Newcomb's Paradox

Logic & Philosophy of Mathematics
535

I haven’t changed anything. It’s very simple. All of these are valid arguments:

Argument A

  1. I will one-box
  2. I will almost certainly be predicted to one-box
  3. Therefore, I will almost certainly win exactly $1,000,000

Argument B

  1. I will two-box
  2. I will almost certainly be predicted to two-box
  3. Therefore, I will almost certainly win exactly $1,000

Argument C

  1. I will one-box
  2. I will almost certainly be predicted to two-box
  3. Therefore, I will almost certainly win exactly $0

Argument D

  1. I will two-box
  2. I will almost certainly be predicted to one-box
  3. Therefore, I will almost certainly win exactly $1,001,000

But, as per the premise of the experiment, if “I will one-box” is true then “I will almost certainly be predicted to one-box” is true, and if “I will two-box” is true then “I will almost certainly be predicted to two-box“ is true, and so only Arguments A and B are applicable to the problem.

Therefore, we are left with:

  1. If I will one-box then I will almost certainly win exactly $1,000,000
  2. If I will two-box then I will almost certainly win exactly $1,000

This is the proof that it is most rational to one-box.