Rational Agents should Win
I don’t know if I’ve linked to Overcoming Bias before or not. It doesn’t deal with gaming, but is interesting and sometimes deals with tangential items of interest (especially to game theory).
Today they are talking about Newcomb’s Paradox (which I first encountered in a math class in middle-school. Thanks, Martin.)
And the following jumped out:
Nonetheless, I would like to present some of my motivations on Newcomb’s Problem – the reasons I felt impelled to seek a new theory – because they illustrate my source-attitudes toward rationality. Even if I can’t present the theory that these motivations motivate…
First, foremost, fundamentally, above all else:
Rational agents should WIN.
Don’t mistake me, and think that I’m talking about the Hollywood Rationality stereotype that rationalists should be selfish or shortsighted. If your utility function has a term in it for others, then win their happiness. If your utility function has a term in it for a million years hence, then win the eon.
But at any rate, WIN. Don’t lose reasonably, WIN.
{I’m adding them to the blogroll and cleaning up some old URLs).
The Tao of Gaming 
I’d never seen Newcomb’s Paradox before, but its interesting. It seems to come down to an issue of causality. If picking box B causes the ‘perfect predictor’ to have predicted that you will pick only B (and thus get the $1M), then B seems like the only reasonable choice. If your choice is truly independant of the prediction, then it makes sense to take both boxes. So really, which choice is rational depends on your understanding of the ‘perfect predictor’. If the predictor truly cannot be wrong, then your choice is between both (1K) and B (1M), and you should pick B. If the predictor can be wrong, then you should pick both.
My way of thinking about it is that the only way the perfect predictor can exist is if your action is causing the predictor’s decision to occur, and thus you should pick B. Another way to look at it: The predictor gets perfect foreknowledge of what you choose. If you end up choosing B, the predictor will have gotten the foreknowledge that you would pick B, and would have put the money in.
Basically, if the predictor can see the future, and puts money into B based on your decision, then your decision actually causes the predictor’s action. Because of that, you should choose B, cause the predictor to put the million into B, and get the big money.
I dont see it as a case of rational vs irrational behavior, but rather about wether or not you believe that this ‘perfect predictor’s action is caused by your choice or not.
Alexfrog
February 1, 2008 at 6:43 pm
I’d never seen Newcomb’s Paradox before, but its interesting. It seems to come down to an issue of causality. If picking box B causes the ‘perfect predictor’ to have predicted that you will pick only B (and thus get the $1M), then B seems like the only reasonable choice. If your choice is truly independant of the prediction, then it makes sense to take both boxes. So really, which choice is rational depends on your understanding of the ‘perfect predictor’. If the predictor truly cannot be wrong, then your choice is between both (1K) and B (1M), and you should pick B. If the predictor can be wrong, then you should pick both.
My way of thinking about it is that the only way the perfect predictor can exist is if your action is causing the predictor’s decision to occur, and thus you should pick B. Another way to look at it: The predictor gets perfect foreknowledge of what you choose. If you end up choosing B, the predictor will have gotten the foreknowledge that you would pick B, and would have put the money in.
Basically, if the predictor can see the future, and puts money into B based on your decision, then your decision actually causes the predictor’s action. Because of that, you should choose B, cause the predictor to put the million into B, and get the big money.
I dont see it as a case of rational vs irrational behavior, but rather about wether or not you believe that this ‘perfect predictor’s action is caused by your choice or not.
Alexfrog
February 1, 2008 at 6:43 pm
I’d never seen Newcomb’s Paradox before, but its interesting. It seems to come down to an issue of causality. If picking box B causes the ‘perfect predictor’ to have predicted that you will pick only B (and thus get the $1M), then B seems like the only reasonable choice. If your choice is truly independant of the prediction, then it makes sense to take both boxes. So really, which choice is rational depends on your understanding of the ‘perfect predictor’. If the predictor truly cannot be wrong, then your choice is between both (1K) and B (1M), and you should pick B. If the predictor can be wrong, then you should pick both.
My way of thinking about it is that the only way the perfect predictor can exist is if your action is causing the predictor’s decision to occur, and thus you should pick B. Another way to look at it: The predictor gets perfect foreknowledge of what you choose. If you end up choosing B, the predictor will have gotten the foreknowledge that you would pick B, and would have put the money in.
Basically, if the predictor can see the future, and puts money into B based on your decision, then your decision actually causes the predictor’s action. Because of that, you should choose B, cause the predictor to put the million into B, and get the big money.
