system
Given the following post, respond as if you're commenting on Reddit:
human
What is the understanding of free will in compatibilism?

So from my understanding, to believe in free will (atleast as characterized in the way of libertarian free will, or “libertarianism”, as seen on the philosophy surveys) necessitates belief in something extra physical that gives an agent power (agency) to actually deliberate a decision themselves rather than simply by determined by their genetic makeup and life experience (like we would say other physical things are). Obviously an example of this would be divine will. 

From my understanding of compatibilism, determinism and free will are not mutually exclusive. I have heard often that this is a way to hold onto some moral systems that hinge on an agent actually having agency, rather than a commentary on free will. If this is the case, what is the compatibilist’s understanding of free will. Is there a secular case for free will?
gpt
The libertarian and the compatibilist both have the same general understanding of free will, viz. that it is the capacity to function as an agent of one's behaviors, through processes like deliberating about what to do, where those deliberations are the significant cause of what one does -- or something like this.

The difference is that incompatibilists (including both libertarians and those who deny we have free will) think that if determinism is true then we cannot have any such capacity, whereas compatibilists think otherwise.