Note: I let it sit in my editor for a day, not being sure how useful this comment is, but figured I’d post it anyway, just in case.
It seems to me that, despite a rather careful analysis of transparent Newcomb’s, some of the underlying assumptions were not explicated:
There is a very accurate predictor, who has placed $10,000 in the big box if and only if they predict that you wouldn’t take the small box regardless of what you see in the big one.
It is crucial to the subsequent reasoning how this “very accurate predictor” functions under the hood, for example:
Does it run a faithful simulation of you and check the outcome?
Does it function as a Laplace’s demon from outside the universe and predict the motion of each particle without running it?
Does it obey Quantum Mechanics and has to run multiple instances of you and your neighborhood of the universe and terminate those that choose “wrong”?
Does it even need to predict anything, or simply kill off the timelines that are “wrong? (Quantum post-selection.) For example, it randomly puts an empty or full second box and kills off the instances where someone takes two full boxes.
Does it run a low-res version of you that does not have any internal experience and is not faithful enough to think about other versions of you?
Does it analyze your past behaviors and calculate your outcome without creating anything that can be called an instance of you?
Does it experiment mostly on those it can predict reasonably well, but occasionally screws up?
In some of those cases it pays to take both boxes when you see them. In other cases it pays to take just the one. Yet in other cases it pays to roll a (weighted) quantum die and rely on its outcome to make your decision.
The usual difference between CDT and UDT is the point in time where a compatibilist equivalent of the libertarian free will* is placed:
In CDT you assume that you get the predictor-unaffectable freedom to change the course of events after you have been presented with the boxes.
In UDT it is the moment when you self-modify/precommit to one-box once you hear about the experiment and think through it.
* Here by free will I don’t mean the divine spirit from outside the universe that imbues every human with this magical ability. Rather, it is a description of some fundamental in-universe unpredictability that not even the Newcomb’s predictor can overcome. Maybe it is some restrictions on computability, or on efficient computability, or maybe it is a version of Scott Aaronson’s freebits, or maybe something else. The important part is that not even the predictor can tap into it.
One way to reformulate this in a way that avoids the confusing language of “decisions” is to frame it as “which agents end up with higher utility?” and explore possible worlds where they exist. Some of these worlds can be deterministic, others probabilistic, yet others MWI-like, yet others where simulated agents are as real as the “real” one. But stepping away from “agent decides” and into “agent that acts a certain way” forces you into the mindset of explicitly listing the worlds instead of musing about causality and precommitment.
For example, for an inconsistent creature, it matters what the creature does, not how it (often unreliably) reasons about themselves. In the 8 am bell setup there is only one Paul who actually does nothing but talk about his preferences. A Monday creature may feel that it wants to “fix” its Tuesday preferences, but as long as the Tuesday behavior is not updated, it doesn’t matter for anything “decision”-related.
This approach does not help with the paradoxes of indexicality though, including those that appear inside some of the worlds that may appear in the Newcomb’s setup, like dealing with simulated agents. Sean Carroll takes a stab at how to deal with something like it in https://www.preposterousuniverse.com/podcast/2022/06/06/200-solo-the-philosophy-of-the-multiverse/ by using Neal’s “fully non-indexical conditioning” (https://arxiv.org/abs/math/0608592), where you condition on everything you know about yourself, except for where you are in the universe. It helps dealing with the Doomsday argument, with the Boltzmann brain problem, with the Sleeping Beauty problem, and with other “Presumptuous Philosopher”-prone setups.
Presumably utility is measured by someone who exists at the moment of action? If you do something on Tuesday that you want to do, that is what matters. You may regret having done something else on Monday, or having to do something you currently don’t like on Wednesday, but it is sort of irrelevant. If your UF is not stable, it is probably not a good description of what is going on.
Note: I let it sit in my editor for a day, not being sure how useful this comment is, but figured I’d post it anyway, just in case.
It seems to me that, despite a rather careful analysis of transparent Newcomb’s, some of the underlying assumptions were not explicated:
It is crucial to the subsequent reasoning how this “very accurate predictor” functions under the hood, for example:
Does it run a faithful simulation of you and check the outcome?
Does it function as a Laplace’s demon from outside the universe and predict the motion of each particle without running it?
Does it obey Quantum Mechanics and has to run multiple instances of you and your neighborhood of the universe and terminate those that choose “wrong”?
Does it even need to predict anything, or simply kill off the timelines that are “wrong? (Quantum post-selection.) For example, it randomly puts an empty or full second box and kills off the instances where someone takes two full boxes.
Does it run a low-res version of you that does not have any internal experience and is not faithful enough to think about other versions of you?
Does it analyze your past behaviors and calculate your outcome without creating anything that can be called an instance of you?
Does it experiment mostly on those it can predict reasonably well, but occasionally screws up?
In some of those cases it pays to take both boxes when you see them. In other cases it pays to take just the one. Yet in other cases it pays to roll a (weighted) quantum die and rely on its outcome to make your decision.
The usual difference between CDT and UDT is the point in time where a compatibilist equivalent of the libertarian free will* is placed:
In CDT you assume that you get the predictor-unaffectable freedom to change the course of events after you have been presented with the boxes.
In UDT it is the moment when you self-modify/precommit to one-box once you hear about the experiment and think through it.
* Here by free will I don’t mean the divine spirit from outside the universe that imbues every human with this magical ability. Rather, it is a description of some fundamental in-universe unpredictability that not even the Newcomb’s predictor can overcome. Maybe it is some restrictions on computability, or on efficient computability, or maybe it is a version of Scott Aaronson’s freebits, or maybe something else. The important part is that not even the predictor can tap into it.
One way to reformulate this in a way that avoids the confusing language of “decisions” is to frame it as “which agents end up with higher utility?” and explore possible worlds where they exist. Some of these worlds can be deterministic, others probabilistic, yet others MWI-like, yet others where simulated agents are as real as the “real” one. But stepping away from “agent decides” and into “agent that acts a certain way” forces you into the mindset of explicitly listing the worlds instead of musing about causality and precommitment.
For example, for an inconsistent creature, it matters what the creature does, not how it (often unreliably) reasons about themselves. In the 8 am bell setup there is only one Paul who actually does nothing but talk about his preferences. A Monday creature may feel that it wants to “fix” its Tuesday preferences, but as long as the Tuesday behavior is not updated, it doesn’t matter for anything “decision”-related.
This approach does not help with the paradoxes of indexicality though, including those that appear inside some of the worlds that may appear in the Newcomb’s setup, like dealing with simulated agents. Sean Carroll takes a stab at how to deal with something like it in https://www.preposterousuniverse.com/podcast/2022/06/06/200-solo-the-philosophy-of-the-multiverse/ by using Neal’s “fully non-indexical conditioning” (https://arxiv.org/abs/math/0608592), where you condition on everything you know about yourself, except for where you are in the universe. It helps dealing with the Doomsday argument, with the Boltzmann brain problem, with the Sleeping Beauty problem, and with other “Presumptuous Philosopher”-prone setups.
If the Monday creature is indeed able to fix its preferences, how do you compare utility between the two alternatives since they have different UFs?
Presumably utility is measured by someone who exists at the moment of action? If you do something on Tuesday that you want to do, that is what matters. You may regret having done something else on Monday, or having to do something you currently don’t like on Wednesday, but it is sort of irrelevant. If your UF is not stable, it is probably not a good description of what is going on.