Newcomb as a Betting Game

June 9, 2007

I.
Imagine that you are invited to play a betting game.

(I will use “bet” in a loose sense since you won’t risk any of your own money. Worst case scenario, you gain nothing.)

The game works like this:
You can bet that A or you can bet that B.
If you bet that A, you get $1,000,000 if you win and $0 if you lose.
If you bet that B, you get $1,001,000 if you win and $1,000 if you lose.
You are informed that there’s a 99.9% chance that A and a 0.1% chance that B.

Given this information, and assuming that you’d like to win as much money as you can get, how do you think it is reasonable to bet? I trust that we’ll all agree that the reasonable thing to do is to bet that A.

The Newcomb Problem has the exact structure of this betting game.

    A: The predictor made a true prediction about how you’ll bet.
    B: The predictor made a false prediction about how you’ll bet.

To bet that A, you take only the closed box.
To bet that B, you take both boxes.
Taking one or both boxes is how you place your bet.

I realize that this talk of placing your bet by taking boxes may sound like trickery, but it isn’t. To see this, we can proceed through a series of variations, from a simple betting game (where the earnings are delivered by a third party) to the standard Newcomb situation. If it is rational to bet that A in (1), I hope it will be conceded that it is equally rational to bet that A in (5). (For ease of reading, I will italicize modifications as they arise.)

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