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# Newcomb's Problem

Last updated Oct 28, 2022 Edit Source

$1M in Box 2$0 in Box 2
Take only box 2 $1M$0
Take both boxes $1M +$1000 $1000 ## # Background There is a predictor that is 99% accurate is predicting whether people will only take box 2 or both boxes ## # Procedure • Predictor makes their prediction • They put$1000 in box 1 (which you know)
• They put $0 in box 2 if they think you will take both and$1M if they think you will only take box 2
• Choose either both boxes or box 2

## # Arguments

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