The Fair Sampling Assumption, as commonly discussed, is implicit in Bell tests: As long as detection efficiency is less than 100%, the observed photon pairs are a representative sample of the total universe of emitted pairs. At this time, no Bell test has satisfactorily closed both the Fair Sampling Assumption and the Strict Locality assumptions (some call them the Detection and Strict Locality loopholes) at the same time, even though they have been closed individually. From Towards a loophole-free test of Bell's inequality with entangled pairs of neutral atoms (2009) "Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). " I was interested in discussing what I call the Unfair Sampling Assumption: If the Fair Sampling Assumption and the Locality Assumptions/Loopholes are still open as a pair, then Local Realism (LR) is still viable. I question this assumption! Take a look at this graph: In the above: a. We have percentages for a hypothetical Local Realistic (Hidden Variable) Theory, labeled as LR(Theta), showing what it predicts the true correlation percentage is for a pair of entangled PDC Type I photons where theta is the angle between the settings (for spacelike separated Alice and Bob). In the graph, 1=100% and 0=0% per convention. There is no specific theory this is supposed to mimic except that it is assumed to be local and realistic. If it is local, then what happens at Alice cannot influence what happens at Bob and vice versa. If it is realistic, then it is assumed that even unobserved polarization settings would have well-defined values independent of the act of observation ("the moon is there even when no one is looking..."). The LR(Theta) line, in blue, is a straight line ranging from 1 at 0 degrees to 0 at 90 degrees. This matches the values that an LR would need to come closest to the predictions of QM, shown in Red. Other LR theories might posit different functions, but if they are out there then they will lead to even greater differences as compared to QM. Keep in mind that the QM predicted values match experiment closely. b. The difference between LR and QM is the detection bias which must exist, which causes us to get an unfair sample (assuming the Unfair Sampling Assumption is true). That is the green line, and you can see that it is positive in one range and negative in another. This is interesting because it means that sometimes it is the LR-supporting pairs which are not detected, and other times it is the QM-supporting pairs that are not detected! c. Finally, there is the Purple line which goes through 0 at all points (it is a little hard to see on the graph). This is interesting because it is the value of 2 special cases of the 8 possible permutations you get when you have 3 settings (2 which can be actually observed, i.e. Alice and Bob, and the third which is hypothesized by the local realistic theory). Case Predicted likelihood of occurance  A+ B+ C+ >=0  A+ B+ C- >=0  A+ B- C+ >=0  A+ B- C- >=0  A- B+ C+ >=0  A- B+ C- >=0  A- B- C+ >=0  A- B- C- >=0 Assuming that we have something like this: A=0 degrees, B=45 degrees, C is between A and B. It turns out that 2 of the above cases are suppressed: permutations  and . The reason is that you cannot have matches at 0 and 45 degrees, but have a mismatch (non-correlation) at an angle in between. The purple line is calculated based on the LRT values (the math is a little complicated and is on a spreadsheet I created). So: IF you assume that LR has function values closest to QM/experiment, such that you don't run afoul of Bell (since Bell still applies), THEN you get the straight line shown in BLUE and you also get the values for cases  and  as being 0 across the board (they need to be non-negative to prove that a Bell inequality is not violated).