Jaynes is misunderstanding the class of hidden-variable theories Bell's theorem rules out: the point is that the hidden variables λ would determine the outcome of measurements, i.e. P(A|aλ) is 0 for certain values of λ and 1 for all other values, and likewise for P(B|bλ), in which case P(A|abλ) must equal P(A|aλ), P(B|Aabλ) must equal P(B|bλ), and eq. 14 does equal eq. 15. (I had noticed this mistake several years ago, but I didn't know whom to tell about.)
Good catch! Jaynes does not seem to restrict the local hidden variables models to just the deterministic ones, but allows probabilistic ones, as well. This seems to defeat the purpose of introducing hidden variables to begin with. Or maybe I misunderstand what he means.
Today's post, Bell's Theorem: No EPR "Reality" was originally published on 04 May 2008. A summary (taken from the LW wiki):
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