## Thursday, December 4, 2014

I learnt about Newcomb's paradox recently. Wikipedia has a nice post on it.
The player of the game is presented with two boxes, one transparent (labeled A) and the other opaque (labeled B). The player is permitted to take the contents of both boxes, or just the opaque box B. Box A contains a visible $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain$1,000,000.
The Predictor is almost infallible.

The range of possibilities are (from Wikipedia):

1. One can say that "A and B" is a superior choice, because given a predicted choice (which one can't control) it offers a better payout.

If the Predictor was not very reliable, then this would certainly be the better choice.

2. One can say that "B only" is a better choice, because the Predictor is almost always right. Thus, the probability of a mismatch between predicted and actual choices is so small that we might ignore it. Therefore, one should look at only the first and last rows in the table above, and "B only" offers a higher payout.

If the Predictor very perfectly reliable, then this would certainly be the better choice.

There is a lot of commentary and nuance to this topic, so go google it.