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SilentCal comments on The trouble with Bayes (draft) - Less Wrong Discussion
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Sure. But if we know or suspect any correlation between A and Y, there's nothing strange about the common information between them being expressed in the prior, right?
Granted, H-T will have nice worst-case performance if we're not confident about A and Y being independent, but that reduces to this debate http://lesswrong.com/lw/k9c/can_noise_have_power/.
I wrote up a pretty detailed reply to Luke's question: http://lesswrong.com/lw/kd4/the_power_of_noise/