It seems to me that the paradox/confusion here comes from asking someone to consider a distribution over a bound variable - i.e. you are asked to examine the odds of X happening in a situation where there are already side effects of whether or not X happened.
In this sense, it reminds me of the puzzle where a man gives you a choice between two envelopes, one of which is specified to contain twice as much money as the other, with the paradox centering on a bystander's argument that you should then switch envelopes, since the other one must have either half or twice your value, giving you a 1.25x higher expected value for switching.
As I understand it, in both cases the "traditional" solution to the problem is to recognize that probability doesn't work that way, and you can't consider distributions over bound variables, but the more interesting solution is to rephrase things in Bayesian terms, in which case the analysis is reasonably straightforward.
I'm a dabbler though; experts please tell me if I'm spouting gibberish.
In this sense, it reminds me of the puzzle where a man gives you a choice between two envelopes, one of which is specified to contain twice as much money as the other, with the paradox centering on a bystander's argument that you should then switch envelopes, since the other one must have either half or twice your value, giving you a 1.25x higher expected value for switching.
As I understand it, in both cases the "traditional" solution to the problem is to recognize that probability doesn't work that way, and you can't consider distributions over bound variables, but the more interesting solution is to rephrase things in Bayesian terms, in which case the analysis is reasonably straightforward.
I'm a dabbler though; experts please tell me if I'm spouting gibberish.