I dont see it as a case of rational vs irrational behavior, but rather about wether or not you believe that this ‘perfect predictor’s action is caused by your choice or not.
Alexfrog
February 1, 2008 at 6:43 pm
“I dont see it as a case of rational vs irrational behavior, but rather about wether or not you believe that this ‘perfect predictor’s action is caused by your choice or not.”
Due to the way the problem is created, you do not get to “believe” anything. That is the setup: assuming a perfect predictor, what should you do?
“Basically, if the predictor can see the future, and puts money into B based on your decision, then your decision actually causes the predictor’s action. Because of that, you should choose B, cause the predictor to put the million into B, and get the big money.”
If the predictor puts money in box B, can you even choose both boxes? Have you already “chosen”? The phrase “you should choose B” does not seem to fit. It is “too late”, you already did choose. At the point when the boxes are placed in front of you, the future is determined. The “choice” is already set.
MrHen
February 2, 2008 at 1:01 pm
In the setup of the ‘paradox’, there are two contradictory implications.
One is that that this perfect predictor has already made the decision and placed the money in the boxes and left: ‘Your decision does not effect what is in the boxes’, and the second is that whatever ends up in the boxes is based on your choice: ‘Your decision DOES effect what is in the boxes’.
If your decision doesnt effect the contents of the boxes, the correct choice is to take both. If your decision DOES effect them, then the correct decision is to take B.
In the conclusion of the paradox, it is assumed that the predictor was right once again, and the chooser of both boxes got $1k, and the other got $1m. It doesnt go over any cases where the predictor was wrong.
I think the most rational way to interpret this whole scenario is that your decision is actually causing the action of the predictor (based on how this is all set up), and thus you choose B, in order to cause it to have the million.
Alexfrog
February 2, 2008 at 3:29 pm
Alex, there’s at least one other way of interpreting this problem. Let’s assume the Predictor is a peerless judge of people and can determine, with great accuracy, how they will act in different situations. So if he thinks you are a “rational” sort, he knows you will choose both boxes (why not, it maximizes return) and will only put in $1000. If, instead, he thinks you are the type who can be ruled by faith/superstition/irrationality (take your choice), he will go with $1,000,000. His abilities go as far as predicting how you will double guess yourself (i.e., how your estimate of the Predictor’s success will affect your decision). In this world view, you could say that if I just choose Box B, the Predictor knew I would eventually come to this conclusion, by whatever tortured logic was necessary, and therefore, he would cough up a mill. If, instead, I just can’t bring myself to only take one box, he figured that out as well and I’ll only wind up with a thou.
I’ve seen the paradox before and it has lots of interesting insights into a variety of topics, including free will and religious thought. In the latter case, of course, it’s easy to equate the Predictor with God.
Larry Levy
February 2, 2008 at 4:51 pm
My personal theory is that if we are assuming a perfect predictor (and obviously it is a troubling point … I’m not a calvinist; I do believe there are limits of free will, but not in this particular case). (“The heart can do what it wants, but it cannot want what it wants.”)
The usual description of Omega is that you’ve seen him make hundreds (thousands) of test before, and he’s never wrong. Perhaps he may be wrong on you, though.
Judging from the commentary over there, casuality does seem to be another big talking point.
Brian
February 2, 2008 at 9:05 pm
My personal theory is that if we are assuming a perfect predictor (and obviously it is a troubling point … I’m not a calvinist; I do believe there are limits of free will, but not in this particular case). (“The heart can do what it wants, but it cannot want what it wants.”)
The usual description of Omega is that you’ve seen him make hundreds (thousands) of test before, and he’s never wrong. Perhaps he may be wrong on you, though.
Judging from the commentary over there, casuality does seem to be another big talking point.
Brian
February 2, 2008 at 9:05 pm
Personally, I think that the paradox simply shows that the assumptions are false.
From a player’s perspective, however, taking Box B is obvious. The choice is roughly break-even if the “infallible” predictor is 50/50, so if you don’t believe it’s infallible or even better than random, there’s minimal upside to taking both. Add in the Important Money Principle (the assumption that $1000 won’t change your life, but $1,000,000 will and that $1,001,000 is essentially equal to $1,000,000), and it’s a no-brainer to hope that the purported perfect predictor is right. If you need $1000 to survive, just take them both, take your $1000 and feel lucky to have had someone give you free money 🙂
JeffG
February 3, 2008 at 10:20 am