Simpson's Paradox is a statistical artifact related to
hidden variables. Here it in terms of quantum entanglement.
Given that
1) A and B are complementary
2) A and B are both true XOR A and B are both false
then, that 1) contradicts 2) is the essence of Simpson's Paradox.
We can make an arbitrary determination that "A is True"
to resolve that paradox, but this choice is arbitrary as we could
equally have chosen to make the determination that
"B is True". Regardless of the choice we can then instantly
determine the complementary variables state as "anti-correlated".
Similarly, in entanglement the arbitrary measurement of
a polarization or spin state will instantly (non-locally)
determine the state of the anti-correlated entangled twin.
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