Did you read the chapter linked at the end of the post?
A hopefully intuitive explanation: A spy watching the experiments and using Bayesian methods to make his own conclusions about the results, will not see any different evidence in each case and so will end up with the same probability estimate regardless of which experimenter he watched.
While the second experimenter might be contributing to publication bias by using that method in general, he nonetheless should not have come up with a different result.
It seems worth noting the tension between this and bottom-line reasoning. Could the second experimenter have come up with the desired result no matter what, given infinite time? And if so, is there any further entanglement between his hypothesis and reality?
Monty Hall is analogous in that we are looking at evidence and trying to make conclusions about likelihoods. It is relevant because the likelihoods are different depending on what was in Monty’s head in the past, after observing the same physical evidence. Monty is not the experimenter; where does that make a difference? Could one reformulate it so that he was? He would be running two different experiments, surely—but then why isn’t that the case for the two researchers?
Did you read the chapter linked at the end of the post?
A hopefully intuitive explanation: A spy watching the experiments and using Bayesian methods to make his own conclusions about the results, will not see any different evidence in each case and so will end up with the same probability estimate regardless of which experimenter he watched.
While the second experimenter might be contributing to publication bias by using that method in general, he nonetheless should not have come up with a different result.
It seems worth noting the tension between this and bottom-line reasoning. Could the second experimenter have come up with the desired result no matter what, given infinite time? And if so, is there any further entanglement between his hypothesis and reality?
Why would a spy watching Monty Hall be different?
Amongst other reasons, Monty isn’t the experimenter. I’m really not sure in precisely what way Monty Hall is analogous to these experiments.
Monty Hall is analogous in that we are looking at evidence and trying to make conclusions about likelihoods. It is relevant because the likelihoods are different depending on what was in Monty’s head in the past, after observing the same physical evidence. Monty is not the experimenter; where does that make a difference? Could one reformulate it so that he was? He would be running two different experiments, surely—but then why isn’t that the case for the two researchers?