Welcome to a two-box version of a mind-bending prediction paradox known as Newcomb's Problem. You will soon have a chance to be a test subject in the experiment which reveals the paradox. This experiment will now be described. There are two sealed boxes, red and blue. Exactly one of them contains $5,000,000. The other box is empty. The box which contains the $5 million was determined at a time in the past, when a Being called the Superpredictor (abbreviated SP) predicted a decision that you are now about to make, namely, to indicate which box is YourBox: red or blue. Based only on a scan of your brain (which occurred, say, 6 weeks ago) SP predicted the box you would choose today as YourBox, and it placed the $5,000,000 there. The boxes have been sealed and under guard since that time, awaiting your decision. Now it is the present and the experiment in which you are the subject begins. You have been aware of the details of this experiment from the beginning.
Phase 1. You step up to the two boxes and point to, for instance, the red box and say "red is MyBox" (it could just as well be blue). You cannot use any randomizing or other external mechanism to make this decision because SP will have predicted this action and left both boxes empty.
Phase 2. You may receive the contents of YourBox. However, before you decide to do that, you are offered a bribe of $10,000 to reject the contents of YourBox and accept the contents of the other box. This $10,000 is up-front and guaranteed. If you decide not to accept this bribe, then you'll receive what's in YourBox.
What should you do? The paradox centers around the following two convincing arguments, which urge opposite courses of action:
Argument (1): You should definitely accept the bribe because, by doing so, you can be paid $10,000 to have the contents of either box! In the end, you must accept the contents of one of the boxes. Suppose you see yourself opening the blue box. In that case, declare red as YourBox, take the bribe and be paid $10,000 to receive what is in the box you are going to open anyway, namely, blue. If you're going to open the blue box and accept its contents, ask yourself: "Do I want it opened with or without a gift of $10,000?" Wouldn't it be insane not to accept this gift? Therefore, decide which box you want opened, declare the other box as YourBox, and accept the bribe.
Argument (2): You should definitely reject the bribe. This experiment has been carried out thousands of times with test subjects much like yourself. The vast majority of bribe-takers have gone home with exactly 10 thousand dollars. Conversely, virtually all those who stuck with TheirBox (rejecting the bribe) won the 5 million dollars. SP hardly ever puts the 5 million in the wrong box. Ask yourself: "Do I want to join this club of multimillionaires or not?" The answer is obvious and you should not accept the bribe.
Try it out!
Here are links to two versions of the Predictor: an Incompetent predictor (which is relatively easy to outwit i.e. get the bribe and the $5,000,000) and a Superpredictor which is much harder to outsmart. For each experiment you must first enter a "Brainscan" number in order to allow the Predictor to calibrate and identify you so it will select the correct set of boxes. You then choose YourBox and decide to accept or reject the bribe. Finally you are shown what you receive.
The tables below show the results of accepting or not accepting the bribe for several different values for each predictor. This information may help you to outsmart the incompetent predictor, but offers little help for the Superpredictor.
Incompetent Predictor
Brainscan Box Chosen Bribe Box Opened Result 1702 Blue Reject Blue You win $5,000,000! 179 Red Reject Red You win nothing! Your box is empty. 123456 Red Accept Blue You only get $10,000. 654321 Blue Accept Red You win $5,000,000 plus $10,000 !!! Superpredictor
Brainscan Box Chosen Bribe Box Opened Result 12354 Red Reject Red You win $5,000,000! 54034 Blue Reject Blue You win nothing! Your box is empty. 54321 Red Accept Blue You only get $10,000. 13991 Blue Accept Red You win $5,000,000 plus $10,000 !!!
Original mathematical design © 2000 by Dean Clark