Quote by zonde
Linear relationship between θ and correlation level follows directly from that assumption.

You're right, it's a fairly direct route from the assumption that there is perfect correlation at identical polarizer settings to the conclusion that the local realist must believe that the correlation is linear. But ThomasT does not agree with this fairly direct line of reasoning, so I'm trying to convince him that it works.
Local realistic theory can not reproduce all predictions of QM.

If I could persuade ThomasT of this, I'd be done.
But local realistic theory can try to reproduce QM predictions in domain where they are experimentally verified. And that domain does not include (something close to) perfect correlations for matching measurement settings.

But that just has to do with practical experimental limitations. The point I'm arguing with him about is whether someone can believe that all the predictions of quantum mechanics are correct and still believe in (nonsuperdeterministic) local realism. I'm trying to show that the answer is no, because one experimental prediction of QM is perfect correlations at identical polarizer settings, from which the local realist is forced to believe in a linear correlation relationship, which is in contradiction with another experimental prediction of QM.
What I think ThomasT is disputing is that given Malus law it is very unreasonable conclusion that there is linear relationship between θ and correlation level.

I agree that this is the point of contention, but keep in mind that he thinks a local realist can believe in the nonlinear correlation given by Malus' law, while at the same time also believing that there is perfect correlation at identical settings. I hope you agree that he's wrong on this point.
No, I am a type of local realist who tries to make falsifiable local realistic explanations agreeing with QM in a domain where it is experimentally tested.

Out of curiosity, which experimental loophole of Bell tests do you cling onto? Detector efficiency, communication, freedom of choice, or something else?