To my understanding, anthropic shadow refers to the absurdum logic in Leslie’s Firing Squad: “Of course I have survived the firing squad, that is the only way I can make this observation. Nothing surprising here”. Or reasonings such as “I have played the Russian roulette 1000 times, but I cannot increase my belief that there is actually no bullet in the gun because surviving is the only observation I can make”.
In the Chinese Roulette example, it is correct that the optimal strategy for the first round is also optimal for any following round. It is also correct if you decide to play for the first round then you will keep playing until kicked out i.e. no way to adjust our strategy. But that doesn’t justify there is no probability update, for each subsequent decision, while all agree to keep playing, can be different. (And they should be different) It seems absurd to say I would not be more confident to keep going after 100 empty shots.
In short, changing strategy implies there is an update, not changing strategy doesn’t imply there is no update.
But the general point I wanted to make is that “anthropic shadow” reflects a fundamental impossibility of drawing useful updates. From within the boundaries of the game, you can’t really say anything other than “well, I’m still playing, so of course I’m still playing”. You can still feel like you update as a person because you wouldn’t cease existing if you lost. But my point was that the essence of the anthropic shadow is that if you think as the player, an entity that in a sense ceases to exist as soon as that specific game is over, then you can’t really update meaningfully. And that is reflected in the fact that you can’t get any leverage out of the update.
At least, that was my thought when writing the post. I am thinking now about whether that can change if we design a game such that you can actually get meaningful in-game updates on your survival; I think having a turn-dependent survival probability might be key for that. I’ll probably return to this.
It seems earlier posts and your post have defined anthropic shadow differently in subtle but important ways. The earlier posts by Christopher and Jessica argued AS is invalid: that there should be updates given I survived. Your post argued AS is valid: that there are games where no new information gained while playing can change your strategy (no useful updates). The former is focusing on updates, the latter is focusing on strategy. These two positions are not mutually exclusive.
Personally, the concept of “useful update” seems situational. For example, say someone has a prior that leads him to conclude the optimal strategy is not to play the Chinese Roulette. However, he was forced to play several rounds regardless of what he thought. After surviving those rounds (say EEEEE), it might very well be that he updates his probability enough to change his strategy from no-play to play. That would be a useful update. And this “forced-to-play” kind of situation is quite relevant to existential risks, which anthropic discussions tend to focus on.
True enough, I guess. I do wonder how to reconcile the two views though, because the approach you describe that allows you to update in case of a basic game is actively worse for the second kind of game (the one with the blanks). In that case, using the approach I suggested actually produces a peaked probability distribution on b that eventually converges to the correct value (well, on average). Meanwhile just looking at survival produces exactly the same monotonically decaying power law. If the latter potentially is useful information, I wonder how one might integrate the two.
To my understanding, anthropic shadow refers to the absurdum logic in Leslie’s Firing Squad: “Of course I have survived the firing squad, that is the only way I can make this observation. Nothing surprising here”. Or reasonings such as “I have played the Russian roulette 1000 times, but I cannot increase my belief that there is actually no bullet in the gun because surviving is the only observation I can make”.
In the Chinese Roulette example, it is correct that the optimal strategy for the first round is also optimal for any following round. It is also correct if you decide to play for the first round then you will keep playing until kicked out i.e. no way to adjust our strategy. But that doesn’t justify there is no probability update, for each subsequent decision, while all agree to keep playing, can be different. (And they should be different) It seems absurd to say I would not be more confident to keep going after 100 empty shots.
In short, changing strategy implies there is an update, not changing strategy doesn’t imply there is no update.
But the general point I wanted to make is that “anthropic shadow” reflects a fundamental impossibility of drawing useful updates. From within the boundaries of the game, you can’t really say anything other than “well, I’m still playing, so of course I’m still playing”. You can still feel like you update as a person because you wouldn’t cease existing if you lost. But my point was that the essence of the anthropic shadow is that if you think as the player, an entity that in a sense ceases to exist as soon as that specific game is over, then you can’t really update meaningfully. And that is reflected in the fact that you can’t get any leverage out of the update.
At least, that was my thought when writing the post. I am thinking now about whether that can change if we design a game such that you can actually get meaningful in-game updates on your survival; I think having a turn-dependent survival probability might be key for that. I’ll probably return to this.
It seems earlier posts and your post have defined anthropic shadow differently in subtle but important ways. The earlier posts by Christopher and Jessica argued AS is invalid: that there should be updates given I survived. Your post argued AS is valid: that there are games where no new information gained while playing can change your strategy (no useful updates). The former is focusing on updates, the latter is focusing on strategy. These two positions are not mutually exclusive.
Personally, the concept of “useful update” seems situational. For example, say someone has a prior that leads him to conclude the optimal strategy is not to play the Chinese Roulette. However, he was forced to play several rounds regardless of what he thought. After surviving those rounds (say EEEEE), it might very well be that he updates his probability enough to change his strategy from no-play to play. That would be a useful update. And this “forced-to-play” kind of situation is quite relevant to existential risks, which anthropic discussions tend to focus on.
True enough, I guess. I do wonder how to reconcile the two views though, because the approach you describe that allows you to update in case of a basic game is actively worse for the second kind of game (the one with the blanks). In that case, using the approach I suggested actually produces a peaked probability distribution on b that eventually converges to the correct value (well, on average). Meanwhile just looking at survival produces exactly the same monotonically decaying power law. If the latter potentially is useful information, I wonder how one might integrate the two.