$1M in Box 2$0 in Box 2
Take only box 2$1M$0
Take both boxes1000$1000


There is a predictor that is 99% accurate is predicting whether people will only take box 2 or both boxes


  • Predictor makes their prediction
  • They put $1000 in box 1 (which you know)
  • They put 1M if they think you will only take box 2
  • Choose either both boxes or box 2


  1. Two-box argument: dominance argument
    1. We can perhaps rule out the dominance argument because it only applies when states are independent of our actions (which is not the case here)
  2. One-box argument: taking only box 2 almost guarantees $1M. Calculate using expected utility
    1. EU(both) = 0.01(1M + 1k) + 0.99(1k) = 11k
    2. EU(box 2) = 0.99(1M) + 0.01(0) = 990k