So, about those two studies on folk perceptions of determinism and incompatibilism; these are two different issues that need to be tested separately. First, do non-philosophers, do Joe and Jane Average believe that the world including ourselves is deterministic or do they believe that we have some magical ability of making decisions independently of cause-and-effect? Second, do they believe that free will, choice, moral responsibility and suchlike are still useful concepts under the assumption of determinism? In the second case, a yes would make them compatibilists, a no would make them incompatibilists. Both studies accordingly made an effort to test these questions one after the other.
The first study, Nahmias et al, presented its participants with a hypothetical supercomputer that could perfectly predict the future. It then first asked them whether such a scenario was possible. Subsequently, the participants were told to assume that all actions had been predicted by the supercomputer, and asked wether a hypothetical person called Jeremy acted out of his own free will and is morally responsible when predictably robbing a bank, going jogging or rescuing a child from death.
Results: The majority of participants answered that the above scenario was impossible. The overwhelming majority of participants answered that Jeremy had both free will and moral responsibility despite the determinist scenario they were told to assume.
The second study, Sarkissian et al, first presented its participants with two hypothetical universes: a universe A which is carefully described as deterministic and a universe B in which human decisions are "not completely caused by the past", and then asked them to decide "which of these universes is most like ours". Subsequently, the researchers asked the participants whether it is "possible for a person to be fully morally responsible for their actions" in the deterministic universe A. Note that this is a much less specific question than that used by Nahmias et al, and Sarkissian et al chose it on purpose, arguing that very specific questions such as about a bank heist would "trigger affective responses" instead of getting at people's theories of moral responsibility.
Result: The overwhelming majority of participants answered that universe B, the one in which human decisions are magically exempt from cause-and-effect, is most similar to our actual universe. The overwhelming majority of participants answered that "full moral responsibility" is not compatible with determinism. Interestingly, a determinist answer to the first question was very highly correlated with a compatibilist answer to the second.
Comparing the two studies we find very similar results on the determinism question. If these are a representative sample, then most people appear to believe that they believe that the world is not deterministic. So far so good; they are simply wrong. They are wrong that human decision-making works independently from cause-and-effect and from the laws of physics, not least because this and random behaviour exhaust the available options.
But they are also wrong about their own beliefs, because on a daily basis all sane humans act like determinists, as they assume that other people's decisions and behaviour can be anticipated from knowing their character, nature, past experiences, and the information currently available to them. In reality and in practice, people are determinists, but these studies show they are not aware that they are.
More surprising are the differences between the two studies with regard to compatibilism. Nahmias et al show people to be compatibilists, assigning moral responsibility to Jeremy even under determinism, but Sarkissian et al show people to be incompatibilists, denying the possibility of moral responsibility under determinism.
There are several possible explanations. The simplest is that people have simply not thought these issues through very well and can easily be influenced by the exact phrasing of the question. However, the researchers in these cases have been very careful with the way the worded their scenarios, and they asked for "moral responsibility" in both studies, so this seems a bit unlikely. What seems more important is the point raised by Sarkissian et al, the potential effects of asking for a judgement on a very specific case versus asking for abstract moral theories. When asked in the abstract, they consider moral responsibility to be impossible in a determinist universe, but when faced with a specific person doing something very concrete, people tend to praise or blame them, to hold them responsible.
Obvious follow-up question: Which of these is the answer we should care about?
This is Sarkissian et al's defense of their decision to focus on abstract reasoning:
Finally, some might object that the experiment is merely getting at people's theories of moral responsibility and not at the way they make actual judgments in particular cases. Here, our reply is twofold. First, we think that the study of people's implicit theories is important in its own right. These theories can offer us fundamental insights both into certain aspects of human cognition and into the philosophical problems that arise in this domain. In particular, if people interpret one another (and the world around them) according to implicit theories, then exploring these theories would be valuable in arriving at a better understanding of their appraisals and judgments. Second, people's incompatibilism actually does show up in their concrete judgments; as long as one gives participants scenarios designed to avoid triggering affective responses (e.g. a story about a man cheating on his taxes), they tend to say that a person in a deterministic universe cannot be fully morally responsible (Nichols and Knobe, 2007).Sorry, but I must say that this is all really weak sauce. Yes, of course implicit theories are interesting. But interesting merely in the same way that it interesting to observe somebody claiming that they are not a racist in the same breath as they stereotype Africans as lazy, unreliable and stupid; or to observe somebody claiming that science is just another ideology and that nobody can know anything for sure right before demonstrating their trust in physics by boarding an aeroplane.
If this sounds similar to my remark above on how people only believe that they believe that the world is not deterministic, that is no coincidence. When we want to know what people really believe we need to look at their actions, not at their abstract claims. This goes for determinism and compatibilism as much as for racism or solipsism. So as far as the folk views on the first two of these are concerned, colour me unconvinced by the answers of the participants. People are still determinists and compatibilists in practice, as demonstrated by their pragmatic behaviour.
What I take from these two studies are then very different insights. First, many people
Second, as Sarkassian et al also remark, at least some people do think more clearly. The minority who adopts determinism has a strong tendency to become compatibilist, presumably because they realize that even given determinism there are still important differences between, say, murders and accidents, and that the perpetrators of the latter have less responsibility than those of the former. It is likely for the same reason that most philosophers, in other words people who professionally think about issues like these, are compatibilists.
Third, I find it amazing how participants in these discussions (and that includes the authors of these studies) can twist and turn to avoid accepting the conclusion they dislike. Based on the available data, all one has to do to arrive at the preferred incompatibilist conclusion that people really do consider free will to be magic is to take their abstract reasoning over their concrete judgements, as Sarkassian et al do. All one has to do to arrive at the opposite conclusion is to take their concrete judgements over their abstract reasoning.
I have given my grounds for doing the latter above, but I do not expect them to convince an incompatibilist, not even one who would adopt exactly my approach of examining practical behaviour instead of abstract claims when faced with somebody who goes "I am not a racist but...". And that is understandable; it is possible that I also simply chose the solution I was more comfortable with.