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Diffstat (limited to 'content/entry/newcombs-paradox-resolved.md')
-rw-r--r-- | content/entry/newcombs-paradox-resolved.md | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/content/entry/newcombs-paradox-resolved.md b/content/entry/newcombs-paradox-resolved.md index a5928f0..1c5d3b2 100644 --- a/content/entry/newcombs-paradox-resolved.md +++ b/content/entry/newcombs-paradox-resolved.md @@ -16,8 +16,8 @@ Here's the problem from Wikipedia ([CC BY-SA 3.0](https://creativecommons.org/li > There is an infallible predictor, a player, and two boxes designated A and B. The player is given a choice between taking only box B, or taking both boxes A and B. The player knows the following: > Box A is clear, and always contains a visible $1,000. > Box B is opaque, and its content has already been set by the predictor: If the predictor has predicted the player will take both boxes A and B, then box B contains nothing. If the predictor has predicted that the player will take only box B, then box B contains $1,000,000. -> -> +> +> > The player does not know what the predictor predicted or what box B contains while making the choice. ## The Paradox @@ -36,13 +36,13 @@ As I suggested in the "telescoping method", we're going to break down the abstra > Let p be the probability that the predictor is correct. Then: > 1000000p is the expected value if you choose only box B. > 1000000(1-p) + 1000 is the expected value if you choose both boxes. -> +> > 1000000p > 1000000(1-p) + 1000 > -> 1000p > 1000(1-p) + 1 > -> 1000p > 1000 - 1000p + 1 > -> 2000p > 1001 > -> p > 0.5005 -> +> > Therefore the expected value if you choose only box B is greater than the expected value if you choose both boxes so long as the predictor is over 50.05% accurate, slightly better than a coin toss. An AI system that can predict slightly better than a fair coin toss could create the Newcomb Paradox. Given what AI is already capable of, this is a realistic scenario. It also shows that the infallible predictor isn't the root cause of the paradox. |