Self-indication assumption is wrong for interesting reasons

Many forms of the anthropic argument just don't hold water. You can bend over backwards to find the fault in the logic, and I applaud your effort here to do that.

I think an easier way to dismiss the set of arguments is to think of two different cases, one in which there are few observers and one in which there are many, and then ask how the subjective observer could use the anthropic argument to distinguish these two. She can't.

Then these arguments can be discounted with the line of reasoning that says if a theory can't tell you which world you're in, then it predicts everything, so it tells you nothing. (Evidence for a given theory is the observation of an event that is more likely to occur if the theory is true than if it is false.)

Consider the argument that since we're observers at a relatively early time in human technological development, this means we should update that there is a higher probability that humans don't persist for a hugely long time after. This argument kind of makes sense when worded exactly as "if humans persisted for billions of years, what is the probability I would be a human in the first .005 billion years?".

But the way to test if that line of reasoning works is to ask, suppose you have two realities, one in which humans persisted for .1 billion years and one in which humans persisted for 100 billion years. How could the set of observers at .005 billion years use the anthropic argument to distinguish between the two? They couldn't. The anthropic argument has no power to select among these two realities; the anthropic principle predicts exactly the same set of observations for the set of observers at time point .005 billion years for the two different realities. Likewise, consider that there are 50 red rooms or 5000 red rooms, and one blue door. The person who wakes in the blue room has no evidence about the number of red rooms, because her observations (a blue room) are exactly the same for both cases.

One suggestion, instead of putting "proof" in suspicion-quotes, you could say "argument" instead. A proof is just an air-tight argument.

Interesting. Consider a more realistic case:

There is a large pool of people (say, the entire world), and we randomly select from that pool to fill the rooms (either picking 1 person or 99 people, depending on the toss of the coin). In this case you should conclude that the door is mostly likely blue, because you must condition on the chance of having been selected at all (which is 99 times greater if 99 people are randomly chosen instead of 1).

The question is does the fact "I was chosen randomly from a pool" in this example affect the probability in the same way that the fact "I exist at all" in your original example does, where the people are created rather than chosen.

If we use frequentist logic and repeat the experiment, then those people that guess 'blue' will be right 99% of the time. But frequentist logic is not to be trusted, I guess?

You may want to make a link to this post. There were a few different descriptions of why that problem (a very similar one) didn't work, and the one I pinpointed as "the pointer problem" is more or less that same as the one you pinpointed.

The flaw here is that we conditioned on person x existing, but person x only became of interest after we saw that they existed (peeked at the data).

Perhaps we could call the error a "pre-selection bias"?

(In a separate daughter comment, I'll summarize the anthropic problem described in the other post, emphasizing the similarity of the problems and the solutions. )

I upvoted this because it is correct, but unfortunately you won't be able to persuade anyone. We had this whole argument on the discussion you linked to.

Sorry, I disagree. If you repeated the coin-flip 200 times, there would be (on average) 9900 people in blue rooms, and 100 people in red rooms. You know only that you are one of these 10000 people. The odds are 99% you are one of those behind a blue door.

You mean "discrete" not "discreet".

I think you have it completely backwards, SIA isn't based on egotism, but precisely the reverse. You're more likely, as a generic observer, to exist in a world with more generic observers, because you AREN'T special, and in the sense of being just a twinkle of a generic possible person, could be said to be equally all 99 people in a 99 people world.

You are more likely to be in a world with more people because it's a world with more of YOU.

Here's the problem. YOU'RE the egoist, in the sense that you're only tallying the score of one random observer out of 99, as though the other 98 don't matter. We have a possible world where one person is right or wrong, and a possible world where 99 people are right or wrong, but for some reason you only care about 1 of those 99 people.

EDIT: more talking

Under anthropic reasoning, if we flip a coin, and create 5 observers if it's heads, or 95 observers if it's tails, and if all you know is that you are an observer created after the coin flip, the way you guess which of the 100 possible observers you are is to pick randomly among them, giving you a 5% chance of being a heads observer and a 95% chance of being a tails observer.

Under nonanthropic reasoning, it's a little more complicated. We have to stretch the probabilities of being the 5 tails-world observers so that they take up as much probability space as the 95 heads-world observers. Because, so the thinking goes, your likelihood to be in a possible world doesn't depend on the number of observers in that world. Unless the number is zero, then it does. Please note that this special procedure is performed ONLY when dealing with situations involving possible worlds, and not when both worlds (or hotels, or whatever) actually exist. This means that nonanthropic reasoning depends on the many-worlds interpretation of quantum mechanics being false, or at least, if it's false, coin flips go back to being covered by anthropic reasoning and we have to switch to situations that are consequent on some digit of pi or something.

This smells a little fishy to me. It seems like there's a spanner in the works somewhere, ultimately based on a philosophical objection to the idea of a counterfactual observer, which results in a well-hidden but ultimately mistaken kludge in which certain data (the number of observers) is thrown out under special circumstances (the number isn't zero and they only exist contingent on some immutable aspect of the universe which we do not know the nature of, such as a particular digit of pi).