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I recommend the major sequences to everybody, but I realize how daunting they look at first. So for purposes of immediate gratification, the following posts are particularly interesting/illuminating/provocative and don't require any previous reading:
- Your Intuitions are Not Magic
- The Apologist and the Revolutionary
- How to Convince Me that 2 + 2 = 3
- Lawful Uncertainty
- The Planning Fallacy
- Scope Insensitivity
- The Allais Paradox (with two followups)
- We Change Our Minds Less Often Than We Think
- The Least Convenient Possible World
- The Third Alternative
- The Domain of Your Utility Function
- Newcomb's Problem and Regret of Rationality
- The True Prisoner's Dilemma
- The Tragedy of Group Selectionism
- Policy Debates Should Not Appear One-Sided
- That Alien Message
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You choose the boxes according to the expected value of each box choice. For a 99% accurate predictor, the expected value of one-boxing is $990,000,000 (you get a billion 99% of the time, and nothing 1% of the time,) while the expected value of two-boxing is $10,001,000 (you get a thousand 99% of the time, and one billion and one thousand 1% of the time.)
The difference between this scenario and the one you posited before, where Ann's mom makes her prediction by reading your philosophy essays, is that she's presumably predicting on the basis of how she would expect you to choose if you were playing Omega. If you're playing against an agent who you know will fill the boxes according to how you would choose if you were playing Omega (we'll call it Omega-1,) then you should always two-box (if you would one-box against Omega, both boxes will contain money, so you get the contents of both. If you would two-box against Omega, only one box would contain money, and if you one-box you'll get the empty one.)
An imperfect predictor with random error is a different proposition from an imperfect predictor with nonrandom error.
Of course, if I were dealing with this dilemma in real life, my choice would be heavily influenced by considerations such as how likely it is that Ann's mom really has billions of dollars to give away.
Ok, but what if Ann's mom is right 99% of the time about how you would choose when playing her?
I agree that one-boxers make more money, with the numbers you used, but I don't think that those are the appropriate expected values to consider. Conditional on the fact that the boxes have already been filled... (read more)