because by the laws of probability theory, if you know your destination, you are already there.
At first, I was like “Yeah!” Because the conclusion is true. But then I thought about how someone who hasn’t read the sequences might thing it was crazy talk to say that the laws of probability say such a thing, so I tried to recreate the argument, because if I can’t create it, I don’t understand it.
Sadly, I don’t understand it. Are we talking about conservation of probability here? Are we talking about how if you already have your conclusion drawn, you have defined P(Conclusion) = P(Conclusion | evidence) + P(Conclusion | ~evidence) = 1? Are we saying P(Conclusion | evidence) = 1 (and P(Conclusion | ~evidence)) = 1, and therefore you can’t get any meaningful answers by invoking Bayes Theorem?
The result Eliezer is referring to is P(Conclusion)=P(Conclusion|Positive Test)P(Positive Test)+P(Conclusion|Negative Test)P(Negative Test)=E(P(Conclusion|Test Result))
If you know what you’ll believe after the test (i.e. your expected belief after the test), then that is your current belief.
At first, I was like “Yeah!” Because the conclusion is true. But then I thought about how someone who hasn’t read the sequences might thing it was crazy talk to say that the laws of probability say such a thing, so I tried to recreate the argument, because if I can’t create it, I don’t understand it.
Sadly, I don’t understand it. Are we talking about conservation of probability here? Are we talking about how if you already have your conclusion drawn, you have defined P(Conclusion) = P(Conclusion | evidence) + P(Conclusion | ~evidence) = 1? Are we saying P(Conclusion | evidence) = 1 (and P(Conclusion | ~evidence)) = 1, and therefore you can’t get any meaningful answers by invoking Bayes Theorem?
The result Eliezer is referring to is P(Conclusion)=P(Conclusion|Positive Test)P(Positive Test)+P(Conclusion|Negative Test)P(Negative Test)=E(P(Conclusion|Test Result))
If you know what you’ll believe after the test (i.e. your expected belief after the test), then that is your current belief.