Edit: and come to think of it I am somewhat less sure about the lower success rates in general. If I can roughly estimate Omega’s prediction about me that would seem to screen off any timeless effect. Like, you could probably pretty reliably predict how someone would answer this question based on variables like Less Wrong participation and having a Phd in philosophy. Using this information, I could conclude that an Omega with 60% accuracy is probably going to classify me as a one-boxer no matter what I decide… and in that case why not two box?
Sorry, by a 50% success rate I meant that Omega correctly predicts your action 50% of the time, and the other half of the time just guesses. Guessing can also yield the right answer, so this isn’t equivalent to a 50% success rate in the sense you meant, which was simply ‘Does Omega put the money in the box he would have wished to?’
If you know that Omega will take into account that you’re a LessWronger, but also know that he won’t take into account any other information about you (including not taking into account the fact that you know that he knows you’re a LessWronger!), then yes, you should two-box. But that’s quite different from merely knowing that Omega has a certain success rate. Let’s suppose we know that 60% of the time Omega makes the decision it would have wished were it omniscient. Then we get:
If I one-box: 60% chance of $1,000,000, 40% chance of $1000.
If I two-box: 60% chance of $1000, 40% chance of $1,001,000.
Then the expected value of one-boxing is $600,400. Expected value of two-boxing is $401,000. So you should one-box in this situation.
A 50% success rate would recommend two boxing.
Edit: and come to think of it I am somewhat less sure about the lower success rates in general. If I can roughly estimate Omega’s prediction about me that would seem to screen off any timeless effect. Like, you could probably pretty reliably predict how someone would answer this question based on variables like Less Wrong participation and having a Phd in philosophy. Using this information, I could conclude that an Omega with 60% accuracy is probably going to classify me as a one-boxer no matter what I decide… and in that case why not two box?
Sorry, by a 50% success rate I meant that Omega correctly predicts your action 50% of the time, and the other half of the time just guesses. Guessing can also yield the right answer, so this isn’t equivalent to a 50% success rate in the sense you meant, which was simply ‘Does Omega put the money in the box he would have wished to?’
If you know that Omega will take into account that you’re a LessWronger, but also know that he won’t take into account any other information about you (including not taking into account the fact that you know that he knows you’re a LessWronger!), then yes, you should two-box. But that’s quite different from merely knowing that Omega has a certain success rate. Let’s suppose we know that 60% of the time Omega makes the decision it would have wished were it omniscient. Then we get:
If I one-box: 60% chance of $1,000,000, 40% chance of $1000.
If I two-box: 60% chance of $1000, 40% chance of $1,001,000.
Then the expected value of one-boxing is $600,400. Expected value of two-boxing is $401,000. So you should one-box in this situation.
This makes sense.