You’re relying on the fact that you have uncertainty about Omega’s prediction, which is really an accidental feature of the problem, not shared by other problems in the same vein.
Imagine a variant where both boxes are transparent and you can see what’s inside, but the contents of the boxes were still determined by Omega’s prediction of your future decision. (I think this formulation is due to Gary Drescher.) I’m a one-boxer in that variant too, how about you? Also see Parfit’s Hitchhiker, where the predictor’s decision depends on what you would do if you already knew the predictor decided in your favor, and Counterfactual Mugging, where you already know that your decision cannot help the current version of you (but you’d precommit to it nonetheless).
The most general solution to such problems that we currently know is Wei Dai’s UDT. Informally it goes something like this: “choose your action so that the fact of your choosing it in your current situation logically implies the highest expected utility (weighted over all apriori possible worlds before you learned your current situation) compared to all other actions you could take in your current situation”.
Extremely counterfactual mugging is the simplest such variation IMO. Though it has the same structure as Parfit’s Hitchhiker, it’s better because issues of trust and keeping promises don’t come into it. Here it is:
Omega will either award you $1000 or ask you to pay him $100. He will award you $1000 if he predicts you would pay him if he asked. He will ask you to pay him $100 if he predicts you wouldn’t pay him if he asked.
Imagine a variant where both boxes are transparent and you can see what’s inside
That seems like a weird situation. Given two boxes, both of them with money, I’d take both. Given instead that one box is empty, I’d just take the one with money. So I’d default to doing whatever Omega didn’t predict, barring me being told in advance about the situation and precommitting to one-boxing.
Sorry for not making things clear from the start. In Gary’s version of the transparent boxes problem, Omega doesn’t predict what you will do, it predicts what you would do if both boxes contained money. Your actions in the other case are irrelevant to Omega. Would you like to change your decision now?
So, basically, I know that if I take both boxes, and both boxes have money, I’m either in a simulation or Omega was wrong? In that case, precommiting to one-boxing seems sensible.
Drescher then goes on to consider the case where you know that Omega has a fixed 99% chance of implementing this algorithm, and a 1% chance of instead implementing the opposite of this algorithm, and argues that you should still one-box in that case if you see the million.
“choose your action so that the fact of your choosing it in your current situation logically implies the highest expected utility (weighted over all apriori possible worlds before you learned your current situation) compared to all other actions you could take in your current situation”.
That sounds awkward. Would you say it’s equivalent to “choose globally winning strategies, not just locally winning actions?”
As far as I know, you understand UDT and can answer that question yourself :-) But to me your formulation sounds a little vague. If a newbie tries to use it to solve Counterfactual Mugging, I think he/she may get confused about the intended meaning of “global”.
And yeah, “globally winning” probably should have been replaced with “optimal,” since the “local” means something specific about payoff matrices and I don’t want to imply the corresponding “global.”
Imagine a variant where both boxes are transparent and you can see what’s inside, but the contents of the boxes were still determined by Omega’s prediction of your future decision. (I think this formulation is due to Gary Drescher.) I’m a one-boxer in that variant too, how about you?
Of course you are, Omega says so! Short of being infinitely confident in Omega’s abilities (and my understanding of them), I’d reach for both boxes. Are you predicting I will see the million will dissolve into thin air?
Are you trying to pre-commit in order to encourage potential Omegas to hand over the money? Is there more extensive discussion of this variant?
No, the problem definition is that if Omega predicts that if you see both boxes full you will take just Box B, then you will see both boxes full, otherwise you will see just Box A full.
Yes, there is a more extensive discussion, in Good and Real. Basically, you act for the sake of what would be the case if you had acted that way.
In this case, there is actually a plausible causal reason to one-box: you could be the instance that Omega is simulating in order to make its prediction. But even if not, there are all sorts of cases where we act for the sake of what would be the case if we did. Good and Real discusses this extensively.
You’re relying on the fact that you have uncertainty about Omega’s prediction, which is really an accidental feature of the problem, not shared by other problems in the same vein.
Imagine a variant where both boxes are transparent and you can see what’s inside, but the contents of the boxes were still determined by Omega’s prediction of your future decision. (I think this formulation is due to Gary Drescher.) I’m a one-boxer in that variant too, how about you? Also see Parfit’s Hitchhiker, where the predictor’s decision depends on what you would do if you already knew the predictor decided in your favor, and Counterfactual Mugging, where you already know that your decision cannot help the current version of you (but you’d precommit to it nonetheless).
The most general solution to such problems that we currently know is Wei Dai’s UDT. Informally it goes something like this: “choose your action so that the fact of your choosing it in your current situation logically implies the highest expected utility (weighted over all apriori possible worlds before you learned your current situation) compared to all other actions you could take in your current situation”.
Extremely counterfactual mugging is the simplest such variation IMO. Though it has the same structure as Parfit’s Hitchhiker, it’s better because issues of trust and keeping promises don’t come into it. Here it is:
That seems like a weird situation. Given two boxes, both of them with money, I’d take both. Given instead that one box is empty, I’d just take the one with money. So I’d default to doing whatever Omega didn’t predict, barring me being told in advance about the situation and precommitting to one-boxing.
Sorry for not making things clear from the start. In Gary’s version of the transparent boxes problem, Omega doesn’t predict what you will do, it predicts what you would do if both boxes contained money. Your actions in the other case are irrelevant to Omega. Would you like to change your decision now?
So, basically, I know that if I take both boxes, and both boxes have money, I’m either in a simulation or Omega was wrong? In that case, precommiting to one-boxing seems sensible.
Drescher then goes on to consider the case where you know that Omega has a fixed 99% chance of implementing this algorithm, and a 1% chance of instead implementing the opposite of this algorithm, and argues that you should still one-box in that case if you see the million.
That sounds awkward. Would you say it’s equivalent to “choose globally winning strategies, not just locally winning actions?”
As far as I know, you understand UDT and can answer that question yourself :-) But to me your formulation sounds a little vague. If a newbie tries to use it to solve Counterfactual Mugging, I think he/she may get confused about the intended meaning of “global”.
I still don’t know if I understand UDT :D
And yeah, “globally winning” probably should have been replaced with “optimal,” since the “local” means something specific about payoff matrices and I don’t want to imply the corresponding “global.”
Of course you are, Omega says so! Short of being infinitely confident in Omega’s abilities (and my understanding of them), I’d reach for both boxes. Are you predicting I will see the million will dissolve into thin air?
Are you trying to pre-commit in order to encourage potential Omegas to hand over the money? Is there more extensive discussion of this variant?
No. Based on your comment, I’m predicting you won’t see the million in the first place.
Isn’t the problem definition that I see both boxes full?
No, the problem definition is that if Omega predicts that if you see both boxes full you will take just Box B, then you will see both boxes full, otherwise you will see just Box A full.
Yes, there is a more extensive discussion, in Good and Real. Basically, you act for the sake of what would be the case if you had acted that way.
In this case, there is actually a plausible causal reason to one-box: you could be the instance that Omega is simulating in order to make its prediction. But even if not, there are all sorts of cases where we act for the sake of what would be the case if we did. Good and Real discusses this extensively.