The Paradox Itself

University of California physicist William Newcomb invented a puzzle in 1960 that philosophers have been talking about for a while now. It is interesting partly because reasonable philosophers disagree with each other about its solution, partly because it has very little to do with jargon and moldering books, and partly because it has to do with free will. It works a bit like The Prisoner's Dilemma...

You are presented with two boxes: Box A contains $1000 no matter what. Box B either contains nothing, or it contains $1,000,000 depending on the decision of some supposedly infallible predictor. The predictor can be whatever you want, an alien intelligence, an angel, a time traveler, or something even weirder.

You can take either Box B alone, or you can take both boxes.

Here's the kicker: If the predictor guesses that you will take only Box B, then a million dollars will be in there. If the predictor guesses that you will take both boxes, then it will withhold the $1,000,000.

What do you do?

Some people argue that no matter what the predictor guessed, you should take both boxes. The people who would choose both tend to reason that they perdictor has already made its guess and all that is necessary is to figure out the optimal choice. This table show's their reasoning:

                         You were predicted to    You were predicted to take 
                         take Box B only.         both Box A and Box B.

You actually take        $1,000,000               $0
Box B only.

You actually take both   $1,001,000               $1,000
Box A and Box B.

It seems obvious that you get a thousand dollars more than a million or more than nothing no matter what the predictor guessed... so take the money and run!

Wait a minute though! Didn't we say the predictor was infallible? What if that part was emphasized in a prologue to the story: You are in a room full of twenty people. Each one before you put their head in a scanner (or looks into the eyes of the angel, or whatever) and then makes a choice. The people who take only Box B keep getting a million dollars. Everyone else receives only $1000 and winds up looking wistfully at the millionaires.

Now it’s your turn, do you want to stand by some silly little chart or join the millionaires club?

The Thing I Read About Newcombe's Paradox That Inspired Me To Do Something

Philosophers seem to think that this paradox has something to do with free will. They are about evenly divided on what the paradox means and what the correct answer is, however. Martin Gardner is one of the people who have inked an opinion on this paradox and falls in with those who would take both boxes as the chart indicates they should do, herd behavior to the contrary. Gardner's opinion on free will is that it (1) involves unpredictability despite the fact that (2) it is not simple randomness and also (3) he has it.

Here's what got to me: Gardner contructed a proof by contradiction between the clearly correct logic for taking both boxes, and the obvious failure of this strategy to produce the most lucrative decision if the predictor really does guess right, to claim that such a predictor was logically impossible. He went so far as to say that attempts to guess what a person would do in a situation so intimately tied to self awareness and prediction were doomed to produce no better accuracy than a coin toss.

Gardner's claim seems to me to be a testable claim regarding free will! We can design a psychological test to predict the choice of a person presented with Newcombe's Paradox. If the test predicts their answer more the 50% of the time after a statistically significant number of subjects have taken the test and then been subjected to the situation using the psychological test as the predictor, we must redefine free will a bit, or simply mark the concept as false.

As a psychology major I have decided that this is going to be my first project when I get to classes where they give us a bit of free rein. If you want to help, /msg me true/false, agree/disagree, and multiple choice questions that you think might be answered differently by people who would tend to take both boxes or just Box B.

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