We are responsible for our actions roughly to the extent that we possess these capacities

From Is Neuroscience the Death of Free Will? by Eddy Nahmias. I like his definition of free will: "a set of capacities for imagining future courses of action, deliberating about one’s reasons for choosing them, planning one’s actions in light of this deliberation and controlling actions in the face of competing desires."

These discoveries about how our brains work can also explain how free will works rather than explaining it away. But first, we need to define free will in a more reasonable and useful way. Many philosophers, including me, understand free will as a set of capacities for imagining future courses of action, deliberating about one’s reasons for choosing them, planning one’s actions in light of this deliberation and controlling actions in the face of competing desires. We act of our own free will to the extent that we have the opportunity to exercise these capacities, without unreasonable external or internal pressure. We are responsible for our actions roughly to the extent that we possess these capacities and we have opportunities to exercise them.

These capacities for conscious deliberation, rational thinking and self-control are not magical abilities. They need not belong to immaterial souls outside the realm of scientific understanding (indeed, since we don’t know how souls are supposed to work, souls would not help to explain these capacities). Rather, these are the sorts of cognitive capacities that psychologists and neuroscientists are well positioned to study.