and make the world better or worse according to one’s values. So, EDT agents might actually reason in this way in the real world.