>>14161125>Can you state the paradox as a logical argument leading to both principles or neither principle being correct?Sure. This is summarizing the arguments in
>>14160957 :
Argument 1:
Consider the expected outcome of the two choices. If you choose to one-box, then there is a chance of (1 - epsilon) for some very small number epsilon that the Predictor predicted this correctly, placed a million dollars in the opaque box, and that your choice will net you a million dollars; and there is a chance of epsilon that the Predictor predicted this incorrectly, placed nothing in the opaque box, and you walk away with nothing. Net expected result is (1 - epsilon) * $1000000.
If you choose to two-box, then there is a chance of (1 - epsilon) that the Predictor predicted this correctly, placed nothing in the opaque box, and your choice will get you $1000; and a chance of epsilon that the Predictor mispredicted this and you get $1001000 instead. Net expected result is $1000 + epsilon * $1000000.
Assuming by the problem statement that the Predictor is very accurate and epsilon is very small, the expected value of one-boxing is much greater than the expected value of two-boxing and therefore the choice with the highest expected value.
(There is actually no need for the two values of epsilon for the two choices are the same, but that more complicated version of the analysis doesn't change the final outcome so I'm using the simplified version here.)
Argument 2: The Predictor already made their decision and placed a certain amount of money in the opaque box, which we'll call X. The decision you make here cannot affect that value X, because it has already been made. No matter what that value of X is, one-boxing gets you $X, and two-boxing gets you $X + $1000, which is strictly higher no matter what X is. Therefore the expected value of two-boxing is greater than the expected value of one-boxing.
[Continued 1/2]
