I've ofter heard the argument that quantum mechanics might somehow make free will possible because it incorporates probabilities into its predictions. For example, this quote by philosopher of science Henry Margenau sums up the viewpoint nicely:
Our thesis is that quantum mechanics leaves our body, our brain, at any moment in a state with numerous (because of its complexity we might say innumerable) possible futures, each with a predetermined probability. Freedom involves two components: chance (existence of a genuine set of alternatives) and choice. Quantum mechanics provides the chance, and we shall argue that only the mind can make the choice by selecting (not energetically enforcing) among the possible future courses.
What are some common counter points against this argument?
Most modern philosophers I know of (Daniel Dennett, Douglas Hofstadter, Sean Carroll) don't take this viewpoint seriously, from what I gather. And I'm inclined to agree since random chance (quantum mechanics) is not the same as having control over an outcome (free will). But at the same time, I can't think of an obvious experiment that could disprove the idea, and I also believe that the meaning of "random chance" is not fully understood or agreed upon by philosophers. So even though I'm inclined to disagree, I'd like to know what the best counter points are.