I've been in a reading frenzy over the past few weeks, partly to make up for lost time - for a combination of reasons, I've been getting little reading done this year, at least by my standards.
Currently, I'm reading Lee M. Silver's new book, Challenging Nature, a defence of biomedical science, and biotechnology more generally, against more or less irrational attacks from both the right and left of politics. It's a goldmine of information, and Silver's thinking is sometimes more sophisticated than that of many philosophers and bioethicists who have considered the same issues. But he does sometimes overreach.
For example, early in the book, he attacks the belief in free will, as if such a belief must be unscientific. He doesn't seem to realise that most philosophers (though, to be fair, perhaps not most philosophers who have been publishing about the problem of free will in recent years) are compatibilists. I.e., we see free will and physical determinism as compatible.
[Note: since writing the above, I see that Silver does briefly describe compatibilism in an endnote, which shows the peril of commenting on a book halfway through reading it and the peril of not always checking the endnotes straightaway. That said, the popularity of compatibilism still provides one reason why it is unwise to criticise people for believing in free will unless their actual beliefs have been probed very carefully.]
On the compatibilist conception, free will is not the freedom to act in a way that somehow transcends physical nature, of which our brains and bodies are part. It simply means the freedom to act without being subject to certain kinds of coercion, manipulation, inner compulsion, etc.
I doubt that there is such a thing as free will in any absolute sense, i.e. we may sometimes know all the facts, with no additional fact of the matter in borderline cases that "this person is acting with free will" and "this person is not". It is just that there are various things we fear, which we see as impediments to acting as we would really like to: we fear people putting guns at our heads; we fear being overtaken by some psychiatric condition that drives us to act in ways that strike us as alien and would cause us trouble; we fear addiction to drugs, which could compel us to act in ways that, again, are against our current values; we fear being tricked into acting against our better judgment; we fear (not very seriously) the science-fictional prospect of a mad scientist taking over control of our personalities by wiring us to his damnable machine. On this conception of free will, I act freely whenever I act in accordance with my own values and beliefs, without being compelled by any of these feared things. It may be a matter of degree, as when economic circumstances may greatly limit my range of options - still, although we do fear poverty we don't usually interpret economic circumstances as taking away free will, exactly. This may be because they (usually) still leave a range of possible actions, rather than compelling one in particular. We can consider ourselves to be acting freely within the boundaries of having limited resources.
It seems to me that this is the only kind of free will worth having (as Daniel Dennett has argued, though Dennett might not agree with all my exposition above). The spooky contra-causal free will that metaphysical libertarians claim we possess does not even make sense to me, and Silver evidently feels the same way. However, I do think that we have free will in the worthwhile and meaningful sense ... at least most of the time, and at least to a large degree.
In short, people who - when asked - say that we possess free will are not necessarily claiming anything incoherent or mystical. If we want to find out how many have the spooky libertarian belief that Silver is deriding, we need to ask a different question. It is not enough just to ask people something like "Do you believe in free will?" I expect most people would answer yes, but would probably not have a metaphysically libertarian theory in mind, or even necessarily some version of compatibilism. They might mean little more than that they are not fatalists, who believe that human decisions are futile, or something of the sort.
Of course, if it turns out that the popular concept of free will is the spooky libertarian one, I am quite happy to be an error theorist about that concept. Unless things are different in the US - and, in fairness to Silver, maybe they are - I doubt that anything like this is meant by most of us when we use the expression in our ordinary lives. In fact, it looks to me like something dreamed up by theologians wanting to explain how there can be evil in the world when an all-powerful, perfect being is supposedly in charge - how could that being somehow not be responsible for evil? Answer: we act in ways that simply have no physical causes and cannot be traced back to the creative acts of God. Belief in free will does not entail commitment to anything as difficult and metaphysical (possibly even irrational) as that.