After the discussion in my previous post I became quite certain that the world can’t work as indicated by SSA (your model), and SIA is by far more likely. If you’re the only person in the world right now, and Omega is about to flip a fair coin and create 100 people in case of heads, then SSA tells you to be 99% sure of tails, while SIA says 50⁄50. There’s just no way SSA is right on this one.
Bostrom talks about such paradoxes in chapter 9 of his book, then tries really hard to defend SSA, and fails. (You have to read and settle this for yourself. It’s hard to believe Bostrom can fail. I was surprised.)
To be fair, Bostrom’s version of SSA (“strong” SSA, or SSSA) does not “[tell] you to be 99% sure of tails” when you are still the only person in the world. In whatever sense his defense might fail, it is not because his SSSA leads to the implication that you describe, because it does not.
ETA: Prior to the copying, there is only one individual in your reference class—namely, the one copy of you. That is, the “reference class” contains only a single individual in all cases, so there is no anthropic selection effect. Therefore, SSSA still says 50⁄50 in this situation.
Bostrom’s proposal fails even harder than “naive” SSA: it refuses to give a definite answer. He says selecting a reference class may be a “subjective” problem, like selecting a Bayesian prior. Moreover, he says that giving the “intuitively right” answer to problems like mine is one of the desiderata for a good reference class, not a consequence of his approach. See this chapter.
Re your ETA: Bostrom explicitly rejects the idea that you should always use subjectively indistinguishable observer-moments as your reference class.
Bostrom’s proposal fails even harder than “naive” SSA: it refuses to give a definite answer. He says selecting a reference class may be a “subjective” problem, like selecting a Bayesian prior. Moreover, he says that giving the “intuitively right” answer to problems like mine is one of the desiderata for a good reference class, not a consequence of his approach.
He does not solve the problem of defining the reference class. He doesn’t refuse to give a definite answer. He just doesn’t claim to have given one yet. As you say, he leaves open the possibility that choosing the reference class is like choosing a Bayesian prior, but he only offers this as a possibility. Even while he allows for this possibility, he seems to expect that more can be said “objectively” about what the reference class must be than what he has figured out so far.
So, it’s a work in progress. If it fails, it certainly isn’t because it gives the wrong answer on the coin problem that you posed.
To me it looks abandoned, not in progress. And it doesn’t give any definite answer. And it’s not clear to me whether it can be patched to give the correct answer and still be called “SSA” (i.e. still support some version of the Doomsday argument). For example, your proposed patch (using indistinguishable observers as the reference class) gives the same results as SIA and doesn’t support the DA.
Anyway. We have a better way to think about anthropic problems now: UDT! It gives the right answer in my problem, and makes the DA go away, and solves a whole host of other issues. So I don’t understand why anyone should think about SSA or Bostrom’s approach anymore. If you think they’re still useful, please explain.
Anyway. We have a better way to think about anthropic problems now: UDT! It gives the right answer in my problem, and makes the DA go away, and solves a whole host of other issues. So I don’t understand why anyone should think about SSA or Bostrom’s approach anymore. If you think they’re still useful, please explain.
When it comes to deciding how to act, I agree that the UDT approach to anthropic puzzles is the best I know. Thinking about anthropics in the traditional way, whether via SSA, SIA, or any of the other approaches, only makes sense if you want to isolate a canonical epistemic probability factor in the expected-utility calculation.
To be fair, Bostrom’s version of SSA (“strong” SSA, or SSSA) does not “[tell] you to be 99% sure of tails” when you are still the only person in the world. In whatever sense his defense might fail, it is not because his SSSA leads to the implication that you describe, because it does not.
ETA: Prior to the copying, there is only one individual in your reference class—namely, the one copy of you. That is, the “reference class” contains only a single individual in all cases, so there is no anthropic selection effect. Therefore, SSSA still says 50⁄50 in this situation.
Bostrom’s proposal fails even harder than “naive” SSA: it refuses to give a definite answer. He says selecting a reference class may be a “subjective” problem, like selecting a Bayesian prior. Moreover, he says that giving the “intuitively right” answer to problems like mine is one of the desiderata for a good reference class, not a consequence of his approach. See this chapter.
Re your ETA: Bostrom explicitly rejects the idea that you should always use subjectively indistinguishable observer-moments as your reference class.
Right. I don’t think that I implied otherwise . . .
He does not solve the problem of defining the reference class. He doesn’t refuse to give a definite answer. He just doesn’t claim to have given one yet. As you say, he leaves open the possibility that choosing the reference class is like choosing a Bayesian prior, but he only offers this as a possibility. Even while he allows for this possibility, he seems to expect that more can be said “objectively” about what the reference class must be than what he has figured out so far.
To me it looks abandoned, not in progress. And it doesn’t give any definite answer. And it’s not clear to me whether it can be patched to give the correct answer and still be called “SSA” (i.e. still support some version of the Doomsday argument). For example, your proposed patch (using indistinguishable observers as the reference class) gives the same results as SIA and doesn’t support the DA.
Anyway. We have a better way to think about anthropic problems now: UDT! It gives the right answer in my problem, and makes the DA go away, and solves a whole host of other issues. So I don’t understand why anyone should think about SSA or Bostrom’s approach anymore. If you think they’re still useful, please explain.
When it comes to deciding how to act, I agree that the UDT approach to anthropic puzzles is the best I know. Thinking about anthropics in the traditional way, whether via SSA, SIA, or any of the other approaches, only makes sense if you want to isolate a canonical epistemic probability factor in the expected-utility calculation.
In the context of the Doomsday Argument, or Great Filter arguments, etc., UDT is typically equivalent to SIA.