I don't think this requires anthropic reasoning.
Here is a variation on the story:
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 a hotel with 1,000,001 rooms. 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 room are we in, I wonder?" you ask.
"Any of them is equally likely," says the presumptuous philosopher. "Because it's bloody obvious and all that. Million to one odds for any given room."
"Rubbish!" you scream. "Rubbish and poppycock! We have a 50% chance of being in room 870,199, and a 50% chance of being in one of the other rooms."
After the presumptuous philosopher stands in baffled silence for a moment, he says, "In that case, I'll make a deal with you. We'll go outside and check, and if we're in room 870,199 I'll give you ten bucks. If we're in one of the other rooms, 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 surrounded by throngs of yourselves and smug looking presumptuous philosophers; you turn around and look at your door, labeled 129,070.
If I'm not mistaken (am I?), this version of the story is exactly isomorphic to PlaidX's original version; the only difference is that it's easier to see why the friend is wrong before you get to the end.
To anyone who agrees with the friend in the original story -- that the most reasonable estimate is that there is an even chance of being in either hotel -- would you disagree that this version is isomorphic to the original?
I thought of this, but then, in the other direction, is the problem non-isomorphic to the original presumptuous philosopher problem? If so, why?
Is it because I used hotels instead of universes? Is it because the existence of both hotels has probability 100% instead of probability 50%? Is it some other thing?
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.