| Here is how one might decide that 1/3 is obvious. Imagine that N people simultaneous undergo the experiment, for a very large N. Half of them end up in the heads group. They wake up on Monday and are questioned. Then they sleep until Wednesday and are released. The other half end up in the tails group, and so are questioned twice (Monday and Tuesday) then released on Wednesday. Because we gain no information during the experiment, we can make our decision before the experiment. Let's count. There will be 3N/2 interviews conducted. N/2 of the will be 'heads' interviews and N will be 'tails' interviews. So going in, we can see that when someone experiences the event 'being asked about the coin', 1/3 of the time the coin will be heads and 2/3 o the time it will be tails. Hence, our credence in the coin being heads should be 1/3. Here is a counterargument. Imagine a slightly different experiment. The people are not asked what their credence in the coin being heads is. They are asked to guess if it is heads or tails. If they are right, the experiment continues and they are eventually released. If they are wrong, this is noted, and the experiment continues until Wednesday, and then they are killed and their home planet is destroyed. As before, we gain no information during the experiment, and so can decide our answer beforehand. No matter what strategy one picks for making that decision, there is a 50/50 chance that one ends up with a destroyed planet. That indicates that our credence in heads should be 1/2. |