“I just flipped a fair coin. I decided, before I flipped the coin, that if it came up heads, I would ask you for $1000. And if it came up tails, I would give you $1,000,000 if and only if I predicted that you would give me $1000 if the coin had come up heads. The coin came up heads—can I have $1000?”
Obviously, the only reflectively consistent answer in this case is “Yes—here’s the $1000”, because if you’re an agent who expects to encounter many problems like this in the future, you will self-modify to be the sort of agent who answers “Yes” to this sort of question—just like with Newcomb’s Problem or Parfit’s Hitchhiker.
Why would I expect that, the next time I encounter an Omega, it will say, “I would give you $1,000,000 if and only if I predicted that you would give me $1000 if the coin had come up heads”, instead of, “I would give you $1,000,000 if and only if I predicted that you would not give me $1000 if the coin had come up heads” ?
Why would I expect that, the next time I encounter an Omega, it will say, “I would give you $1,000,000 if and only if I predicted that you would give me $1000 if the coin had come up heads”, instead of, “I would give you $1,000,000 if and only if I predicted that you would not give me $1000 if the coin had come up heads” ?