I thought about it more, and I am now convinced that the paper is right (at least in the specific example I proposed).
The thing I didn’t get at first is that given a certain prior over P(extinction), and a number of iterations survived, there are “more surviving worlds” where the actual P(extinction) is low relative to your initial prior, and that this is exactly accounted for by the Bayes factor.
I also wrote a script that simulates the example I proposed, and am convinced that the naive Bayes approach does in fact give the best strategy in Jack’s case too (I haven’t proved that there isn’t a counterexample, but was convinced by fiddling with the parameters around the boundary of cases where always-option-1 dominates vs always-option-2).
I thought about it more, and I am now convinced that the paper is right (at least in the specific example I proposed).
The thing I didn’t get at first is that given a certain prior over P(extinction), and a number of iterations survived, there are “more surviving worlds” where the actual P(extinction) is low relative to your initial prior, and that this is exactly accounted for by the Bayes factor.
I also wrote a script that simulates the example I proposed, and am convinced that the naive Bayes approach does in fact give the best strategy in Jack’s case too (I haven’t proved that there isn’t a counterexample, but was convinced by fiddling with the parameters around the boundary of cases where always-option-1 dominates vs always-option-2).
Thanks, this has actually updated me a lot :)