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prase comments on Open Thread: July 2010 - Less Wrong
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It is strange. Shall Bob discount his observation after being told that he is selected? What does it actually mean to be selected? What if Bob finds 25 big fish and then Charlie tells him, that there are 3^^^3 other observers and he (Charlie) decided to "select" one of those who observe 25 big fish and talk to him, and that Bob himself is the selected one (no later confrontation with AI). Should this information cancel the Bob's observations? If so, why?
Yes, it should, if it is known that Charlie hasn't previously "selected" any other people who got precisely 25.
The probability of being selected (taken before you have found any fish) p[chosen] is approximately equal regardless of whether there are 25% or 75% big fish.
And the probability of you being selected if you didn't find 25 p[chosen|not25] is zero
Therefore, the probability of you being selected, given as you have found 25 big fish p[chosen|found25] is approximately equal to p[chosen]/p[found25]
The information of the fact you've been chosen directly cancels out the information from the fact you found 25 big fish.
Glad to see we're on the same page.