Newcomb's Paradox

Logic & Philosophy of Mathematics
468

Both Game 3s are the same.

Game 3a

  1. There is an empty red box and an empty blue box
  2. You are asked to choose between either a) the red box or b) the blue box
  3. If you chose (a) and were predicted to choose (a) then you win $1,000,000
  4. If you chose (b) and were predicted to choose (b) then you win $1,000
  5. If you chose (a) and were predicted to choose (b) then you win $0
  6. If you chose (b) and were predicted to choose (a) then you win $1,001,000

Game 3b

  1. There is an empty red box and an empty blue box
  2. You are asked to choose between either a) the red box or b) the blue box
  3. Your clone is asked to choose between either a) the red box or b) the blue box
  4. If you chose (a) and your clone chose (a) then you win $1,000,000
  5. If you chose (b) and your clone chose (b) then you win $1,000
  6. If you chose (a) and your clone chose (b) then you win $0
  7. If you chose (b) and your clone chose (a) then you win $1,001,000

The clone is just the tool used to make the prediction in Game 3b. It may in fact be the tool used to make the prediction in Game 3a, which is left unspecified.

In Game 3b it is most rational to choose the red box and so in Game 3a it is most rational to choose the red box.