I’m using “probability” “credence” and “betting odds” mostly interchangeably to refer to my subjective state of knowledge. The 50% number comes from the symmetry of having two indistinguishable experiences being had by two people, one of which is me. Without any additional information to break that symmetry (such as learning that multiple copies were created or that the copying sometimes fails), I should assign equal credence to each possibility.
(to be clear, everything I’ve said also flows from the principle of indifference; if you cannot tell the difference between N states of the world, then the probability 1/N describes your uncertainty about those N states)
It’s not that I wouldn’t care which one I am (they’re identical), but there would be no way for me to differentiate the experiences.
Suppose the scientist told me before the procedure that he would with probability 2⁄3 waken the original in a blue room and the clone in a red room and with probability 1⁄3 reverse the colors. If I were to wake up in a blue room afterward, my credence that I’m the original would be 2⁄3.
I was asking if your reasoning for equal probabilities of Original vs Clone can be summarized as the Principle of Indifference. Not suggesting you do not care which copy you are. Would I be wrong to assume you endorse POI in this problem?
Problem is POI is not a solid theory to rely on and it often lead to paradoxes. In anthropic problems in particular, it is unclear what exactly should be regarded indifferent. See this post for an example.
I’m using “probability” “credence” and “betting odds” mostly interchangeably to refer to my subjective state of knowledge. The 50% number comes from the symmetry of having two indistinguishable experiences being had by two people, one of which is me. Without any additional information to break that symmetry (such as learning that multiple copies were created or that the copying sometimes fails), I should assign equal credence to each possibility.
Would you say your reasoning is a principle of indifference between “I am the Original” vs “I am the Clone”?
(to be clear, everything I’ve said also flows from the principle of indifference; if you cannot tell the difference between N states of the world, then the probability 1/N describes your uncertainty about those N states)
It’s not that I wouldn’t care which one I am (they’re identical), but there would be no way for me to differentiate the experiences.
Suppose the scientist told me before the procedure that he would with probability 2⁄3 waken the original in a blue room and the clone in a red room and with probability 1⁄3 reverse the colors. If I were to wake up in a blue room afterward, my credence that I’m the original would be 2⁄3.
I was asking if your reasoning for equal probabilities of Original vs Clone can be summarized as the Principle of Indifference. Not suggesting you do not care which copy you are. Would I be wrong to assume you endorse POI in this problem?
I would say POI applies here.
Problem is POI is not a solid theory to rely on and it often lead to paradoxes. In anthropic problems in particular, it is unclear what exactly should be regarded indifferent. See this post for an example.