Free will is compatible with panpsychism. Below is a look at how this would work in one possible description of a panpsychisc system.
In quantum monadology, freewill is preserved since individual monad states are influenced by the states of the various monads around them. This means that there is choice going on at the individual level of monads (ie, the electrons and quarks), which, having been partly influenced by the thinking of those around them, but also a group choice. The assemblages of monads will have group memories and the ability to learn and base their decisions on their own and their groups’ collective memory.
More technically, for each monad, say the
j-th monad in a group, the tendency to make a choice of a new group element g in G is proportional to a universal constant c and the expectation value of the jump transformation with respect to the world state belonging to the j-th monad. Such a change of the world states belonging to all the monads induces the actual time flow, and the freedom to choose the group element is understood as the fundamental element of mind; thus the origin of free will can be identified here.
An analogy of the relationship between humans and their society will help explain the situation faced by these monads. Each human has a choice of how to act (ie, free will) as a thinking, aware and conscious being. Take the example of Ben, for example, who went to the park with a football on Thursday afternoon with his son. It is Ben’s intention to help his son with his goal-keeping skills and he thus took shots at the goal and after 30 minutes went home. They came back at the next day, but this time there was a game of football already going on and although Ben and his son could have used the same goal for practice it is understood by them, due to their experience that is not what should happen. So, in this case, Ben asked if he could join in and his son still got his keeping practice and Ben shot and scored in the other end and they stayed until the end of the match, as was fitting in that social situation. There were other things Ben and his son could have done, but they went with the consensus. It remains beyond the scope of this paper to consider how free Ben was to choose to use the goal when there was already a match in progress, but essentially this is the freewill that quantum monadology is suggesting. It is suggesting free will, but a freewill conditioned by the actions, expectations, and the situations around it.
Monads, then, are the same as Ben in regards to free will. Monads are endowed with free will, and have genuine choices, but they also take into account the actions of their neighbours which leads to a group action. In quantum monadology, this can be considered the effect of quantum superposition which is roughly analogous to groupthink, peer-pressure and, society in the human world.
In this picture, the free-will of a human is the aggregate of the decisions of all the aggregated monads in a particular configuration. In this view, there is a hierarchy of consciousness and decision making within any group. In this view the configuration of the monads is critical to the outcome of the decisions being made and so the structure of DNA (plants, animals, virus, bacteria, etc) will have a big influence over the decisions made as will the memories and experiences of the monad group but it does not follow that there is determinism. There is genuine free will, but there is, depending on the situation a higher probability of one outcome than another due to groupthink. Just as it more likely that Ben and his son would join in a game rather than start their own football game so it is with the probabilities with individual or smaller groups of monads. Improbable things can and do happen because of this free will, but it is the exception rather than the rule. In fact, in this view, it is a natural outcome that you would see a much higher range of uncertainty and randomness when looking at individual or small groups of people or monads than you’d find in larger groups and this what indeed happens in both cases.