nm@hou2b.UUCP (10/31/83)
Imagine, if you can, the following choice in what I shall call a "Newcomb situation." You are offered the contents of one or two boxes. The first is open and is seen to contain a thousand dollars; the other is closed and is said to contain either a million dollars or nothing. You may take whatever the closed box contains (call this the modest choice) or, if you prefer, the contents of both boxes (the ambitious choice). You are supposed to have the following information: (i) The set-up has been arranged by some superb predictor (SP) who has always correctly predicted your choice in similar situations and has nearly always correctly predicted the choices of other persons who resemble you. You therefore confidently expect that SP has correctly predicted your choice on this occasion. (ii) SP has already placed a million dollars in the closed box, if he predicted a "modest" choice. However, if he expected you to make the "ambitious" choice, or to evade a reasoned choice by tossing a coin (or randomising in some other way), he has left the closed box empty. Given that you are in such a "Newcob situation," how should you choose?
halle1@houxz.UUCP (11/01/83)
I think this is misstated. As given, obviously you take the modest choice. Then you are guaranteed a million. I remember (vaguely) the discussion in Sci. Am. a couple years back, but forget the details. I think the correct "modest choice" is the open box, and the correct ambitious choice is the closed one.
stuart@rochester.UUCP (Stuart Friedberg) (11/01/83)
Unless there is some penalty to making the ambitious choice, I'd always take both boxes. I'm guaranteed the contents of the open box and possibly another million dollars. Perhaps you intended that the ambitious choice be *just* the closed box? Or perhaps I have missed something basic about the problem? Stu Friedberg stuart@rochester {seismo, allegra}!rochester!stuart
wolit@rabbit.UUCP (11/01/83)
If you believe in the Supreme Predictor, it's obvious that you should take the closed box alone, since you'll get $1,000,000 instead of only $1,000 (which you'd get if you take both the open box -- containing the $1,000 -- and the closed one -- which the SP left empty, since He/She/It knew you'd try to be greedy). I'm an atheist. I also believe that a bird in the hand PLUS one in the bush is a LOT better that just the one in the bush. I'll take both boxes. The math here is trivial. The "problem" is interesting for reasons that have nothing to do with math. Let's leave things like this for net.religion. Jan Wolitzky, AT&T Bell Laboratories, Murray Hill, NJ
marla@ssc-vax.UUCP (Marla S Baer) (11/01/83)
[this line intentionally left not blank] You should take both boxes. The person setting up the boxes has two possible decisions: either the selector will take both boxes, or only the closed box. The chooser also has two choices. A table of the options looks like this: setter closed both c |-------------------------- h | o closed| $1,000,000 $0 o | s both | $1,001,000 $1,000 e | r In both cases, the selecter will make out better by choosing both boxes. Marla S. Baer !ssc-vax!marla (Seattle, WA) s e r
thomas@utah-gr.UUCP (Spencer W. Thomas) (11/02/83)
We went through this one about 6 months ago. It generated LOTS of traffic. Let's not do it again, ok? =Spencer