I see a problem with the proposed method. Your program learns how often, on average, its opponent one-boxes or two-boxes. If I (as Omega) learn that someone is a one-boxer, then I can predict that they will one-box next time, put money in box B, and be proved right. But then, in an iterated game, if the one-boxer learns that I am not predicting his decision in the individual case, but have made a general prediction once and for all and thereafter always filling box B, then he can with impunity take both boxes and prove my prediction wrong.
A true Omega needs to make both P(box B full | take one box) and P(box B empty | take both boxes) high. The proposed scheme ensures that P(box B full | habitual one-boxer) and P(box B empty | habitual two-boxer) are high, which is not quite the same.
Similarly, suppose I convince Eliezer that I’m Omega. He has publicly avowed one-boxing on Newcomb, so I can skip the learning phase, fill box B, and be proved right. But if, for some reason, he suspects that I’m not a superintelligent superbeing with superpowers of prediction, and in a series of games, experiments with two-boxing, I will be exposed as an impostor.
Iterated Newcomb played between programs given access to each other’s source code would be an interesting challenge. I assume Omega doesn’t care about the money, but plays for the gratification of correctly predicting the other player’s choice. The other player is playing for the money.
A simpler, zero-sum game also suggests itself to me. This is more like Rock-Paper-Scissors than Newcomb, but again the point is to play using knowledge of the other person’s code. Each player chooses 0 or 1. Player A wins if the choices are the same, player B wins if they are different.
(This might look as if A is trying to predict B and B is trying to avoid being predicted, but the game is actually symmetric, both players doing both of these things. Swap the labels on B’s choices and B wins on equality and A on inequality.)
In classical game theory, the optimal strategy is to toss a coin, and the expected payoff is zero. The challenge is to do better against real opponents.
A true Omega needs to make both P(box B full | take one box) and P(box B empty | take both boxes) high. The proposed scheme ensures that P(box B full | habitual one-boxer) and P(box B empty | habitual two-boxer) are high, which is not quite the same.
If I understand correctly the distinction you’re making between habitual one boxer and take one box the first kind would be about the past player history and the other one about the future. If so I guess you are right. I’m indeed using the past to make my prediction, as using the future is beyond my reach.
But I believe you’re missing the point. My program is not an iterated Newcomb’s Problem because Omega does not perform any prediction along the way. It will only perform one prediction. And that will be for the last game and the human won’t be warned. It does not care at all about the reputation of the player, but only on it’s acts in situations where he (the human player) can’t know if he is playing of not.
But another point of view is possible, and that is what comes to mind when you run the program: it is coercing the player to be either a one boxer or a two boxer if he wan’t to play at all. Any two-boxing and the player will have to spend a very long time one-boxing to reach the state when he is again seen as a one boxer. As it is written, the program is likely (to the chosen accuracy level) to make it’s prediction while the player is struggling to be a one boxer.
As a human player what comes through my mind while running my program is ok: I want to get a million dollars, henceforth I have to become a one boxer.
I see a problem with the proposed method. Your program learns how often, on average, its opponent one-boxes or two-boxes. If I (as Omega) learn that someone is a one-boxer, then I can predict that they will one-box next time, put money in box B, and be proved right. But then, in an iterated game, if the one-boxer learns that I am not predicting his decision in the individual case, but have made a general prediction once and for all and thereafter always filling box B, then he can with impunity take both boxes and prove my prediction wrong.
A true Omega needs to make both P(box B full | take one box) and P(box B empty | take both boxes) high. The proposed scheme ensures that P(box B full | habitual one-boxer) and P(box B empty | habitual two-boxer) are high, which is not quite the same.
Similarly, suppose I convince Eliezer that I’m Omega. He has publicly avowed one-boxing on Newcomb, so I can skip the learning phase, fill box B, and be proved right. But if, for some reason, he suspects that I’m not a superintelligent superbeing with superpowers of prediction, and in a series of games, experiments with two-boxing, I will be exposed as an impostor.
Iterated Newcomb played between programs given access to each other’s source code would be an interesting challenge. I assume Omega doesn’t care about the money, but plays for the gratification of correctly predicting the other player’s choice. The other player is playing for the money.
A simpler, zero-sum game also suggests itself to me. This is more like Rock-Paper-Scissors than Newcomb, but again the point is to play using knowledge of the other person’s code. Each player chooses 0 or 1. Player A wins if the choices are the same, player B wins if they are different.
(This might look as if A is trying to predict B and B is trying to avoid being predicted, but the game is actually symmetric, both players doing both of these things. Swap the labels on B’s choices and B wins on equality and A on inequality.)
In classical game theory, the optimal strategy is to toss a coin, and the expected payoff is zero. The challenge is to do better against real opponents.
If I understand correctly the distinction you’re making between habitual one boxer and take one box the first kind would be about the past player history and the other one about the future. If so I guess you are right. I’m indeed using the past to make my prediction, as using the future is beyond my reach.
But I believe you’re missing the point. My program is not an iterated Newcomb’s Problem because Omega does not perform any prediction along the way. It will only perform one prediction. And that will be for the last game and the human won’t be warned. It does not care at all about the reputation of the player, but only on it’s acts in situations where he (the human player) can’t know if he is playing of not.
But another point of view is possible, and that is what comes to mind when you run the program: it is coercing the player to be either a one boxer or a two boxer if he wan’t to play at all. Any two-boxing and the player will have to spend a very long time one-boxing to reach the state when he is again seen as a one boxer. As it is written, the program is likely (to the chosen accuracy level) to make it’s prediction while the player is struggling to be a one boxer.
As a human player what comes through my mind while running my program is ok: I want to get a million dollars, henceforth I have to become a one boxer.