I retract my endorsement of Simon’s last comment. Simon writes that S == (F or not W). False: S ==> (F or not W), but the converse does not hold (because even if F or not W, we could all be killed by, e.g., a giant comet). Moreover, Simon writes that F ==> S. False (for the same reason). Finally, Simon writes, “Note that none of these probabilities are conditional on survival,” and concludes from that that there are no selection effects. But the fact that a true equation does not contain any explicit reference to S does not mean that any of the propositions mentioned in the equation are independent or conditionally independent of S. In other words, we have established neither P(W|F) == P(W|F,S) nor P(F|W) == P(F|W,S) nor P(W) == P(W|S) nor P(F) == P(F|S), which makes me wonder how we can conclude the absence of an observational selection effect.
I retract my endorsement of Simon’s last comment. Simon writes that S == (F or not W). False: S ==> (F or not W), but the converse does not hold (because even if F or not W, we could all be killed by, e.g., a giant comet). Moreover, Simon writes that F ==> S. False (for the same reason). Finally, Simon writes, “Note that none of these probabilities are conditional on survival,” and concludes from that that there are no selection effects. But the fact that a true equation does not contain any explicit reference to S does not mean that any of the propositions mentioned in the equation are independent or conditionally independent of S. In other words, we have established neither P(W|F) == P(W|F,S) nor P(F|W) == P(F|W,S) nor P(W) == P(W|S) nor P(F) == P(F|S), which makes me wonder how we can conclude the absence of an observational selection effect.