Quote by billschnieder
Let us change the original scenario a little as follows: We remove the source altogether and replace it with a mystical being who governs a mystical parameter (x) which combines with their chosen angles to produce a +/1 result. Each day over many years, he instantly decides what parameter (x) is, the instant before Alice and Bob make their measurements, whoever does it first. The only condition being that the same (x) parameter is governing both experiments.
Then (as in a standard Bellanalysis) Alice's results are represented by (1) A(a, x) = ±1 where a is any analyzer orientation of her choosing; Bob's by (2) B(b, x) = ±1 where b is any analyzer orientation of his choosing; (3) 0 ≤ ρ(x); (4) ∫ρ(x) dx = 1.
I wonder what the CHSH inequality will look like. I can bet it will be identical to the one derived by gill1109 above, even though the scenario is manifestly nonlocal. What gives?

Bill, you talkin' to me? (In that you cite gill1109.)
1. Not sure about your mystical being? Purpose =? (Is something more needed to clarify the OP?)
2. The CHSH inequality formulation will be the same, imho: since the experimental outcomes are ±1, no matter the settings
a,
b, etc.
3. To clarify the OP (if that's your issue): Having derived the expectation E(AB) for the classical setting  from your functions for A and B = ±1  what then is the related maximum value that that classical setting might yield for the CHSH inequality? That is: What
a,
b,
c,
d settings yield the maximum value in the CHSH formula, and what is that maximum?
4. Is it gill1109's +2?
5. Did you mean to say "the scenario is manifestly LOCAL"???
6. So  addressing your "What gives"  just give me your answers to the OP  or tell me why you can't. Especially as it seems that Bell might think you can; the given situation being wholly classical and involving no more than Bell's proposed (1964, etc.) analytical formulation.