Why is the paper (also) filed under categories "High Energy Physics - Theory" and "Popular Physics"??? (The main category "Physics - Data Analysis" is wrong too.)

I read the full pre-print Monday and today. I commented to a friend that I was happy to see that you had solved anthropics. Thanks for that!

Actually, I do think Anthropic Decision Theory resolves much of the confusion in the most well-known anthropic problems -- which is very exciting -- but I am still curious what you think are the most interesting remaining open problems or confusions in anthropics left to tackle?

After having done a lot of research on the Sleeping Beauty Problem as it was the topic of my bachelor's thesis (philosophy), I came to the conclusion that anthropic reasoning is wrong in the Sleeping Beauty Problem. I will explain my argument (shortly) below:

The principle that Elga uses in his first paper to validate his argument for 1/3 is an anthropic principle he calls the Principle of Indifference:

"Equal probabilities should be assigned to any collection of indistinguishable, mutually exclusive and exhaustive events."

The Principle of Indifference is in fact a more restricted version of the Self-Indication Assumption:

"All other things equal, an observer should reason as if they are randomly selected from the set of all possible observers."

Both principles are to be accepted a priori as they can not be attributed to empirical considerations. They are therefore vulnerable to counterarguments...

The counterargument:

Suppose that the original experiment is modified a little:

If the outcome of the coin flip is Heads, they wake Beauty up at exactly 8:00. If the outcome of the first coin flip is Tails, the reasearchers flip another coin. If it lands Heads they wake Beauty at 7:00, if Tails at 9:00. That means that when Beauty wakes up she can be in one of 5 situations:

1. Heads and Monday 8:00

2. Tails and Monday 7:00

3. Tails and Monday 9:00

4. Tails and Tuesday 7:00

5. Tails and Tuesday 9:00

Again, these situations are mutually exclusive, indistinguishable and exhaustive. Hence thirders are forced to conclude that P(Heads) = 1/5.

Thirders might object that the total surface area under the probability curve in the Tails-world would still have to equal 2/3, as Beauty is awakened twice as many times in the Tails-world as in the Heads-world. They are then forced to explain why temporal uncertainty regarding an awakening (Monday or Tuesday) is different from temporal uncertainty regarding the time (7:00 or 9:00 o’clock). Both classify as temporal uncertainties within the same possible world, what could possibly set them apart?

An explanation could be that Beauty is only is asked for her credence in Heads during an awakening event, regardless of the time, and that such an event occurs twice in the Tails-world. That is, out of the 4 possible observer-moments in the Tails-world there are only two in which she is interviewed. That means that simply the fact that she is asked the same question twice is reason enough for thirders to distribute their credence, and it is no longer about the number of observer moments. So if she would be asked the same question a million times then her credence in Heads would drop to 1/1000001!

We can magnify the absurdity of this reasoning by imagining a modified version of the Sleeping Beauty Problem in which a coin is tossed that always lands on Tails. Again, she is awakened one million times and given an amnesia-inducing potion after each awakening. Thirder logic would lead to Beauty’s credence in Tails being 1/1000000, as there are one million observer-moments where she is asked for her credence within the only possible world; the Tails-world. To recapitulate: Beauty is certain that she lives in a world where a coin lands Tails, but due to the fact that she knows that she will answer the same question a million times her answer is 1/1000000. This would be tantamount to saying that Mt. Everest is only 1m high when knowing it will be asked 8848 times! It is very hard to see how amnesia could have such an effect on rationality.

Conclusion:

The thirder argument is false. The fact that there are multiple possible observer-moments within a possible world does not justify dividing your credences equally among these observer-moments, as this leads to absurd consequences. The anthropic reasoning exhibited by the Principle of Indifference and the Self-Indication Assumption cannot be applied to the Sleeping Beauty Problem and I seriously doubt if it can be applied to other cases...

A key sentence in your conclusion is this:

Anthropic decision theory is a new way of dealing with anthropic problems, focused exclusively on finding the correct decision to make, rather than the correct probabilities to assign.

You then describe ADT as solving the Sleeping Beauty problem. This may be the case if we re-formulate the latter as a decision problem, as you of course do in your paper. But Sleeping Beauty isn't a decision problem, so I'm not sure if you take yourself to be actually solving it, or if you just think it's unimportant once we solve the decision problem.

The question, which may have an obvious answer, but always puzzles me in the Sleeping Beauty problem, is the meaning of the word "probability" in the mouth of the Beauty. Is it frequentist, Bayesian or any other probability?

If we define it from expected payoff, we will immediately solve the problem in one way or another? If the sleeping beauty problem is run many times, it would also solve it in direction of 1/3?

A selfish agent is one whose preferences are only about their own personal welfare; a pure hedonist would be a good example.

What does that mean in terms of parametric invariances of his preference function? Is a selfish person's preferences supposed to be invariant to how clean his car is? How clean your car is? How clean you are? Similarly, what is his personal welfare supposed to be invariant to?

I suspect that I misunderstand the question, but my inclination is to answer the question of what day it is [nearly ]experimentally, by simulating a large number of Sleeping Beauties and figuring out the odds this way. In this case you have basically done the simulation in your first picture, and the odds are 2:1 that it is Monday/Room 1, and 2:1 for tails. This matches your "Self-Indicating Assumption" of being "randomly selected from the set of all possible observers".

The other approach has the assumption that "Sleeping Beauty, before being put to sleep, expects that she will be awakened in future," which makes no sense to me, as it is manifestly false on Monday+Heads and unconditionally on Tuesday, and she knows that full well.

Additionally, I do not understand how her utility function (and any amount of money or chocolate) can change the odds in any way. I also do not understand what this has to do with any decision theory, given that her fate is predetermined and there is nothing she can do to avoid being or not being awoken, so her decision doesn't matter in the slightest.

My suspicion is that the Sleeping Beauty problem is a poor illustration for whatever concept you are advancing, but it is entirely possible that I simply missed your point.