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.
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.