Erik Mesoy
Core Tester / Intern
"The following may well be the most controversial dilemma in the history of decision theory."
Assume that you're playing the game in the above situation and that the rules have been explained to you, then vote in the poll.
The usual positions in the argument are as follows.
TWO-BOXER:
ONE-BOXER:
One-boxers are usually confident that their opinion is correct and that picking two boxes is silly. Two-boxers are usually confident that their opinion is correct and that picking one box is silly. Nonetheless, people tend to be about evenly split on the issue.
Let the arguing begin. Which do you pick, and why?
Addendum: "iff" in the starting quote means "if and only if".
http://pastie.caboo.se/195189.txtA superintelligence from another galaxy, whom we shall call Omega, comes to Earth and sets about playing a strange little game. In this game, Omega selects a human being, sets down two boxes in front of them, and flies away.
Box A is transparent and contains a thousand dollars.
Box B is opaque, and contains either a million dollars, or nothing.
You can take both boxes, or take only box B.
And the twist is that Omega has put a million dollars in box B iff Omega has predicted that you will take only box B.
Omega has been correct on each of 100 observed occasions so far - everyone who took both boxes has found box B empty and received only a thousand dollars; everyone who took only box B has found B containing a million dollars. (We assume that box A vanishes in a puff of smoke if you take only box B; no one else can take box A afterward.)
Before you make your choice, Omega has flown off and moved on to its next game. Box B is already empty or already full.
Omega drops two boxes on the ground in front of you and flies off.
Do you take both boxes, or only box B?
Assume that you're playing the game in the above situation and that the rules have been explained to you, then vote in the poll.
The usual positions in the argument are as follows.
TWO-BOXER:
Spoiler :
Gogf said:Why you should pick both boxes:
The key here is that Omega (the alien) has already put the money is the boxes before you decide whether to take both boxes or just box b. In other words, your decision cannot affect what is in the boxes, because the money was put there IN THE PAST.
That means there are two possible scenarios: either there is $1,000,000 in box b, or there is not. Remember that your choice of box does not determine which of these scenarios actually exists... that is arbitrarily chosen by the alien. Now, for either scenario, taking both boxes will get you whatever is in box b AND $1,000 extra dollars. That means that regardless of what is in the two boxes, taking both will ALWAYS get you $1,000 more than if you had just taken box b. It is stupid, then, not to take both... unless you don't like money!
Erik will doubtless argue that he will be "$900,000 richer than you," but while this may be true, you are $1,000 richer than you would have been if you had taken box b, so his good fortune has no bearing on how much money YOU have. The alien having been right 100% of the time before is equally irrelevant: the implication is supposed to be that he was automatically right this time, but that is untrue. The alien made his decision, and you then made yours; the two were unrelated, and all you did was maximize your profits.
ONE-BOXER:
Spoiler :
Erik said:Knowing that Omega has a 100/100 correctness rate so far, I assign at least a 99% probability that he'll be correct in predicting what I pick. So my expectation from picking both boxes is (0.99*1000 + 0.01*1000) + (0.99*0 + 0.01 * 1000000) = $11000, while my expectation from picking box B is (0.99 * 1000000 + 0.01*0) = $990000. Thus I should pick box B.
Or to make it simpler, anyone who agrees with my point of view should expect a million dollars, and anyone who disagrees should expect a thousand dollars. By any sane metric of reasonable thought, mine is preferable.
One-boxers are usually confident that their opinion is correct and that picking two boxes is silly. Two-boxers are usually confident that their opinion is correct and that picking one box is silly. Nonetheless, people tend to be about evenly split on the issue.
Let the arguing begin. Which do you pick, and why?
Addendum: "iff" in the starting quote means "if and only if".