You're reading a little more into what I said than was actually there. I was just remarking on the change of dependence between the parts of the problem, without having thought through what the consequences would be.
Now that I have thought it through, I agree with the presumptuous philosopher in this case. However I don't agree with him about the size of the universe. The difference being that in the hotel case we want a subjective probability, whereas in the universe case we want an objective one. Subjectively, there's a very high probability of finding yourself in a big universe/hotel. But subjective probabilities are over subjective universes, and there are very very many subjective large universes for the one objective large universe, so a very high subjective probability of finding yourself in a large universe doesn't imply a large objective probability of being found in one.
I don't understand what you mean by subjective and objective probabilities. Would you still agree with the philosopher in my problem if omega flipped a coin (or looked at binary digit 5000 of pi) and then built the small hotel OR the big hotel?
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.