if the information in a case is identical, the probability should be too
So if I have a biased coin that comes up heads 90% of the time, flip it and hide the result from you, your credence for heads should be 50%? Nah. I’m willing to believe in the principle of indifference only if the cases are completely identical, not just observably identical. In our problem the cases aren’t completely identical—you may be the sole child or one of 10 children, and these correspond to very different and non-symmetrical states of the world.
It seems to me that you’re confused. Sleeping Beauty isn’t tricky at all, but our problem is. If rwallace’s post didn’t work for you, try this.
So if I have a biased coin that comes up heads 90% of the time, flip it and hide the result from you, your credence for heads should be 50%? Nah. I’m willing to believe in the principle of indifference only if the cases are completely identical, not just observably identical. In our problem the cases aren’t completely identical—you may be the sole child or one of 10 children, and these correspond to very different and non-symmetrical states of the world.
It seems to me that you’re confused. Sleeping Beauty isn’t tricky at all, but our problem is. If rwallace’s post didn’t work for you, try this.