I'm trying to figure out whether compatibilism (SEP, Wikipedia) is falsifiable, a metaphysic, or something else. One way to get at this is to take a Popperian approach, and ask whether any conceivable observation could prove compatibilism to be false. This is different from proving libertarianism to be true; I would be interested in knowing if it has to be compatibilism or libertarianism, or whether there are other options.
One answer I've come across is that if we could show that there is no such thing as 'mind', then compatibilism would be trivially false. That is, suppose that there is too much overlap between my mind and your mind, then the thing that makes a decision is some combination of the two minds, putting into question the idea that individual minds make decisions. I'm skeptical of this type of answer, because it seems to merely beg the question of whether 'mind' was defined properly before getting to compatibilism.
It may be interesting to note that dualism does not rescue us from compatibilism, unless we allow [apparent] paradox to reside there, instead of insisting that the logic that applies to particles and fields applies to whatever is in the other realm. There is no reason to suppose that 'reasoning' and 'logic' and 'choice' would be thought of differently in a nonphysical realm. Either the choice was founded in reasoning and observation, or it was random. Or we could say that choices have rational and irrational components. Where would the room for libertarian free choice be found? Surely purely random choices cannot be considered 'libertarian'? Here I'm assuming a dichotomy between compatibilism and libertarianism, which may be in error. Consider this paragraph a search for what might falsify compatibilism, a search which failed.