  The so-called "free will axiom" is an essential ingredient in many
discussions concerning hidden variables in quantum mechanics. In this paper we
argue that "free will" can be defined in different ways. The definition usually
employed is clearly invalid in strictly deterministic theories. A different,
more precise formulation is proposed here, defining a condition that may well
be a more suitable one to impose on theoretical constructions and models. Our
axiom, to be referred to as the `unconstrained initial state' condition, has
consequences similar to "free will", but does not clash with determinism, and
appears to lead to different conclusions concerning causality and locality in
quantum mechanics. Models proposed earlier by this author fall in this
category. Imposing our `unconstrained initial state' condition on a
deterministic theory underlying Quantum Mechanics, appears to lead to a
restricted free-will condition in the quantum system: an observer has the free
will to modify the setting of a measuring device, but has no control over the
phase of its wave function. The dismissal of the usual "free will" concept does
not have any consequences for our views and interpretations of human activities
in daily life, and the way our minds function, but it requires a more careful
discussion on what, in practice, free will actually amounts to.
