lump of clay

^ 6 Comments...

1. Seb
   April 12th, 2007 at 9:13 am

   I hate this puzzle. But I think an argument for either case can be made from the vantage point of expected utility, since there seems to be a couple different ways you could model the problem. (If you are modeling it in such a way that strict domination applies, that _still_, given a model in which that is valid, implies a greater expected value for the dominating option, right?)

2. Jonathan
   April 12th, 2007 at 9:43 am

   Hmm, I’m not sure if I follow. I take the puzzle largely to be about whether and in what circumstances domination applies.

   The way I was thinking about it, a two-boxer can cite dominance, even granting high subjective probability of the box having money, given that he picks only one, and low subjective probability of the box having money, given that he picks both. But once you’ve granted those, the expected value calculus looks pretty set, doesn’t it?

   Are you saying that there’s a way to model the choice, even granting those things above, such that there’s higher expected value in two-boxing? I don’t see how that would go. (But I recognize that I might simply be not seeing it.)

   Why do you hate this puzzle?

3. Michelle
   April 12th, 2007 at 2:04 pm

   Jonathan, you hurt my head. This is not the sort of fluffly, light reading I like to sit down in the morning with. Besides that, Captain Counterexample is my hero.

4. Savannah
   April 12th, 2007 at 4:01 pm

   I haven’t been keeping up with this webcomic, but I love Captain Counterexample (and the clipart you chose for him).

   But I think the puzzle was different last time you told it to me! I thought it seemed difficult to decide which to choose last time, but now it seems completely obvious that you pick Box B. Could you have told me a different version before, or have some of my logic gates been closed for repairs due to space being taken up by large froofy cupcake dresses?

5. Charlie Green
   April 12th, 2007 at 7:48 pm

   I’m not a philosopher; I am a results-oriented technician. And i think this is a politicians’ puzzle. I would not even need a minute to choose both boxes. Screw all the philosophy; grab the money and run, before CC adds a loophole. As the philosophers at Mad Magazine said, “A bird in the hand makes it hard to blow your nose.”.

   Is CC a lawyer? Are lawyers philosophers?

6. Seb
   April 17th, 2007 at 8:12 pm

   Yes, I’m saying that a two-boxer can still use the expected value principle, if they model it when dominance applies. They can do this by simply insisting that there is a fixed subjective probability RIGHT NOW, unconditional on my choice, that the Captain put money in both boxes.

   So the question is how one should apply subjective probability judgments, not whether one should maximize expected utility.

   Funny. I just suddenly turned into a two-boxer.

   But I actually got satisfying explanation for why the one-box case might be so compelling. It’s kind of a virtue argument: If you are the _kind of person_ who chooses one box regularly in these situations, you will make more money than the 2-boxer in life. So it’s worth it to be a die-hard 1-boxer…at least for now.

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