You basically have two strategies—“1-box” or “2-box” (We’ll ignore mixed strategies). So what you do is try to figure out what the payoff from each strategy is, given what you know about your opponent. Then you pick the strategy with the highest expected payoff.
In our Newcomb’s problem game, “what you know about your opponent” includes that they know what move you take, and then get to make their own move. That is, their move actually depends on which move you make / strategy you use. So you should predict that if you use “1-box,” Omega will take the action that maximizes their payoff, and if you use “2-box,” Omega will take the action that maximizes their payoff.
Now that you have used your information to predict Omega’s action for each of your strategies, you can read off the payoffs: $1M for “1-box” and $1k for “2-box.” Then you use the strategy that results in the highest payoff.
That is, their move actually depends on which move you make / strategy you use.
You’re getting this the other way around. It is Omega who plays first. By the time you enter the room and the boxes are in place, it is already determined if $1000000 is in the box or not. Your move depends on Omega’s, not the other way around. Omega’s move depends on the knowledge it has about you.
Omega plays first if you take at as “what happens first”, but chooses second if you take that as having the privileged position of knowing what your opponent does before you must make your choice.
Not really; in Nozick’s original formulation omega doesn’t know what the player chooses, it can only guess. Sure it’s guess may be highly likely to be correct, but it’s still a guess. This distinction is important because if omega is absolutely certain what the player chooses it will always win. The player will only get $1000000 or $1000 but never $1001000.
Fine, replace “knowing what your opponent does” with “having a high degree of confidence in what the other player has or is going to choose”. My point stands—“knowing” is pretty much just a short way of talking about the justified high degree of confidence, anyways.
You basically have two strategies—“1-box” or “2-box” (We’ll ignore mixed strategies). So what you do is try to figure out what the payoff from each strategy is, given what you know about your opponent. Then you pick the strategy with the highest expected payoff.
In our Newcomb’s problem game, “what you know about your opponent” includes that they know what move you take, and then get to make their own move. That is, their move actually depends on which move you make / strategy you use. So you should predict that if you use “1-box,” Omega will take the action that maximizes their payoff, and if you use “2-box,” Omega will take the action that maximizes their payoff.
Now that you have used your information to predict Omega’s action for each of your strategies, you can read off the payoffs: $1M for “1-box” and $1k for “2-box.” Then you use the strategy that results in the highest payoff.
You’re getting this the other way around. It is Omega who plays first. By the time you enter the room and the boxes are in place, it is already determined if $1000000 is in the box or not. Your move depends on Omega’s, not the other way around. Omega’s move depends on the knowledge it has about you.
Fair enough—replace”depends on” with “is ~100% correlated with.”
Omega plays first if you take at as “what happens first”, but chooses second if you take that as having the privileged position of knowing what your opponent does before you must make your choice.
Not really; in Nozick’s original formulation omega doesn’t know what the player chooses, it can only guess. Sure it’s guess may be highly likely to be correct, but it’s still a guess. This distinction is important because if omega is absolutely certain what the player chooses it will always win. The player will only get $1000000 or $1000 but never $1001000.
Fine, replace “knowing what your opponent does” with “having a high degree of confidence in what the other player has or is going to choose”. My point stands—“knowing” is pretty much just a short way of talking about the justified high degree of confidence, anyways.