One day, you and the presumptuous philosopher are walking along, arguing about the size of the universe, when suddenly Omega jumps out from behind a bush and knocks you both out with a crowbar. While you're unconscious, she builds two hotels, one with a million rooms, and one with just one room. Then she makes a million copies of both of you, sticks them all in rooms, and destroys the originals.
You wake up in a hotel room, in bed with the presumptuous philosopher, with a note on the table from Omega, explaining what she's done.
"Which hotel are we in, I wonder?" you ask.
"The big one, obviously" says the presumptuous philosopher. "Because of anthropic reasoning and all that. Million to one odds."
"Rubbish!" you scream. "Rubbish and poppycock! We're just as likely to be in any hotel omega builds, regardless of the number of observers in that hotel."
"Unless there are no observers, I assume you mean" says the presumptuous philosopher.
"Right, that's a special case where the number of observers in the hotel matters. But except for that it's totally irrelevant!"
"In that case," says the presumptuous philosopher, "I'll make a deal with you. We'll go outside and check, and if we're at the small hotel I'll give you ten bucks. If we're at the big hotel, I'll just smile smugly."
"Hah!" you say. "You just lost an expected five bucks, sucker!"
You run out of the room to find yourself in a huge, ten thousand story attrium, filled with throngs of yourselves and smug looking presumptuous philosophers.
Yes. Omega chooses first. That's Newcomb's. The other one isn't.
It seems that the fact that both my decision and Omega's decision are determined (quantum acknowledged) by the earlier state of the universe utterly bamboozles your decision theory. Since that is in fact how this universe works your decision theory is broken. It is foolish to define a problem as 'ill-defined' simply because your decision theory can't handle it.
The current state of my brain influences both the decisions I will make in the future and the decisions other agents can make based on what they can infer of my from their observations. This means that intelligent agents will be able to predict my decisions better than a coin flip. In the case of superintelligences they can get a lot better than than 0.5.
Just how much money does Omega need to put in the box before you are willing to discard 'Serious' and take the cash?