While I’m happy to have had the confidence of Richard, I thought my last comment could use a little improvement.
What we want to know is P(W|F,S)
As I pointed out F=> S so P(W|F,S) = P(W|F)
We can legitimately calculate P(W|F,S) in at least two ways:
1. P(W|F,S) = P(W|F) = P(F|W)P(W)/P(F) ← the easy way
2. P(W|F,S) = P(F|W,S)P(W|s)/P(F|S) ← harder, but still works
there are also ways you can get it wrong, such as:
3. P(W|F,S) != P(F|W,S)P(W)/P(F) ← what I said other people were doing last post
4. P(W|F,S) != P(F|W,S)P(W)/P(F|S) ← what other people are probably actually doing
In my first comment in this thread, I said it was a simple application of Bayes’ rule (method 1) but then said that Eliezer’s failure was not to apply the anthropic principle enough (ie I told him to update from method 4 to method 2). Sorry if anyone was confused by that or by subsequent posts where I did not make that clear.
Allan: your intuition is wrong here too. Notice that if Zeus were to have independently created a zillion people in a green room, it would change your estimate of the probability, despite being completely unrelated.
Eliezer: F ⇒ S -!-> P(X|F) = P(X|F,S)
All right, give me an example.
And yeah, anthropic reasoning is all about conditioning on survival, but you have to do it consistently. Conditioning on survival in some terms but not others = fail.
Richard: your first criticism has too low an effect on the probability to be significant. I was of course aware that humanity could be wiped out in other ways but incorrectly assumed that commenters here would be smart enough to understand that it was a justifiable simplification. The second is wrong: the probabilities without conditioning on S are “God’s eye view” probabilities, and really are independent of selection effects.
While I’m happy to have had the confidence of Richard, I thought my last comment could use a little improvement.
What we want to know is P(W|F,S)
As I pointed out F=> S so P(W|F,S) = P(W|F)
We can legitimately calculate P(W|F,S) in at least two ways:
1. P(W|F,S) = P(W|F) = P(F|W)P(W)/P(F) ← the easy way
2. P(W|F,S) = P(F|W,S)P(W|s)/P(F|S) ← harder, but still works
there are also ways you can get it wrong, such as:
3. P(W|F,S) != P(F|W,S)P(W)/P(F) ← what I said other people were doing last post
4. P(W|F,S) != P(F|W,S)P(W)/P(F|S) ← what other people are probably actually doing
In my first comment in this thread, I said it was a simple application of Bayes’ rule (method 1) but then said that Eliezer’s failure was not to apply the anthropic principle enough (ie I told him to update from method 4 to method 2). Sorry if anyone was confused by that or by subsequent posts where I did not make that clear.
Allan: your intuition is wrong here too. Notice that if Zeus were to have independently created a zillion people in a green room, it would change your estimate of the probability, despite being completely unrelated.
Eliezer: F ⇒ S -!-> P(X|F) = P(X|F,S)
All right, give me an example.
And yeah, anthropic reasoning is all about conditioning on survival, but you have to do it consistently. Conditioning on survival in some terms but not others = fail.
Richard: your first criticism has too low an effect on the probability to be significant. I was of course aware that humanity could be wiped out in other ways but incorrectly assumed that commenters here would be smart enough to understand that it was a justifiable simplification. The second is wrong: the probabilities without conditioning on S are “God’s eye view” probabilities, and really are independent of selection effects.