I asked a friend recently what he would do if encountering Newcomb’s problem. Instead of giving either of the standard answer, he immediately attempted to create a paradoxical outcome and, as far as I can tell, succeeded. He claims that he would look inside the possibly-a-million-dollars box and do the following:
If the box contains a million dollars, take both boxes.
If the box contains nothing, take only that box (the empty one).
What would Omega do if he predicted this behavior or is this somehow not allowed in the problem setup?
Not allowed. You get to look into the second box only after you have chosen. And even if both boxes were transparent, the paradox is easily fixed. Omega shouldn’t predict what will you do (because that’s assuming that you will ignore the content of the second box and Omega isn’t stupid like that) but what will you do if box B contains a million dollars. Then it would correctly predict that your friend would two-box in that situation, so it wouldn’t put the million dollars into the second box and your friend would take only the empty box according to his strategy. So yeah.
There actually is a variant where you’re allowed to look into the boxes—Newcomb’s problem with transparent boxes.
And yes, it is undefined if you apply the same rules. However, there are two ways to re-define it.
1: Reduce the scope of the inputs. For example, Omega could operate on the following program: “If the contestant would take only one box when the million dollars is there, put the million dollars there.” Before, Omega was looking at both situations, and now it’s only looking at one.
2: Increase the scope of the program. There are two possible responses in two possible situations for a total of four inputs, so you just need to define Omega’s response for all four. It’s interesting that Omega now treats you differently depending on your thoughts, not just depending on which box you take, so this changes the genre of the problem.
An unusual answer to Newcomb’s problem:
I asked a friend recently what he would do if encountering Newcomb’s problem. Instead of giving either of the standard answer, he immediately attempted to create a paradoxical outcome and, as far as I can tell, succeeded. He claims that he would look inside the possibly-a-million-dollars box and do the following: If the box contains a million dollars, take both boxes. If the box contains nothing, take only that box (the empty one).
What would Omega do if he predicted this behavior or is this somehow not allowed in the problem setup?
Not allowed. You get to look into the second box only after you have chosen. And even if both boxes were transparent, the paradox is easily fixed. Omega shouldn’t predict what will you do (because that’s assuming that you will ignore the content of the second box and Omega isn’t stupid like that) but what will you do if box B contains a million dollars. Then it would correctly predict that your friend would two-box in that situation, so it wouldn’t put the million dollars into the second box and your friend would take only the empty box according to his strategy. So yeah.
That’s a nice simple way to reword it. Thanks.
There actually is a variant where you’re allowed to look into the boxes—Newcomb’s problem with transparent boxes.
And yes, it is undefined if you apply the same rules. However, there are two ways to re-define it.
1: Reduce the scope of the inputs. For example, Omega could operate on the following program: “If the contestant would take only one box when the million dollars is there, put the million dollars there.” Before, Omega was looking at both situations, and now it’s only looking at one.
2: Increase the scope of the program. There are two possible responses in two possible situations for a total of four inputs, so you just need to define Omega’s response for all four. It’s interesting that Omega now treats you differently depending on your thoughts, not just depending on which box you take, so this changes the genre of the problem.