Newcomb’s Paradox And Probability

http://wmbriggs.com/blog/?p=2769 ^ | William M. Briggs

[mattstat]

When he was at the Lawrence Livermore Laboratory—a place that used to do nukes, but has now decided that orthodox global warming pays better—William Newcomb devised the following puzzle, which some say is a paradox.

You will play a game against an evil entity that can perfectly predict your future actions. Just for the sake of giving the evil one a name, let’s call him “Bill”. Bill is evil because he likes to taunt you with the possibility of making money, only to jerk that chance away from you at the last moment.

Here’s what Bill does, as traditionally described. Later, we add clarifications and twists. Bill puts $1,000 in a clear box, and then also presents you with an opaque box inside of which might contain $1 million. You will be allowed to take both boxes, or just the opaque one. To clarify: you may not take the $1,000 without also taking the opaque box. Obviously, you may keep the contents of whatever box or boxes you take.

Now for the evil part. If Bill predicts—and remember, he’s never wrong—that you will take just the opaque box, he will leave it full of money. But if he predicts that you will greedily take both boxes, then he will put nada in the opaque box, which, after mandatory donations to our betters in Washington, nets you only about $550.

Why Bill would ever want to play this strange game is never mentioned. Anyway, the easiest way to short his ...

[IronJack]

Make your decision dependent on his prediction.

By the way, in the Appropriate Name Department, I’d like to nominate a Livermore bomb scientist named “Newcomb.”