Then it would repeat the same process for t=1 and the copy. Conditioned on “I will see C” at t=1, it will conclude “I will see CO” with probability 1⁄2 by the same reasoning as above. So overall, it will assign:p(“I will see OO”) = 1⁄2,p(“I will see CO”) = 1⁄4,p(“I will see CC”) = 1⁄4
If we look at the situation in 0P, the three versions of you at time 2 all seem equally real and equally you, yet in 1P you weigh the experiences of the future original twice as much as each of the copies.
Suppose we change the setup slightly so that copying of the copy is done at time 1 instead of time 2. And at time 1 we show O to the original and C to the two copies, then at time 2 we show them OO, CO, CC like before. With this modified setup, your logic would conclude P(“I will see O”)=P(“I will see OO”)=P(“I will see CO”)=P(“I will see CC”)=1/3 and P(“I will see C”)=2/3. Right?
Similarly, if we change the setup from the original so that no observation is made at time 1, the probabilities also become P(“I will see OO”)=P(“I will see CO”)=P(“I will see CC”)=1/3.
Suppose we change the setup from the original so that at time 1, we make 999 copies of you instead of just 1 and show them all C before deleting all but 1 of the copies. Then your logic would imply P(“I will see C”)=.999 and therefore P(“I will see CO”)=P(“I will see CC”)=0.4995, and P(“I will see O”)=P(“I will see OO”)=.001.
This all make me think there’s something wrong with the 1⁄2,1/4,1/4 answer and with the way you define probabilities of future experiences. More specifically, suppose OO wasn’t just two letters but an unpleasant experience, and CO and CC are both pleasant experiences, so you prefer “I will experience CO/CC” to “I will experience OO”. Then at time 0 you would be willing to pay to switch from the original setup to (2) or (3), and pay even more to switch to (4). But that seems pretty counterintuitive, i.e., why are you paying to avoid making observations in (3), or paying to make and delete copies of yourself in (4). Both of these seem at best pointless in 0P.
But every other approach I’ve seen or thought of also has problems, so maybe we shouldn’t dismiss this one too easily based on these issues. I would be interested to see you work out everything more formally and address the above objections (to the extent possible).
If we look at the situation in 0P, the three versions of you at time 2 all seem equally real and equally you, yet in 1P you weigh the experiences of the future original twice as much as each of the copies.
Suppose we change the setup slightly so that copying of the copy is done at time 1 instead of time 2. And at time 1 we show O to the original and C to the two copies, then at time 2 we show them OO, CO, CC like before. With this modified setup, your logic would conclude P(“I will see O”)=P(“I will see OO”)=P(“I will see CO”)=P(“I will see CC”)=1/3 and P(“I will see C”)=2/3. Right?
Similarly, if we change the setup from the original so that no observation is made at time 1, the probabilities also become P(“I will see OO”)=P(“I will see CO”)=P(“I will see CC”)=1/3.
Suppose we change the setup from the original so that at time 1, we make 999 copies of you instead of just 1 and show them all C before deleting all but 1 of the copies. Then your logic would imply P(“I will see C”)=.999 and therefore P(“I will see CO”)=P(“I will see CC”)=0.4995, and P(“I will see O”)=P(“I will see OO”)=.001.
This all make me think there’s something wrong with the 1⁄2,1/4,1/4 answer and with the way you define probabilities of future experiences. More specifically, suppose OO wasn’t just two letters but an unpleasant experience, and CO and CC are both pleasant experiences, so you prefer “I will experience CO/CC” to “I will experience OO”. Then at time 0 you would be willing to pay to switch from the original setup to (2) or (3), and pay even more to switch to (4). But that seems pretty counterintuitive, i.e., why are you paying to avoid making observations in (3), or paying to make and delete copies of yourself in (4). Both of these seem at best pointless in 0P.
But every other approach I’ve seen or thought of also has problems, so maybe we shouldn’t dismiss this one too easily based on these issues. I would be interested to see you work out everything more formally and address the above objections (to the extent possible).