Re: “If we are being asked about the probability of our coin flip associated with this iteration of the experiment, then the answer is 1⁄2. If we are being asked about the probability of the coin flip associated with this particular awakening, then it must be 1⁄3.”
What is actually asked at each awakening is:
“What is your credence now for the proposition that our coin landed heads?”
I figure that makes the answer 1⁄3 - and not 1⁄2.
If the question had been: “What is your credence that this is the last time you awaken and our coin landed heads-up?”
Re: “If we are being asked about the probability of our coin flip associated with this iteration of the experiment, then the answer is 1⁄2. If we are being asked about the probability of the coin flip associated with this particular awakening, then it must be 1⁄3.”
What is actually asked at each awakening is:
“What is your credence now for the proposition that our coin landed heads?”
I figure that makes the answer 1⁄3 - and not 1⁄2.
If the question had been: “What is your credence that this is the last time you awaken and our coin landed heads-up?”
...then the answer would have been 1⁄2.
...but that wasn’t the question that was asked.
Cool story bro