Do you think that gets rid of the problem? ‘It might be possible to outsmart Omega’ strikes me as fairly irrelevant. As long as it’s logically possible that you don’t successfully outsmart Omega, the original problem can still be posed. You still have to make a decision, in those cases where you don’t catch Omega in a net.
I am not saying there isn’t a problem, I am saying the problem is about clarifying volition (in a way not too dissimilar to the “choshi dori” trick in my anecdote). Punching empty air is “losing.” Does this then mean we should abstain from punching? Seems a bit drastic.
Many problems/paradoxes are about clarification. For example the Simpson’s paradox is about clarifying causal vs statistical intuitions.
More specifically, what I am saying is that depending on what commitments you want to make about volition, you would either want to one box, or two box in such a way that Omega can be defeated. The problem is “non-identified” as stated. This is equivalent to choosing axioms in set theory. You don’t get to say someone fails set theory if they don’t like Choice.
1 - Supposing I have no philosophical views at all about volition, I would be rationally obliged to one-box. In a state of ignorance, the choice is clear simply provided that I value whatever is being offered. Why should I then take the time to form a theory of volition, if you’re right and at most it can only make me lose more often?
We don’t know what the right answer to Newcomb-like problems will look like, but we do know what the wrong answers will look like.
2 - Supposing I do have a view about volition that makes me think I should two-box, I’ll still be rationally obliged to one-box in any case where my confidence in that view is low enough relative to the difference between the options’ expected values.
For instance, if we assign to two-boxing the value ‘every human being except you gets their skin ripped off and is then executed, plus you get $10’ and assign to one-boxing the value ‘nobody gets tortured or killed, but you miss out on the $10’, no sane and reasonable person would choose to two-box, no matter how confident they (realistically) thought they were that they have a clever impossibility proof. But if two-boxing is the right answer sometimes, then, pace Nozick, it should always be the right answer, at least in cases where the difference between the 2B and 1B outcomes is dramatic enough to even register as a significant decision. Every single one of the arguments for two-boxing generalize to the skin-ripping-off case, e.g., ‘I can’t help being (causal-decision-theory-)rational!’ and ‘it’s unfair to punish me for liking CDT; I protest by continuing to employ CDT’.
3 - You seem to be under the impression that there’s something implausible or far-fetched about the premise of Newcomb’s Problem. There isn’t. If you can’t understand a 100% success rate on Omega’s part, then imagine a 99% success rate, or a 50% one. The problem isn’t altered in substance by this.
Edit: and come to think of it I am somewhat less sure about the lower success rates in general. If I can roughly estimate Omega’s prediction about me that would seem to screen off any timeless effect. Like, you could probably pretty reliably predict how someone would answer this question based on variables like Less Wrong participation and having a Phd in philosophy. Using this information, I could conclude that an Omega with 60% accuracy is probably going to classify me as a one-boxer no matter what I decide… and in that case why not two box?
Sorry, by a 50% success rate I meant that Omega correctly predicts your action 50% of the time, and the other half of the time just guesses. Guessing can also yield the right answer, so this isn’t equivalent to a 50% success rate in the sense you meant, which was simply ‘Does Omega put the money in the box he would have wished to?’
If you know that Omega will take into account that you’re a LessWronger, but also know that he won’t take into account any other information about you (including not taking into account the fact that you know that he knows you’re a LessWronger!), then yes, you should two-box. But that’s quite different from merely knowing that Omega has a certain success rate. Let’s suppose we know that 60% of the time Omega makes the decision it would have wished were it omniscient. Then we get:
If I one-box: 60% chance of $1,000,000, 40% chance of $1000.
If I two-box: 60% chance of $1000, 40% chance of $1,001,000.
Then the expected value of one-boxing is $600,400. Expected value of two-boxing is $401,000. So you should one-box in this situation.
You are not listening to me. Suppose this fellow comes by and offers to play a game with you. He asks you to punch him in the face, where he is not allowed to dodge or push your hand. If you hit him, he gives you 1000 dollars, if you miss, you give him 1000 dollars. He also informs you that he has a success rate of over 90% playing this game with randomly sampled strangers. He can show you videos of previous games, etc.
This game is not a philosophical contrivance. There are people who can do this here in physical reality where we both live.
Now, what is the right reaction here? My point is that if your right reaction is to not play then you are giving up too soon. The reaction to not play is to assume a certain model of the situation and leave it there. In fact, all models are wrong, and there is much to be learned about e.g. how punching works in digging deeper into how this fellow wins this game. To not play and leave it at that is incurious.
Certainly the success rate this fellow has with the punching game has nothing to do with any grand philosophical statement about the lack of physical volition by humans.
Learning about how punching works, rather than winning 1000 dollars, is the entire point of this game.
My answer to Newcomb’s problem is to one-box if and only if Omega is not defeatable and two-box in a way that defeats Omega otherwise. Omega can be non-defeatable only if certain things hold. For example if it is possible to fully simulate in physical reality a given human’s decision process at a particular point in time, and have this simulation be “referentially transparent.”
My answer to Newcomb’s problem is to one-box if and only if Omega is not defeatable and two-box in a way that defeats Omega otherwise
But now you’ve laid out your decision-making process, so all Omega needs to do now is to predict whether you think he’s defeatable. ;-)
In general, I expect Omega could actually be implemented just by being able to tell whether somebody is likely to overthink the problem, and if so, predict they will two-box. That might be sufficient to get better-than-chance predictions.
