Nick wrote to Fred: "Both Joy and Richard want a CHSH experiment with four parameters, I assume in order to come as close as possible to the current standard QM protocol. The Aspect experiments were of course CHSH although d'Espagnat and Bell (both of whom sat on the committee which conferred his doctorate) were closely involved. I imagine Richard and Joy want any outcome to be minimally vulnerable to potential challenge."
The reasons for me to want a CHSH experiment are manifold. Remember, Joy and I are hoping that the experiment will be done as part of a bet between the two of us concerning his claims in http://arxiv.org/abs/1211.0784 and in particular concerning the experiment described in Section 4 of that paper. Some aspects of the description of that experiment are perhaps ambiguous and all ambiguity must be removed in advance.
Also because we are talking about a bet, the criterium for who wins and who loses must be totally unambiguous. CHSH lends itself to bets very well, since it focusses on *one final number*, a combination of just *four correlations*. One theory says that number can't exceed 2 (in the limit of infinitely many runs!), the other theory says it could equal 2 sqrt 2 (in the limit of infinitely many runs!).
There will only be finitely many runs and who knows what kinds of experimental error are possible, as well as the obvious statistical error. So I propose to set the criterion for win/lose at exactly half way between 2 and 2 sqrt 2. Isn't that reasonable?
We have to decide the number of runs (or perhaps, a minimal number). And we have to decide the scheme by which settings are provided to the experimenters in the lab. I propose to prepare in advance two streams of random choices (a or a' for Alice, b or b' for Bob); i.e., in each run, just one of Alice's two settings are in operation, just one of Bob's two settings. Out will come a binary outcome for Alice and a binary outcome for Bob. I'll generate my setting streams using the pseudo random number generator in R using a seed which I'll keep secret but I'll have written down, so I can reproduce the exactly same settings, any time anyone wants to check. The adjudicators of the bet will, in advance, get my setting streams and may check them any way they like, and if they like reject them and ask for new streams. I trust they'll keep them secret from the experimenters "on the ground", so to speak.
Now Joy believes Bell's theorem is wrong, and I believe it is true. Because I believe it is true I am able to do calculations on the basis of the experimental set-up just described, which enable me to enter this bet with a wager of say 5000 Euro and with very high confidence that I'll win. Obviously, Joy knows that Bell is wrong and he is going to win. For me, the way I prepare the settings is very important, because my probability calculation of the chance I'll win the bet, assuming local realism, depends on the probability distribution of the settings. For N runs I need 2N coin tosses to generate my settings, and I assume in my calculation of my risk of losing the bet that all 2^(2N) sets of outcomes are equally likely.
