Experimental philosophy consists of opinion polls on common philosophical questions, intended to quantify the positions of the philosophically naive or untrained public, the so-called "folk" of "folk psychology."
While this offers little of empirical value for questions that might be answered some day by science (notably neuroscience), "X-Phi" has proved popular in introductory philosophy classes, and there is a flourishing community of experimental philosophers with an active X-phi blog.
One of the X-Phi surveys attempted to establish the "folk" intuitions on the classic philosophical question of free will and determinism. Unfortunately, experimental philosophers follow John Martin Fischer and define free will as the "control condition" for moral responsibility. So their questions were really about the moral responsibility of two kinds of agents, one completely determined and another assumed to have libertarian free will.
The experimental philosophers established that many of those interviewed want to hold agents responsible for their crimes, especially when the crime raises emotions, either because it is a particularly heinous crime or because it harms someone close to the person being interviewed.
In relatively abstract situations, the idea that the agent was determined (by any number of determining factors) was enough to provide mitigating circumstances. But as the crime stirred up strong emotions in the person judging the action, the agent was more likely to be held morally responsible, even if the agent was clearly determined.
"Here we will focus especially on the role of affect in generating intuitions about moral responsibility. Our hypothesis is that, when people are confronted with a story about an agent who performs a morally bad behavior, this can trigger an immediate emotional response, and this emotional response can play a crucial role in their intuitions about whether the agent was morally responsible. In fact, people may sometimes declare such an agent to be morally responsible despite the fact that they embrace a theory of responsibility on which the agent is not responsible."
(Moral Responsibility and Determinism: The Cognitive Science of Folk Intuitions, Shaun Nichols and Joshua Knobe.)
Sadly, experimental philosophers describe these results as whether the folk have "incompatibilist" or "compatibilist" intuitions. This jargon makes interpretations difficult.
William James called compatibilism a "quagmire of evasion." By comparison, incompatibilism is a "tarpit of confusion."
The proper interpretation should be that when their emotions rise up, those judging an action are more likely to react with an attitude of blame and seek punishment for the action. Holding an agent morally responsible is a function of how hurtful their action is to the one judging the action. This result is quite believable for normal persons. It is the reason jurors are selected from persons with no connections to the accused or the plaintiff.
Two Universes and Moral Responsibility
The canonical X-Phi experiment is to describe two universes. In universe A, every event is caused by a causal chain that goes back to the beginning of the universe. In universe B, human decisions are not caused by the immediate preceding conditions of the universe, let alone chains back to the origin, but every other event is.
The first question asked by experimental philosophers is, "Which universe most closely resembles our own?" Most of the folk say universe B.
The second question is, "In universe A, can persons be morally responsible for their actions?" Most of the folk say no.
These answers imply what X-Phi calls an "incompatibilist intuition," namely that free will is incompatible with the determinism of a completely causal universe.
In terms of the traditional determinism-libertarian dichotomy that is the basis for our taxonomy of free will positions, we would say that the second question should be "In universe A, do persons have free will?"
Experimental Philosopher Hagop Sarkissian Explains the Free Will Experiment