To put it yet another way: if you’re trying to outsmart Omega, that means you’re trying to figure out a rationalization that will let you two-box… which means Omega should predict you’ll two-box. ;-)
Do you think that gets rid of the problem? ‘It might be possible to outsmart Omega’ strikes me as fairly irrelevant. As long as it’s logically possible that you don’t successfully outsmart Omega, the original problem can still be posed. You still have to make a decision, in those cases where you don’t catch Omega in a net.
I am not saying there isn’t a problem, I am saying the problem is about clarifying volition (in a way not too dissimilar to the “choshi dori” trick in my anecdote). Punching empty air is “losing.” Does this then mean we should abstain from punching? Seems a bit drastic.
Many problems/paradoxes are about clarification. For example the Simpson’s paradox is about clarifying causal vs statistical intuitions.
More specifically, what I am saying is that depending on what commitments you want to make about volition, you would either want to one box, or two box in such a way that Omega can be defeated. The problem is “non-identified” as stated. This is equivalent to choosing axioms in set theory. You don’t get to say someone fails set theory if they don’t like Choice.
1 - Supposing I have no philosophical views at all about volition, I would be rationally obliged to one-box. In a state of ignorance, the choice is clear simply provided that I value whatever is being offered. Why should I then take the time to form a theory of volition, if you’re right and at most it can only make me lose more often?
We don’t know what the right answer to Newcomb-like problems will look like, but we do know what the wrong answers will look like.
2 - Supposing I do have a view about volition that makes me think I should two-box, I’ll still be rationally obliged to one-box in any case where my confidence in that view is low enough relative to the difference between the options’ expected values.
For instance, if we assign to two-boxing the value ‘every human being except you gets their skin ripped off and is then executed, plus you get $10’ and assign to one-boxing the value ‘nobody gets tortured or killed, but you miss out on the $10’, no sane and reasonable person would choose to two-box, no matter how confident they (realistically) thought they were that they have a clever impossibility proof. But if two-boxing is the right answer sometimes, then, pace Nozick, it should always be the right answer, at least in cases where the difference between the 2B and 1B outcomes is dramatic enough to even register as a significant decision. Every single one of the arguments for two-boxing generalize to the skin-ripping-off case, e.g., ‘I can’t help being (causal-decision-theory-)rational!’ and ‘it’s unfair to punish me for liking CDT; I protest by continuing to employ CDT’.
3 - You seem to be under the impression that there’s something implausible or far-fetched about the premise of Newcomb’s Problem. There isn’t. If you can’t understand a 100% success rate on Omega’s part, then imagine a 99% success rate, or a 50% one. The problem isn’t altered in substance by this.
A 50% success rate would recommend two boxing.
Edit: and come to think of it I am somewhat less sure about the lower success rates in general. If I can roughly estimate Omega’s prediction about me that would seem to screen off any timeless effect. Like, you could probably pretty reliably predict how someone would answer this question based on variables like Less Wrong participation and having a Phd in philosophy. Using this information, I could conclude that an Omega with 60% accuracy is probably going to classify me as a one-boxer no matter what I decide… and in that case why not two box?
Sorry, by a 50% success rate I meant that Omega correctly predicts your action 50% of the time, and the other half of the time just guesses. Guessing can also yield the right answer, so this isn’t equivalent to a 50% success rate in the sense you meant, which was simply ‘Does Omega put the money in the box he would have wished to?’
If you know that Omega will take into account that you’re a LessWronger, but also know that he won’t take into account any other information about you (including not taking into account the fact that you know that he knows you’re a LessWronger!), then yes, you should two-box. But that’s quite different from merely knowing that Omega has a certain success rate. Let’s suppose we know that 60% of the time Omega makes the decision it would have wished were it omniscient. Then we get:
If I one-box: 60% chance of $1,000,000, 40% chance of $1000.
If I two-box: 60% chance of $1000, 40% chance of $1,001,000.
Then the expected value of one-boxing is $600,400. Expected value of two-boxing is $401,000. So you should one-box in this situation.
This makes sense.
You are not listening to me. Suppose this fellow comes by and offers to play a game with you. He asks you to punch him in the face, where he is not allowed to dodge or push your hand. If you hit him, he gives you 1000 dollars, if you miss, you give him 1000 dollars. He also informs you that he has a success rate of over 90% playing this game with randomly sampled strangers. He can show you videos of previous games, etc.
This game is not a philosophical contrivance. There are people who can do this here in physical reality where we both live.
Now, what is the right reaction here? My point is that if your right reaction is to not play then you are giving up too soon. The reaction to not play is to assume a certain model of the situation and leave it there. In fact, all models are wrong, and there is much to be learned about e.g. how punching works in digging deeper into how this fellow wins this game. To not play and leave it at that is incurious.
Certainly the success rate this fellow has with the punching game has nothing to do with any grand philosophical statement about the lack of physical volition by humans.
Learning about how punching works, rather than winning 1000 dollars, is the entire point of this game.
My answer to Newcomb’s problem is to one-box if and only if Omega is not defeatable and two-box in a way that defeats Omega otherwise. Omega can be non-defeatable only if certain things hold. For example if it is possible to fully simulate in physical reality a given human’s decision process at a particular point in time, and have this simulation be “referentially transparent.”
edit: fixed a typo.
There is a typo here.
But now you’ve laid out your decision-making process, so all Omega needs to do now is to predict whether you think he’s defeatable. ;-)
In general, I expect Omega could actually be implemented just by being able to tell whether somebody is likely to overthink the problem, and if so, predict they will two-box. That might be sufficient to get better-than-chance predictions.
To put it yet another way: if you’re trying to outsmart Omega, that means you’re trying to figure out a rationalization that will let you two-box… which means Omega should predict you’ll two-box. ;-)