treated as random variables, as befits their status as the locus of free choice. It would be unreasonable to require a theory of local beables to predict the probability that the experimenters make one free choice rather than another: but treating $a,b$ as random variables (as in Bell’s formulation of \[Factorizability\]) would imply the existence of probabilities of the form $Pr(a|\lambda )$, $Pr(b|\lambda $).

By symmetry, interchanging ‘1’ with ‘2’, ‘$A$’ with ‘$B$’ and ‘$a$’ with ‘b’ implies$$Pr_{a,b}(B|A,\lambda )=Pr_{b}(B|\lambda )  \tag{4b}  \label{4b}$$

Seevinck and Uffink \[2011\] offer equations (\[4a\]) and (\[4b\]) as their mathematically sharp and clean (re)formulation of the condition of local causality. Together, these equations imply the condition$$Pr_{a,b}(A,B|\lambda )=Pr_{a}(A|\lambda )\times \ Pr_{b}(B|\lambda ) 
\tag{Factorizability$_{SU}$}  \label{FactorizabilitySU}$$used to derive CHSH inequalities. Experimental evidence that these inequalities are violated by the observed correlations in just the way quantum theory leads one to expect may then be taken to disconfirm Bell’s intuitive causality principle.

In more detail, Seevinck and Uffink \[2011\] claim that orthodox quantum mechanics violates the statistical sufficiency conditions (commonly known as Outcome Independence, following Shimony)$$\begin{aligned}
Pr_{a,b}(A|B,\lambda ) &=&Pr_{a,b}(A|\lambda )  \TCItag{5a}  \label{5a} \\
Pr_{a,b}(B|A,\lambda ) &=&Pr_{a,b}(B|\lambda )  \TCItag{5b}  \label{5b}\end{aligned}$$

while conforming to the functional sufficiency conditions (commonly known as Parameter 