Assuming the objective is to maximize my money, there is no good strategy. You can make the decision as you described, but how do you justify it being the correct decision? I either get the money or not as I am either L or not. But there is no explanation as to why. The decimal numbers never appeared for just me.
The value calculated is meaningful if applied to all copies. The decimal numbers are the relative fractions. It is correct to say if every copy makes decisions this way then they will have more money combined. But there is no first-person in this. Why would this decision also be the best for me specifically? There is no reason. Unless we make an additional assumption such as “I am a random sample from these copies.”
Ultimately though, there is some answer to my question “What move would you personally actually make in each of these games, and why?”: whether or not there is a “correct” move or a “mathematically justified” move, etc, there is some move you personally would make. What is it, and why? If you personally would make a different move from me, then I want to know what it is! And if you would make the same move as me and write down the same math as me as your reason, then the only remaining disagreement is that I call that move “correct” while you call it “the move I would make because it somehow makes sense even though it’s not fundamentally correct”, and at that point it’s just definitions arguments.
I would say there is no “why” to which person I am. So there is no way to say which action is right or wrong. I could very well choose to guess “I am not L”. And it would be as good/bad a guess as yours. There is no math to write down at all.
If you say guessing “I am L” is the correct action while guessing “I am not L” is wrong. Then you would need to come up with a reason for it. “I choose to guess I’m not L and you say I am wrong to do so. Then tell me why.” There isn’t any justification. Considering all the copies does not work unless you assume the first person as a random sample.
It sounds like you are misinterpreting my question, since the “why” in it is not “why are you person L or not person L”, it’s “why in the game would you speak the words ‘I am L’ or ‘I am not L’”. Let me try one more time to make the question extremely clear: if you actually played my games, some thoughts (call these X) would actually go through your head, and then some words (call these Y) would actually come out of your mouth. What is Y, and what is X? Whether or not the “correct” move is undefined (I still don’t care to argue definitions), you can’t seriously expect me to believe that X and Y are undefined—I assume you know yourself well enough to know what you personally would actually do. So what are X and Y?
Y=‘I am L’ in game 1 and ‘I am LR’ in game 2.
X=”Hmm, well there’s no law governing which answer is right, so I might as well say the thing that might get me the bigger number of dollars.”
Y=‘I am not L’ in game 1 and ‘I am not LR’ in game 2.
X=”No known branch of math has any relevance here, so when faced with this game (or any similar stupid game with no right answer) I’ll fall back on picking whatever option was stated most recently in the question, since that’s the one I remember hearing better.”
Provided the objective is to maximize my money. There is no way to reason about it. So either of your example answers is fine. It is not more valid/invalid than any other answers.
Personally, I would just always guess a positive answer and forget about it. As it saves more energy. So “I am L”, and “I am LR” to your problems. If you think that is wrong I would like to know why.
Your answer based on expected value could maximize the total money of all copies. (Assuming everyone has the same objective and makes the same decision.) Maximizing the benefit of people similar to me (copies) at the expense of people different from me (the bet offerer) is an alternative objective. People might choose it due to natural feelings, after all, it is a beneficial evolution trait. That’s why this alternative objective seems attractive, especially when there is no valid strategy to maximize my benefit specifically. But as I have said, it does not involve self-locating probability.
By the way I apologize for not directly addressing your points. The reason I’m not talking about indexicals or anything directly is that I think I can demonstrate a probable flaw in your argument while treating it entirely as a black box. The way that works: as an extreme example, imagine that I successfully demonstrated that a) every person on this site including you would, when actually dropped into these games, make the same moves as me, and that b) in order to come up with that answer, every person on this site including you goes through a mental process that looks a whole lot like “0.5 * 1000 > 0.5 * 999” and “0.25 * 1000 < 0.75 * 999″ even if they don’t have any words justifying why they are doing it that way. If that were the case, then I’d posit the following: 1) there is, with extremely high probability, some very reasonable sense in which those moves are “correct”/”mathematically justified”/”good strategies” etc, even if, for any specific one of those terms, we’re not comfortable labeling the moves as such, and therefore 2) with extremely high probability, any theory like yours which suggests that there is no correct move is at least one of a) using a new set of definitions but with no practical difference to actions (e.g. it will refuse to call the moves “correct”, but then will be forced to come up with some new term like “anthropically correct” to explain why they “anthropically recommend” that you make those moves even though they’re certainly not actually “correct”, in which case I don’t care about the wording), and/or b) flawed somewhere, even if I cannot yet figure out which sentence in the argument is wrong.
Essentially what Gunnar_Zarncke said.
Assuming the objective is to maximize my money, there is no good strategy. You can make the decision as you described, but how do you justify it being the correct decision? I either get the money or not as I am either L or not. But there is no explanation as to why. The decimal numbers never appeared for just me.
