I came up with what I believe to be a convincing argument for double halfer. Beauty's credence should be 1/2 after waking up and remains at 1/2 after learning it is Monday. I have no channel for publishing so just putting this out here. It is a bit long, but the reasoning is not hard to follow. Any input is appreciated. The pdf can be found here:Paper
To make you intrigued consider this question:
Prometheus’ Guess
Prometheus is being punished by Zeus as follows: A fair die will be tossed tonight, Prometheus will have to guess the result of the toss next morning. However he only need to guess if the result is “One” or “Not one”. If Prometheus guessed correctly then nothing happens, otherwise Zeus’ eagle will eat his liver. Furthermore If the die toss actually resulted in One then Prometheus’ memory of the day will be erased and his body will regenerate at night. So next morning when he wake up he will have no clue about previous awakening(s), and he will be asked to guess the die toss result again with the same consequences. It will repeat until he is asked 6 times in total. On the other hand if the die toss result in any number other than One, Prometheus will be only asked one time and no memory wipe or regeneration will happen. The question is how should Prometheus guess if he knows the punishment setup?
And this question:
Cloning Adam
Adam is taking part in an experiment. He is put to sleep and will be cloned only if a coin land on Tails. The clone is an exact copy of Adam including his mental state. The original and the clone, if it exists, will be put into two separate rooms while still sleeping. The subjects does not know the coin toss result and does not know if he is the original or the clone. Bob knows the experiment setup and he can check one room. Upon opening the door Bob sees an Adam sitting on the bed. Bob told the Adam the probability for Heads is 1/3 because the picked room is not empty. The Adam disagrees because according to him, “the chance of you picking the room I am in is 1/2 regardless the coin toss result”, so seeing Bob is not giving him any new information so the probability of Heads is still 1/2. Now Adam and Bob is sharing the same information but is in disagreement with each other. How could this be possible?
The answers to the above questions are provided in the paper. Again, any input is appreciate.