Demystifier said:
I strongly disagree. If you interpret these theories as being COMPLETE, i.e., if you assume that these theories describe EVERYTHING, including the behavior of experimentalists themselves, then measurements CANNOT be freely chosen. Instead, the measurements themselves are determined by these physical laws.
Conversely, if you assume that experiments CAN be freely chosen, then you cannot avoid the conclusion that the physical laws we know are not complete. There is something (the free will) that cannot be described by them. In this case, there is a free will theorem that says that if humans have free will, then quantum particles have free will as well.
Concerning the Bell theorem, one of its ASSUMPTIONS is ability to choose experiments at will. If you give up that assumption, as 't Hooft does, then it IS possible to have a local hidden variable compatible with QM. In fact, Bohmian mechanics can also be reformulated in this way, as a local superdeterministic theory. The problem with such a reformulation is that Bohmian mechanics then looks much more complicated and artificial, but it is possible to do that.
I disagree with your disagreement.

You are discussing the meaning of the word "complete" which as you know is full of multiple meanings. I prefer to avoid that debate.
1. Clearly, the issue is not really free will. That actually has no meaning at all the debate per se.
The true question: is the subensemble of detected events representative of the universe of possible measurements? And I am saying that logically, one could assert that with any physical theory, it is not. There is nothing special about QM in particular that makes this an issue. But is that assertion scientific at any time?
I consider it axiomatic that science must necessarily involve sampling, and that all physical laws are attempts to develop patterns of behavior that have organizational or predictive value. I fail to see how the "anti-fair sampling hypothesis" has any meaning in this context.
On the other hand, you could easily assert that even in experiments such as Rowe, fair sampling is not strictly ruled out anyway! Sure, you look at all events that are sampled. But of course that is merely a subsample too. Perhaps there was still a conspiracy to force the experimenter to think they chose the time and place of the experiment, and their settings at that time, when in reality these were not freely chosen. I.e. there is no free will. And yet that wouldn't matter unless the subensemble of events is not representative of the entire universe of events. (Don't get me wrong, I am not arguing that closing the fair sampling loophope is not an important achievement: it certainly shows there is no obvious mechanism causing bias in non-detection.)
I conclude: (free will)=false does not imply (detected subensemble)=not representative. I.e. superdeterminism does not imply anti-fair sampling assumption any more than it implies the fair sampling assumption. You could have (free will)=false AND (detected subensemble)=representative just as easily. And in my opinion, fair sampling hypothesis is an axiom of science. It is necessary because that justifies the use of physical laws to predict the outcome of experiments. On the other hand, if this assumption were not justified, we could not use physical laws to predict the outcomes of experiments.2. A local realist may attempt to use the superdeterminism argument to justify their stance. They are really saying is that:
a) The world is local realistic (both reasonable ideas I quite agree);
b) Bell's Theorem usual conclusion (QM incompatible with LR) is OK, but QM is wrong;
c) Specifically QM's cos^2 theta rule for correlations is wrong, to avoid Bell;
b) that experiments in support of that rule are also wrong because fair sampling is wrong;
c) superdeterminism is the mechanism that allows fair sampling to be violated.
But I say that is unscientific per above. For their argument to make sense (since superdeterminism does not imply anti-fair sampling hypothesis), the local realist needs to advance a superdeterministic theory that violates fair sampling AND agrees with QM predictively on the matter of the cos^2 rule. Certainly 't Hooft is not supplying this, nor is he claiming to. He is simply trying to show a path which might be explored to produce such.
The cos^2 rule IS useful, and its utility justifies it. (Sort of like the argument that a history of the sun rising every day does not prove the sun will rise tomorrow.) So even at the end of the day, if 't Hooft got his wish and produced such a theory, we are guaranteed no more predictive power than what we have today. Rather seems pointless to me. As I read Bell's words, I believe he fully concluded the same: "although there is an escape route there, it is hard for me to believe that quantum mechanics works so nicely for inefficient practical set-ups, and is yet going to fail badly when sufficient refinements are made."3. As to Bohmian perspective: why would you need to assert the anti-fair sampling hypothesis when the non-local nature provides the explicit mechanism to explain entanglement correlations?