weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (03/21/86)
I am presenting a famous dilemma originally proposed by the physicist William Newcomb. I think it can be of interest to the readers of all the newsgroups I've posted to, because it touches on the nature of faith and reason, but I am directing all followups to net.puzzle only. In particular, I'd like to know if it has any bearing on the possibilities of either perfect precognition or rational decision making. ------------------------------------------------------------------------- The situation involves a being X. X is precognizant. In the first version of the problem, X is perfect in this power. If you like, X is God. In the second version, X is only partially precognizant, but has a very very good track record--at least 99% accurate according to all studies. X is also very rich and completely honest. X puts an unknown amount of money in two boxes A and B. X tells you that he put $1K (= one thousand dollars) in box A. X also tells you that he put either $0 or $1M (= one million dollars) in box B. You are now given one chance to earn some quick and easy money. Your only options are (1) the one-boxer option: Open box B only. (2) the two-boxer option: Open box A and B both. You are not going to be given a second chance nor a third option. X furthermore tells you that he put $1M in box B if X predicted you would follow option (1) only. He then tells you he put $0 in box B if he predicted you would follow option (2) only, or if you end up deciding to use a randomization device (other than, if you wish, your own free will). The question is, what do you pick, in either version? And why? Let me emphasize, there is no retroactive changing of the contents of box B. Either there is a million dollars waiting for you in box B or there isn't. There definitely is a thousand dollars waiting for you in box A. And if it all seems too simple to you, would it make any difference if the boxes were transparent? ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720
js2j@mhuxt.UUCP (sonntag) (03/24/86)
I've deleted the problem statement here. Hopefully, everyone's read a copy of it by now. > The question is, what do you pick, in either version? And why? > > And if it all seems too simple to you, would it make any difference if > the boxes were transparent? > ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720 In the first case, with a perfect precogniter, choosing only box B nets you a million dollars. Choosing the two box option gets you $1000. And, of course, it would make no difference if the boxes were transparent, I'll still take the million bucks in box B. If there weren't a million bucks in box B, I'd still choose it, just so I could show this precognitor to be a charlatan. In the second case, with a 99% accurate precogniter, choosing only box B yields an expected payoff of $990,000. Choosing both boxes yields an expected payoff of $10,990. With opaque boxes, I'd have to choose just box B. With transparent boxes, I'd arrive with a blindfold on, and open just box B, and hope the precogniter hadn't made a mistake. It would be tempting to peek, and choose the other option if there was no megabuck in B, or to choose the two-box option in order to get the extra kilobuck. However, if I do this, unless the precognitor was in error, I'm liable to find only $1000 there, and choose the two-box option, just as predicted. It's this kind of paradox that suggests the impossibility of precognition. If X predicts that I'll open both boxes, and so doesn't put the megabuck in box B, peekers will see that and choose both boxes. If X predicts that I'll open just box B, greedy peekers will pick both boxes, invalidating X's prediction. Non-greedy peekers will fullfill the prophesy, of course. What does this have to do with faith? I'm really not sure, but the non-peekers made out best in this carefully produced example which assumes the existence of a precogniter. Maybe it's meant to point out that the faithful will make out best if there exists a god who has made up certain arbitrary rules? I feel compelled to note that they'll do less well than the peekers if they're wrong about this assumption. -- Jeff Sonntag ihnp4!mhuxt!js2j
kort@hounx.UUCP (B.KORT) (03/25/86)
I agree with Jeff Sonntag that Newcomb's Paradox suggests that perfect precognition is impossible. Another convincing proof appears in a charming piece by Smullyan entitled Is God Stubborn? Smullyan sets up a scenario where an omniscient God cannot *reveal* his prediction of which breakfast cereal the stubbornly willful and defiant mortal will select. The mortal has vowed to select the opposite choice from the prediction. (Of course, if *I* were doing the prediction, I'd starve the bastard into submission by predicting that he'd eat at least one of his choices.) --Barry Kort ...ihnp4!hounx!kort