In principle, you could base your decision of whether to one-box or two-box
on anything you like: for example, on whether the name of some obscure childhood friend had an
even or odd number of letters. However, this suggests that the problem of predicting whether
you will one-box or two-box is “you-complete.” In other words, if the Predictor can solve this
problem reliably, then it seems to me that it must possess a simulation of you so detailed as to
constitute another copy of you (as discussed previously).
But in that case, to whatever extent we want to think about Newcomb’s paradox in terms of
a freely-willed decision at all, we need to imagine two entities separated in space and time—the
“flesh-and-blood you,” and the simulated version being run by the Predictor—that are nevertheless
“tethered together” and share common interests. If we think this way, then we can easily explain
why one-boxing can be rational, even without backwards-in-time causation. Namely, as you
contemplate whether to open one box or two, who’s to say that you’re not “actually” the simulation?
If you are, then of course your decision can affect what the Predictor does in an ordinary, causal
way.
This is because Newcomb’s problem is not reliant on the predictor being perfectly accurate. All they need to do is predict you so well that people who one-box walk away with more expected utility than people who two-box. This is easy—even humans can predict other humans this well (though we kinda evolved to be good at it).
So if it’s still worth it to one-box even if you’re not being copied, what good is an argument that relies on you being copied to work?
In response to this, I want to roll back to saying that while you may not actually be simulated, having the programming to one-box is what causes there to be a million dollars in there. But, I guess that’s the basic intuition behind one-boxing/the nature of prediction anyway so nothing non-trivial is left (except the increased ability to explain it to non-LW people).
It seems way simpler to leave out the “freely willed decision” part altogether.
If we posit that the Predictor can reliably predict my future choice based on currently available evidence, it follows that my future choice is constrained by the current state of the world. Given that, what remains to be explained?
Yes, I agree with you—but when you tell some people that the question arises of what is in the big-money box after Omega leaves… and the answer is “if you’re considering this, nothing.”
A lot of others (non-LW people) I tell this to say it doesn’t sound right. The bit just shows you that the seeming closed-loop is not actually a closed loop in a very simple and intuitive way** (oh and it actually agrees with ‘there is no free will’), and also it made me think of the whole thing from a new light (maybe other things that look like closed loops can be shown not to be in similar ways).
** Anna Salamon’s cutting argument is very good too but a) it doesn’t make the closed-loop-seeming thing any less closed-loop-seeming and b) it’s hard to understand for most people and I’m guessing it will look like garbage to people who don’t default to compatibilist.
I suppose. When dealing with believers in noncompatibilist free will, I typically just accept that on their view a reliable Predictor is not possible in the first place, and so they have two choices… either refuse to engage with the thought experiment at all, or accept that for purposes of this thought experiment they’ve been demonstrated empirically to be wrong about the possibility of a reliable Predictor (and consequently about their belief in free will).
That said, I can respect someone refusing to engage with a thought experiment at all, if they consider the implications of the thought experiment absurd.
As long as we’re here, I can also respect someone whose answer to “Assume Predictor yadda yadda what do you do?” is “How should I know what I do? I am not a Predictor. I do whatever it is someone like me does in that situation; beats me what that actually is.”
I usually deal with people who don’t have strong opinions either way, so I try to convince them. Given total non-compatibilists, what you do makes sense.
Also, it struck me today that this gives a way of one-boxing within CDT. If you naively blackbox prediction, you would get an expected utility table {{1000,0},{1e6+1e3,1e6}} where two-boxing always gives you 1000 dollars more.
But, once you realise that you might be a simulated version, the expected utility of one-boxing is 1e6 but of two-boxing is now is 5e5+1e3. So, one-box.
A similar analysis applies to the counterfactual mugging.
Further, this argument actually creates immunity to the response ‘I’ll just find a qubit arbitrarily far back in time and use the measurement result to decide.’ I think a self-respecting TDT would also have this immunity, but there’s a lot to be said for finding out where theories fail—and Newcomb’s problem (if you assume the argument about you-completeness) seems not to be such a place for CDT.
