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ControlsFreak


				

				

				

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ControlsFreak


								

								

								
								
								

								
							
					
 
				


				

				
				
				

				

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					joined 2022 October 02 23:23:48 UTC
				


				
					

					
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				Recursive thinking, Newcomb's problem, and free will
			
		

	

	

	

		
			

			

				

			

		

			


				

					
Ok, so I'm trying to follow. The clock we're analyzing has all of the access it needs in order to do y', which is what it's going to do, and which we've observed is suboptimal. But then, I guess, we're like, hypothesizing that we could conjure up some faster-than-light travel for something, waves hands, to this clock. And that, somehow, waves hands, I guess if we, like, change the design of the clock or something, which we can't do, somehow, waves hands, could end up in it doing action y instead of y'.


Like, what is the problem here? What is the space of possible actions? What am I trying to solve for?


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
				Recursive thinking, Newcomb's problem, and free will
			
		

	

	

	

		
			

			

				

			

		

			


				

					


you don't have access




I don't follow. Every part of you that is necessary to follow the clockwork has appropriate access to the mechanisms of the clock, at least to the extent that is necessary for it to be able to follow the clockwork. If there were some part of you that didn't have such access, then it wouldn't be able to follow the clockwork, and we would reach a contradiction.


Like, maybe try to explain how this works directly on the example of analyzing an actual clock, with determined suboptimal action y' and a hypothesized optimal action y. What doesn't have access to what?


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
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I think I have now concluded my argument that there is no contradiction, once one tries to explain how the contradiction is supposed to work.


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
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I don't see a contradiction at all. This proposed unmoved mover is already clearly an exception to the general rule of requiring a prior mover, apparently preferring avoiding infinite regress over having an exception. It is simply not moved by some prior cause. That's kind of it? I think you'll have to be more explicit about how you find a contradiction.


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
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What's confusing is that I'm missing an argument. Some sort of, "Here are some premises, and here's a conclusion," sort of thing.


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
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I'm not quite seeing an argument yet. Go on?


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
				Recursive thinking, Newcomb's problem, and free will
			
		

	

	

	

		
			

			

				

			

		

			


				

					
I mean, kinda no? That's where the Wolpert/Benford critique comes in. You can't formalize the problem in terms of game theory without adding additional assumptions. If your additional assumptions to formalize it are, "It's actually a clock, and there's no feasible action set with cardinality greater than one," then sure, you have a suitable formalization... but it's kinda not game theory. If you want to back away from that being your additional assumption, it's kinda still on you to state other formal additional assumptions that make it a well-posed game.


EDIT: Perhaps another way of describing it would be as follows. Suppose one is just analyzing a clock. We'll discretize time for now just to make it simple. Say that we observe from our analysis that in the transition from time t_1 to t_2, the clock will become one second slow compared to some 'objective' time (handwave any difficulties here). We could observe that this is, in some sense, suboptimal, sure.


Now, does it make sense to say something like, "What if we just call this suboptimal action y' and hypothesize an alternative action y that doesn't result in being one second slow?" Would it make sense to say that we have constructed a decision theory problem? Note that we're not specifying anything about any sort of real policy space or anything; it's not like we're saying, "Here is the policy space of possible mechanisms that a non-clock can choose from to design the clock."1 We just have a clock.


Suppose we say that there is some being, Omega, who will accurately predict that said clock will take action y' and become one second slow, and then put some quantity of money in front of the clock. Suppose we say, "Well, imagine the clock took hypothetical action y, which it can't do, then imagine that Omega would put a different quantity of money in front of the clock in that case." Does this become a game theory problem? If so, what am I supposed to solve for? What is the space of possible solutions?


1 - This is perhaps related to my comment about what Yud did to the prisoner's dilemma problem. He created some different policy space about source codes.


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
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I think this is non-responsive to my comment. Isn't god himself a "mover" in classical theology?


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
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Jesus moves and changes yet he's the god that is not supposed to do either of those things




I already don't really follow. I thought the second word of "unmoved mover" was "mover". I didn't think classical theology posited an unmoved unmover.


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
				Recursive thinking, Newcomb's problem, and free will
			
		

	

	

	

		
			

			

				

			

		

			


				

					
In a clockwork universe, is there such a thing as decision theory, or a subset thereof known as game theory? It would seem to me that, sure, one could have a mathematical theory of optimization, extremal values, or even min-max theory, but it would not seem to me that one could view any such results as being prescriptive - I.e., "If you are trying to accomplish X, you should choose Y." Instead, it would simply observe, "You might by chance (or deterministic integration of physical differential equations or whatever) take action Y or Y', and it turns out that we can compute that Y is optimal for purpose X, while Y' is suboptimal."


That is, if one is an adherent to this conception of a clockwork universe, I think the way they would state their position on Newcomb's problem would be something more like, "You will either 1-box or 2-box, based on the movements of the clock. We can also compute from axioms regarding the clock's movements that 1-boxers will possess more money," and less like, "You're in this hypothetical situation where you need to think about the rational way to proceed optimally, and here is why you should choose to act in the following way." I think if such proponents presented their perspective in this way, it would be less amenable to criticism that their problem is ill-posed as a decision/game theory problem.


