In any case, Bell's derivation requires us to assert that each measurement is a "free" action, independent of the causal past, which is inconsistent with even the most limited construal of determinism

“God is clever, but not dishonest.”

Why do we call this result the Free Will theorem? It is usually tacitly
assumed that experimenters have sufficient free will to choose the settings of
their apparatus in a way that is not determined by past history. We make this
assumption explicit precisely because our theorem deduces from it the more surprising fact that the particles’ responses are also not determined by past
history.

11.2. Free versus Random? Although we find ourselves unable to give an
operational definition of either “free” or “random,” we have managed to dis-
tinguish between them in our context, because free behavior can be twinned,
while random behavior cannot (a remark that might also interest some philo-
sphers of free will). Bassi and Ghirardi remark that it follows from Gisin’s
theorem that their “hits” must involve a stochastic element in order to make
the GRW theory relativistically invariant. We have shown that what the hits
really need is some freedom (to be precise, that they must be at least semi-
free). It is for reasons including these that we prefer to describe our particles’
behavior as “free” rather than “random,” “stochastic,” or “indeterminate.”

We have defined “free will” to be the opposite of “determinism” despite the
fact...

‏¹http://arxiv.org/PS_cache/quant-ph/pdf/0604/0604079....

Humpty Dumpty sat on a wall.
Humpty Dumpty had a great fall.
All the king's horses and the king's men
Couldn't put Humpty together again.

Do we really have free will, or, as a few determined folk maintain, is it all
an illusion? We don’t know, but will prove in this paper that if indeed there
exist any experimenters with a modicum of free will, then elementary particles
must have their own share of this valuable commodity.

Abstract The proof of Bell's inequality is based on the assumption that distant observers can freely and independently choose their experiments. As Bell's inequality isexperimentally violated, it appears that distant physical systems may behave as a single, nonlocal, indivisible entity. This apparent contradiction is resolved. It is shown that the free will assumption is, under usual circumstances, an excellent approximation.

The proof of Bell's inequality is based on the assumption that distant observers can freely and independently choose their experiments