Disclaimer: My formal knowledge of CDT is from wikipedia and can be summarised as ‘choose A that maximises
%20=%20\Sigma_i%20P(A%20\rightarrow%20O_i)%20D(O_i)$) where D is the desirability function and P the probability function.’
I like his causal answer to Newcomb’s problem:
Simple but misleading.
This is because Newcomb’s problem is not reliant on the predictor being perfectly accurate. All they need to do is predict you so well that people who one-box walk away with more expected utility than people who two-box. This is easy—even humans can predict other humans this well (though we kinda evolved to be good at it).
So if it’s still worth it to one-box even if you’re not being copied, what good is an argument that relies on you being copied to work?
In response to this, I want to roll back to saying that while you may not actually be simulated, having the programming to one-box is what causes there to be a million dollars in there. But, I guess that’s the basic intuition behind one-boxing/the nature of prediction anyway so nothing non-trivial is left (except the increased ability to explain it to non-LW people).
Also, the calculation here is wrong.
Ok, in that case, am I allowed to roll a dice to determine whether to one box?
Depends on the rules. Who do I look like, Gary Drescher?
What sort of rules would you implement to keep Newcomb’s problem interesting in the fact of coins that you can’t predict?
Why would I want to keep the problem interesting? I want to solve it.
Because the solution to the problem is worthless except to the extent that it establishes your position in an issue it’s constructed to illuminate.
It seems way simpler to leave out the “freely willed decision” part altogether.
If we posit that the Predictor can reliably predict my future choice based on currently available evidence, it follows that my future choice is constrained by the current state of the world. Given that, what remains to be explained?
Yes, I agree with you—but when you tell some people that the question arises of what is in the big-money box after Omega leaves… and the answer is “if you’re considering this, nothing.”
A lot of others (non-LW people) I tell this to say it doesn’t sound right. The bit just shows you that the seeming closed-loop is not actually a closed loop in a very simple and intuitive way** (oh and it actually agrees with ‘there is no free will’), and also it made me think of the whole thing from a new light (maybe other things that look like closed loops can be shown not to be in similar ways).
** Anna Salamon’s cutting argument is very good too but a) it doesn’t make the closed-loop-seeming thing any less closed-loop-seeming and b) it’s hard to understand for most people and I’m guessing it will look like garbage to people who don’t default to compatibilist.
I suppose.
When dealing with believers in noncompatibilist free will, I typically just accept that on their view a reliable Predictor is not possible in the first place, and so they have two choices… either refuse to engage with the thought experiment at all, or accept that for purposes of this thought experiment they’ve been demonstrated empirically to be wrong about the possibility of a reliable Predictor (and consequently about their belief in free will).
That said, I can respect someone refusing to engage with a thought experiment at all, if they consider the implications of the thought experiment absurd.
As long as we’re here, I can also respect someone whose answer to “Assume Predictor yadda yadda what do you do?” is “How should I know what I do? I am not a Predictor. I do whatever it is someone like me does in that situation; beats me what that actually is.”
I usually deal with people who don’t have strong opinions either way, so I try to convince them. Given total non-compatibilists, what you do makes sense.
Also, it struck me today that this gives a way of one-boxing within CDT. If you naively blackbox prediction, you would get an expected utility table {{1000,0},{1e6+1e3,1e6}} where two-boxing always gives you 1000 dollars more.
But, once you realise that you might be a simulated version, the expected utility of one-boxing is 1e6 but of two-boxing is now is 5e5+1e3. So, one-box.
A similar analysis applies to the counterfactual mugging.
Further, this argument actually creates immunity to the response ‘I’ll just find a qubit arbitrarily far back in time and use the measurement result to decide.’ I think a self-respecting TDT would also have this immunity, but there’s a lot to be said for finding out where theories fail—and Newcomb’s problem (if you assume the argument about you-completeness) seems not to be such a place for CDT.
Disclaimer: My formal knowledge of CDT is from wikipedia and can be summarised as ‘choose A that maximises