The axioms of decision/game theory seem to conflict with the axioms that seem to appear here. I guess one way to put words to that would be that one has a feasible action set within the underlying dynamical system that has cardinality greater than one. Perhaps another way to put it is that it does not seem to me that decision/game theory is applicable to clocks. The feasible action set of clocks has cardinality one. One does not ask how a clock should choose among non-identical actions, though one may observe whether a clock's deterministic actions are/are not optimal according to some metric.


Taking this alternative position would, I think, sidestep the criticism I relayed above from Wolpert/Benford, as what they were fundamentally trying to do was to formalize the problem within decision/game theory, where players have feasible action sets with cardinality larger than one. They observed that if you do this, you run into contradictions without further specification. But it would seem like, sure, if you give up on that, give up on saying that it has anything to do with decision/game theory, that it's more like just making an observation about clocks and optimality/suboptimality, then I think you do avoid the critique.


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
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My sense from the text is probably annihilationism.


You probably have to go more for AI atheists to find a god that makes future contingents like sea battles or box picking necessary and then also sets up a basilisk to torture you forever for the future contingents that it retroactively would have made necessary.


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
				Recursive thinking, Newcomb's problem, and free will
			
		

	

	

	

		
			

			

				

			

		

			


				

					
My sense tracks with that of @MathWizard. If you add some particular assumptions about the form of the problem, you can code it up, and likely, for a wide range of parameters, 1-boxing is higher EV.


I think the criticism of Wolpert/Benford is also similar in type. (Again, not really having spent sufficient time with it.) That is, they construct two possible interpretations. Either of them, you could just sit down and code. It may even be the case that for a wide range of parameters, EV still points to 1-boxing for both versions. However, my understanding of their claim is that those two codes will be very different. Even the strategy spaces are fundamentally different in their claim. And for a similarly wide range of parameters, the joint distributions will be contradictory. The point is not that the sign may be the same for this particular ratio of prizes; it's that there are just multiple contradictory ways to construct it.


Of course, someone could take the time and search out what ratio of prizes in the respective boxes produces maximum tension between the two interpretations, so that rather than having the two EV calcs mostly pointing in the same direction, we could maximize how often they conflict. That's kind of not the point of the critique, but I suppose it could be done if one found it necessary to really grok the difference between a well-posed and ill-posed problem. Though, like you put it, I probably can't be arsed to do it.


That said, I am almost motivated enough to try it (but it would probably have to wait a few weeks, and then, I'll probably be bored with it). I certainly don't know that we can for sure find parameters where the two possible games differ in terms of sign. If this problem was actually relevant to my research interests, I would absolutely just do it, because it's one where I have a vague sense of, "Wouldn't it have to be amazingly coincidental if the values were different, but the signs were always the same?" And when I sniff at the possibility that there could be an amazing coincidence like that, it's usually an indicator of a really interesting theoretical opportunity.


				

				

						

							

								
							

						


						
					

				
			


			

	


			
			
				

			
		

	






		

			
			
				Recursive thinking, Newcomb's problem, and free will
			
		

	

	

	

		
			

			

				

			

		

			


				

					
Wolpert and Benford argue that the problem is ill-posed for almost any error rate, so it's not clear that stuffing in a particular number actually helps resolve the problem. I haven't spent all that much time with this problem yet, so I'm not going to commit to saying that I think they're right about this, but it jives with my intuition.


Generally speaking, in order to have a well-posed game, one must be very formal and precise in many details. Particularly things like order of operations, allowable policy spaces, information sets, and details around estimators. I've become more annoyed by estimators in various problems over time, even apart from the relatively minimal thinking I've done on Newcomb's problem. One of the greatest sources of my criticisms in reviews of submitted papers (or even when my collaborators come to me with a problem set-up and/or proposed solution) revolves around not taking sufficient care around estimators.


I do think that Wolpert/Benford at least suffice in arguing that there are at least two possible formalizations that are sufficiently well-posed. I think it's probably on someone else to either bite the bullet and say they are clearly choosing one form or the other... or to provide a sufficient alternative formalization that makes the details more clear.


Aside on Yudkowsky, relevant for the discussion below and my thoughts generally on these sorts of problems. I wouldn't be surprised if he has/had something in mind like what he did to the prisoners' dilemma problem, with the business about source codes and such. There could be a way to try to resolve Newcomb's problem in a similar fashion, but my perspective is that it would still be proposing a very specific formalization... and one that is not at all just a clear instantiation of the initial problem statement. I might go so far as to say that in the prisoners' dilemma case, he just proposed a different problem, with different policy spaces. Interesting in its own right, sure. Probably correct for that particular formalization of that particular version of the problem, sure. But also kind of just a different problem. In general, even minor tweaks to these aspects of the formulation can result in different games.


Similarly for Newcomb's problem, unless one takes the step of clearly laying out in a formal way exactly what they're going to specify for the domain of the problem (and then, I guess, argue that this is like, 'the one true interpretation of the original problem' or something), then I'm probably going to lean toward just thinking that the original problem is so informally stated as to be ill-posed.