The Existence of Free Will: Newcomb’s Problem

William Newcomb, a physicist at the Livermore Radiation Lab in California, in 1960 posed a problem, about which the great Philosopher Robert Nozick said, “it is a beautiful problem. I wish it were mine.”It’s a problem that highlights the trouble with the idea of Free Will. To illustrate it, I am using the Game Theoretic interpretation of this problem used by Philip D. Straffin, in his book “Game Theory and Strategy.”

To quote Straffin:

Suppose there are two black boxes which you cannot see into. Box #1 contains $1000. Box #2 contains either $1,000,000 or nothing, depending on something we’ll mention in a moment. You have two choices.

1. you may take both boxes, or

2. you may take only box #2

Now, let us assume there is a God, or someone with equally powerful predictive powers. Sometime in the past, God made a prediction about which box you, today, are going to choose.

If God predicted that you were a greedy bastard with no sense of adventure, and would choose option number 1, taking both boxes, then he would smite you and leave box number 2 empty.

On the other hand, if God thought you the gambling type, and predicted that you’d choose option 2, taking only the mystery box, then he would have rewarded your future gutsy-ness by putting in the full 1 million.

The next key is that you, of course, as a good Religious person, believe that God is one heck of a good predictor of outcomes. He may not be perfect, but you assume he’s right at least a good 90% percent of the time. You trust him.

But, then again, as a learned child of the enlightenment, you also strongly believe that God gave us all free will. That we have a choice in life. Life, and our actions are not all predetermined.

What would you do?

Next time we’ll go over the arguments to be made for both choices and what Robert Nozick had to say about them.

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5 Responses

  1. Well- trying to think like a game theoretician… If I decide to let chance play a role and assume that God is 90% likely to correctly guess the roll of a die (or output from a random number generator), then… Letting the probability of only taking box #2 be P and taking both boxes be (1-P), I get four outcomes:

    Take both: God’s right: odds 0.9(1-P): get 1000
    Take #2 : God’s right: odds 0.9(P) : get 1000000
    Take both: God’s wrong: odds 0.1(1-P): get 1001000
    Take #2 : God’s wrong: odds 0.1(P) : get 0

    So lets sum the payout weighted by the odds:

    Expected payout is 101000 + 899000P, with a maximum expected payout at P=1 being the full 1000000 (as we would guess)… But – and I expect Saij to use his full arsenal of quantum game theoretic techniques to prove this – I have an itchy feeling that there is a more complex strategy I could adopt that would lead to an expected payout of more than 1000000…

    Of course, I am not even sure I did the calculation of the classical expected payout correctly!

    And the question arises, “Am I more interested in maximizing what I get, or guaranteeing that I get more than 0 – which is a possibility if God is wrong about my intent!”

    ex animo-
    Felicis

  2. It occurs to me – why can’t I just take box #1 and leave with the thousand? 😉

    ex animo-
    Eric

  3. If that didn’t violate the game, that would work. (when you can’t win by the rules, change the rules,lol).

  4. […] in Interesting Stuff, Philosophy at 7:10 pm by saij I promise to soon finish my discussion about Newcomb’s freewill/god paradox, but in lieu of that, here’s a post by MarkCC ranting about yet another “proof” of […]

  5. […] in Game Theory, Philosophy at 12:18 pm by saij In the last post on Newcomb’s problem and Free Will, we went over a 2 person game to be played with God.  The key problem we were facing was whether or […]

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