Infallible Predictor Newcomb: An Argument

December 17, 2007

I’m working up a paper on Newcomb and am seeking feedback on an argument for one-boxing in the infallible predictor version.

The case:

You are brought into a room with two boxes sitting on a table. One box is opaque; you are informed that it contains either $1,000,000 or nothing. The other box is transparent and contains $1,000. You are invited to either take only the opaque box (i.e. “one-box”) or take both boxes (“two-box”). Any money that you collect is yours to keep.

However, prior to making your choice, you receive the following information: Before you entered the room, an infallible predictor made a complete assessment of your psychology. If she predicted that you’d one-box, she put a million dollars in the opaque box. If she predicted that you’d two-box, she put nothing in it.

If you’re greedy and you believe everything you’ve been told (e.g. that the predictor is infallible), what is the rational choice?

The argument:

    1. The predictor made a true prediction.
    2. If the predictor made a true prediction, then [(you will two-box iff you’ll receive exactly $1,000) and (you will one-box iff you’ll receive exactly $1,000,000)].
    3. You will two-box iff you’ll receive exactly $1,000.
    4. You will one-box iff you’ll receive exactly $1,000,000.
    5. Either you’ll two-box or you’ll one-box.
    6. Either you’ll receive exactly $1,000 or you’ll receive exactly $1,000,000.
    7. $1,000,000 is more money than $1,000.
    8. If [(you’ll receive either exactly $1,000 or exactly $1,000,000) and ($1,000,000 is more money than $1,000)], then you prefer to receive exactly $1,000,000.
    9. You prefer to receive exactly $1,000,000.
    10. If [(you prefer to receive exactly $1,000,000) and (you will one-box iff you’ll receive exactly $1,000,000)], then you ought to one-box.
    11. You ought to one-box.

Thoughts? Rejectable premises?
(I don’t deny that there is also a very compelling argument for two-boxing in this case.)

Later addition (1/6/08):
Read the rest of this entry »

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