The value calculated is meaningful if applied to all copies. The decimal numbers are the relative fractions. It is correct to say if every copy makes decisions this way then they will have more money combined. But there is no first-person in this. Why would this decision also be the best for me specifically? There is no reason. Unless we make an additional assumption such as “I am a random sample from these copies.”
Ultimately though, there is some answer to my question “What move would you personally actually make in each of these games, and why?”: whether or not there is a “correct” move or a “mathematically justified” move, etc, there is some move you personally would make. What is it, and why? If you personally would make a different move from me, then I want to know what it is! And if you would make the same move as me and write down the same math as me as your reason, then the only remaining disagreement is that I call that move “correct” while you call it “the move I would make because it somehow makes sense even though it’s not fundamentally correct”, and at that point it’s just definitions arguments.
I would say there is no “why” to which person I am. So there is no way to say which action is right or wrong. I could very well choose to guess “I am not L”. And it would be as good/bad a guess as yours. There is no math to write down at all.
If you say guessing “I am L” is the correct action while guessing “I am not L” is wrong. Then you would need to come up with a reason for it. “I choose to guess I’m not L and you say I am wrong to do so. Then tell me why.” There isn’t any justification. Considering all the copies does not work unless you assume the first person as a random sample.
It sounds like you are misinterpreting my question, since the “why” in it is not “why are you person L or not person L”, it’s “why in the game would you speak the words ‘I am L’ or ‘I am not L’”. Let me try one more time to make the question extremely clear: if you actually played my games, some thoughts (call these X) would actually go through your head, and then some words (call these Y) would actually come out of your mouth. What is Y, and what is X? Whether or not the “correct” move is undefined (I still don’t care to argue definitions), you can’t seriously expect me to believe that X and Y are undefined—I assume you know yourself well enough to know what you personally would actually do. So what are X and Y?
Example answers:
Y=‘I am L’ in game 1 and ‘I am LR’ in game 2. X=”Hmm, well there’s no law governing which answer is right, so I might as well say the thing that might get me the bigger number of dollars.”
Y=‘I am not L’ in game 1 and ‘I am not LR’ in game 2. X=”No known branch of math has any relevance here, so when faced with this game (or any similar stupid game with no right answer) I’ll fall back on picking whatever option was stated most recently in the question, since that’s the one I remember hearing better.”
Provided the objective is to maximize my money. There is no way to reason about it. So either of your example answers is fine. It is not more valid/invalid than any other answers.
Personally, I would just always guess a positive answer and forget about it. As it saves more energy. So “I am L”, and “I am LR” to your problems. If you think that is wrong I would like to know why.
Your answer based on expected value could maximize the total money of all copies. (Assuming everyone has the same objective and makes the same decision.) Maximizing the benefit of people similar to me (copies) at the expense of people different from me (the bet offerer) is an alternative objective. People might choose it due to natural feelings, after all, it is a beneficial evolution trait. That’s why this alternative objective seems attractive, especially when there is no valid strategy to maximize my benefit specifically. But as I have said, it does not involve self-locating probability.
You make a good point about the danger of alternate objectives creeping in if the original objective is unsatisfiable; this helps me see why my original thought experiment is not as useful as I’d hoped. What are your thoughts on this one? https://www.lesswrong.com/posts/heSbtt29bv5KRoyZa/the-first-person-perspective-is-not-a-random-sample?commentId=75ie9LnZgBEa66Kp8
No problem. I am actually very happy we can get some agreement. Which is not very often in discussions of anthropics.
By the way I apologize for not directly addressing your points. The reason I’m not talking about indexicals or anything directly is that I think I can demonstrate a probable flaw in your argument while treating it entirely as a black box. The way that works: as an extreme example, imagine that I successfully demonstrated that a) every person on this site including you would, when actually dropped into these games, make the same moves as me, and that b) in order to come up with that answer, every person on this site including you goes through a mental process that looks a whole lot like “0.5 * 1000 > 0.5 * 999” and “0.25 * 1000 < 0.75 * 999″ even if they don’t have any words justifying why they are doing it that way. If that were the case, then I’d posit the following: 1) there is, with extremely high probability, some very reasonable sense in which those moves are “correct”/”mathematically justified”/”good strategies” etc, even if, for any specific one of those terms, we’re not comfortable labeling the moves as such, and therefore 2) with extremely high probability, any theory like yours which suggests that there is no correct move is at least one of a) using a new set of definitions but with no practical difference to actions (e.g. it will refuse to call the moves “correct”, but then will be forced to come up with some new term like “anthropically correct” to explain why they “anthropically recommend” that you make those moves even though they’re certainly not actually “correct”, in which case I don’t care about the wording), and/or b) flawed somewhere, even if I cannot yet figure out which sentence in the argument is wrong.